title

Machine Learning 1 - Linear Classifiers, SGD | Stanford CS221: AI (Autumn 2019)

description

For more information about Stanfordâ€™s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3nAk9O3
Topics: Linear classification, Loss minimization, Stochastic gradient descent
Percy Liang, Associate Professor & Dorsa Sadigh, Assistant Professor - Stanford University
http://onlinehub.stanford.edu/
Associate Professor Percy Liang
Associate Professor of Computer Science and Statistics (courtesy)
https://profiles.stanford.edu/percy-liang
Assistant Professor Dorsa Sadigh
Assistant Professor in the Computer Science Department & Electrical Engineering Department
https://profiles.stanford.edu/dorsa-sadigh
To follow along with the course schedule and syllabus, visit:
https://stanford-cs221.github.io/autumn2019/#schedule
#machinelearningcourse

detail

{'title': 'Machine Learning 1 - Linear Classifiers, SGD | Stanford CS221: AI (Autumn 2019)', 'heatmap': [{'end': 1455.91, 'start': 1402.529, 'weight': 0.933}, {'end': 1548.943, 'start': 1488.413, 'weight': 0.742}, {'end': 1645.287, 'start': 1593.196, 'weight': 0.72}, {'end': 1838.744, 'start': 1690.094, 'weight': 0.903}, {'end': 2467.111, 'start': 2415.984, 'weight': 0.944}, {'end': 3872.592, 'start': 3818.893, 'weight': 0.835}, {'end': 4207.127, 'start': 4157.538, 'weight': 0.845}, {'end': 4495.837, 'start': 4442.704, 'weight': 0.774}], 'summary': 'Covers machine learning basics, linear prediction, interpreting weights in regression models, loss functions, optimization, and stochastic gradient descent in python, emphasizing the powerful framework of loss minimization and decision-making for learning algorithms.', 'chapters': [{'end': 243.618, 'segs': [{'end': 81.338, 'src': 'embed', 'start': 6.058, 'weight': 0, 'content': [{'end': 10.28, 'text': "Okay So let's, uh, get started with the actual, uh, technical content.", 'start': 6.058, 'duration': 4.222}, {'end': 14.363, 'text': 'So remember from last time, we gave an overview of the class.', 'start': 10.34, 'duration': 4.023}, {'end': 21.607, 'text': "We talked about different types of models that we're gonna explore reflex models, state-based models, variable-based models and logic models,", 'start': 14.983, 'duration': 6.624}, {'end': 23.108, 'text': "which we'll see throughout the course.", 'start': 21.607, 'duration': 1.501}, {'end': 26.43, 'text': 'But underlying all of this is, you know, machine learning.', 'start': 23.428, 'duration': 3.002}, {'end': 32.893, 'text': "Because machine learning is what allows you to take data and um tune the parameters of the model so you don't have to,", 'start': 26.81, 'duration': 6.083}, {'end': 34.815, 'text': 'uh work as hard designing the model.', 'start': 32.893, 'duration': 1.922}, {'end': 42.583, 'text': "Um. so in this lecture I'm gonna start with the simplest of the models of reflex-based models, um,", 'start': 35.755, 'duration': 6.828}, {'end': 45.747, 'text': 'and show how machine learning can be applied to these type of models.', 'start': 42.583, 'duration': 3.164}, {'end': 52.334, 'text': "And throughout the class, uh, we're going to talk about different types of models and how learning will help with those as well.", 'start': 46.067, 'duration': 6.267}, {'end': 54.928, 'text': "So there's gonna be three parts.", 'start': 53.627, 'duration': 1.301}, {'end': 60.45, 'text': "We're gonna talk about linear predictors, um, which includes classification regression, um loss minimization,", 'start': 55.008, 'duration': 5.442}, {'end': 67.312, 'text': 'which is basically setting objective function of how you, uh, want to train your machine learning model, and then stochastic gradient descent,', 'start': 60.45, 'duration': 6.862}, {'end': 70.694, 'text': 'which is an algorithm that allows you to actually, uh, do the work.', 'start': 67.312, 'duration': 3.382}, {'end': 77.635, 'text': "So let's start with, uh, perhaps the most, um, cliched example of, uh, you know, machine learning.", 'start': 72.051, 'duration': 5.584}, {'end': 81.338, 'text': 'So you have- we wanted to do spam classification.', 'start': 77.795, 'duration': 3.543}], 'summary': 'Introduction to different types of models and machine learning applied to reflex-based models, focusing on linear predictors, loss minimization, and stochastic gradient descent.', 'duration': 75.28, 'max_score': 6.058, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw6058.jpg'}, {'end': 157.711, 'src': 'embed', 'start': 132.871, 'weight': 4, 'content': [{'end': 138.116, 'text': "Um, there's regression where you're trying to predict a numerical value, for example, let's say housing price.", 'start': 132.871, 'duration': 5.245}, {'end': 148.166, 'text': "Um, there's a multi-class classification where y is, uh, not just two items, but possibly um a 100 items, maybe cat dog,", 'start': 138.957, 'duration': 9.209}, {'end': 150.749, 'text': 'truck tree and different kind of image categories.', 'start': 148.166, 'duration': 2.583}, {'end': 156.29, 'text': "Um, there's ranking where the output, um, is a permutation of input.", 'start': 151.469, 'duration': 4.821}, {'end': 157.711, 'text': 'This could be useful, for example,', 'start': 156.31, 'duration': 1.401}], 'summary': 'Transcript covers regression, multi-class classification, and ranking in machine learning.', 'duration': 24.84, 'max_score': 132.871, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw132871.jpg'}, {'end': 232.647, 'src': 'embed', 'start': 204.761, 'weight': 5, 'content': [{'end': 207.803, 'text': 'And a training data or a set of examples.', 'start': 204.761, 'duration': 3.042}, {'end': 212.487, 'text': 'the training set is going to be simply a list or a multi-set of examples.', 'start': 207.803, 'duration': 4.684}, {'end': 216.671, 'text': 'So you can think about this as a partial specification of behavior.', 'start': 213.388, 'duration': 3.283}, {'end': 220.655, 'text': "So remember, we're trying to design a system that has certain certain types of behaviors,", 'start': 216.812, 'duration': 3.843}, {'end': 223.578, 'text': "and we're gonna show you examples of what that system should do.", 'start': 220.655, 'duration': 2.923}, {'end': 232.647, 'text': "If I have some e-mail message that has CS221, then it's not spam, but if it has, um, lots of, uh, dollar signs, then it might, um, um, be spam.", 'start': 224.179, 'duration': 8.468}], 'summary': 'Training data is a list of examples for system behavior, e.g., email with cs221 is not spam, but with dollar signs might be spam.', 'duration': 27.886, 'max_score': 204.761, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw204761.jpg'}], 'start': 6.058, 'title': 'Machine learning basics', 'summary': 'Introduces machine learning basics, including reflex-based models, linear predictors, objective function, stochastic gradient descent, types of prediction problems, and the importance of training data.', 'chapters': [{'end': 60.45, 'start': 6.058, 'title': 'Introduction to machine learning models', 'summary': 'Discusses the application of machine learning to different types of models, including reflex-based models and linear predictors, emphasizing the use of machine learning to tune model parameters and minimize loss.', 'duration': 54.392, 'highlights': ['The chapter introduces different types of models, including reflex models, state-based models, variable-based models, and logic models. The chapter provides an overview of the various types of models to be explored in the course.', 'Machine learning is emphasized as the technique to tune model parameters and reduce the effort in designing models. The discussion highlights the role of machine learning in adjusting model parameters, reducing the need for manual design.', 'The lecture focuses on the application of machine learning to the simplest reflex-based models. The lecture delves into the application of machine learning to reflex-based models as an initial step in the course.', 'The upcoming topics include linear predictors, classification, regression, and loss minimization with the aid of learning. The chapter outlines the subsequent topics to be covered, such as linear predictors, classification, regression, and loss minimization with the assistance of learning techniques.']}, {'end': 243.618, 'start': 60.45, 'title': 'Machine learning basics', 'summary': 'Introduces the basics of machine learning, including objective function, stochastic gradient descent, types of prediction problems, and the importance of training data.', 'duration': 183.168, 'highlights': ['The first step in machine learning is setting the objective function for training the model, followed by using stochastic gradient descent to perform the training.', 'The chapter explains various types of prediction problems, including binary classification, regression, multi-class classification, ranking, and structure prediction.', 'Training data is crucial for machine learning, as it serves as a partial specification of behavior and is essential for designing a system with the desired behaviors.']}], 'duration': 237.56, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw6058.jpg', 'highlights': ['The chapter introduces different types of models, including reflex models, state-based models, variable-based models, and logic models.', 'The lecture focuses on the application of machine learning to the simplest reflex-based models.', 'The upcoming topics include linear predictors, classification, regression, and loss minimization with the aid of learning.', 'The first step in machine learning is setting the objective function for training the model, followed by using stochastic gradient descent to perform the training.', 'The chapter explains various types of prediction problems, including binary classification, regression, multi-class classification, ranking, and structure prediction.', 'Training data is crucial for machine learning, as it serves as a partial specification of behavior and is essential for designing a system with the desired behaviors.', 'Machine learning is emphasized as the technique to tune model parameters and reduce the effort in designing models.']}, {'end': 752.199, 'segs': [{'end': 298.824, 'src': 'embed', 'start': 269.693, 'weight': 2, 'content': [{'end': 278.6, 'text': "And the predictor, remember, is what? It's actually itself a function that, um, takes an input x and maps it to an output y.", 'start': 269.693, 'duration': 8.907}, {'end': 281.774, 'text': "So there's kind of two levels here.", 'start': 279.492, 'duration': 2.282}, {'end': 287.037, 'text': 'And you can understand this in terms of the modeling inference learning paradigm.', 'start': 282.114, 'duration': 4.923}, {'end': 294.381, 'text': 'So modeling is about the question of what should the types of predictors f you should consider are.', 'start': 287.497, 'duration': 6.884}, {'end': 298.824, 'text': 'Inference is about how do you compute y given x.', 'start': 294.482, 'duration': 4.342}], 'summary': 'Understanding predictors as a function mapping x to y in modeling and inference.', 'duration': 29.131, 'max_score': 269.693, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw269693.jpg'}, {'end': 357.459, 'src': 'embed', 'start': 326.401, 'weight': 0, 'content': [{'end': 327.883, 'text': 'So this is an abstract framework.', 'start': 326.401, 'duration': 1.482}, {'end': 335.344, 'text': "Okay So let's dig in a little bit to this actual, um, an actual problem.", 'start': 330.6, 'duration': 4.744}, {'end': 346.013, 'text': "Um, so just to simplify, uh, the email problem, let's, uh, consider a task of, um, predicting whether a string is an email address or not.", 'start': 336.505, 'duration': 9.508}, {'end': 354.637, 'text': "Okay? Um, so the input is an e- is a string and, uh, the output is, it's a binary classification problem.", 'start': 346.793, 'duration': 7.844}, {'end': 357.459, 'text': "It's either 1 if it's an e-mail or minus 1 if it's not.", 'start': 354.657, 'duration': 2.802}], 'summary': 'Framework for predicting email addresses as binary classification.', 'duration': 31.058, 'max_score': 326.401, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw326401.jpg'}, {'end': 555.634, 'src': 'embed', 'start': 528.57, 'weight': 1, 'content': [{'end': 532.173, 'text': "It's kind of distilling complex objects into lists of numbers,", 'start': 528.57, 'duration': 3.603}, {'end': 537.379, 'text': "which we'll see is what the the kind of the lingua franca of these machine learning algorithms is.", 'start': 532.173, 'duration': 5.206}, {'end': 542.149, 'text': "Okay So I'm gonna write some concepts on the board.", 'start': 538.908, 'duration': 3.241}, {'end': 547.851, 'text': "There's gonna be a bunch of, um, concepts I'm gonna introduce and I'll just keep them up on the board for reference.", 'start': 542.209, 'duration': 5.642}, {'end': 551.412, 'text': 'So feature vector is a kind of important notion.', 'start': 548.491, 'duration': 2.921}, {'end': 555.634, 'text': "It's denoted phi, um, of x, an input.", 'start': 551.832, 'duration': 3.802}], 'summary': 'Distilling complex objects into feature vectors for machine learning algorithms.', 'duration': 27.064, 'max_score': 528.57, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw528570.jpg'}, {'end': 710.697, 'src': 'embed', 'start': 679.395, 'weight': 4, 'content': [{'end': 685.517, 'text': 'your prediction is going to be, uh, the dot product between the weight vector and the feature vector.', 'start': 679.395, 'duration': 6.122}, {'end': 698.168, 'text': "Okay, So um that's written w dot phi of x, um, which is um written out as basically looking at all the features and multiplying the feature,", 'start': 686.84, 'duration': 11.328}, {'end': 702.551, 'text': 'value times, the weight of that feature, and summing up all those numbers.', 'start': 698.168, 'duration': 4.383}, {'end': 710.697, 'text': "So for this example um, it would be minus 1.2,, that's the weight of the first feature times 1, that's the feature value.", 'start': 702.611, 'duration': 8.086}], 'summary': 'Prediction is the dot product of weight vector and feature vector, for example: -1.2 * 1', 'duration': 31.302, 'max_score': 679.395, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw679395.jpg'}, {'end': 752.199, 'src': 'embed', 'start': 725.307, 'weight': 3, 'content': [{'end': 732.35, 'text': 'is that, uh, supposed to be like an automated process or does it require manual extraction of specification features? Yeah,', 'start': 725.307, 'duration': 7.043}, {'end': 736.052, 'text': 'So the question is is the feature extraction manual or automatic??', 'start': 732.39, 'duration': 3.662}, {'end': 743.715, 'text': 'So, uh, phi, is going to be implemented as, uh, a function like in- in code, right?', 'start': 736.712, 'duration': 7.003}, {'end': 752.199, 'text': "Um, you're going to write this function manually, but you know the- the function itself is run automatically on examples.", 'start': 744.355, 'duration': 7.844}], 'summary': 'The feature extraction process involves manual implementation but is automatically run on examples.', 'duration': 26.892, 'max_score': 725.307, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw725307.jpg'}], 'start': 243.958, 'title': 'Linear prediction and feature extraction', 'summary': 'Covers linear prediction, modeling, inference, and learning paradigm, as well as feature extraction in the context of predicting email addresses. it also explains feature extraction in machine learning, including feature vectors, weight vectors, and their impact on prediction scores.', 'chapters': [{'end': 394.776, 'start': 243.958, 'title': 'Introduction to linear prediction', 'summary': 'Introduces the concept of linear prediction, with a focus on the modeling, inference, and learning paradigm, as well as the process of feature extraction in the context of predicting email addresses.', 'duration': 150.818, 'highlights': ['The predictor produced by the learning algorithm is a function that maps input x to output y, representing the modeling and inference paradigm in the context of machine learning.', 'Introduction of a binary classification problem for predicting email addresses, where the input is a string and the output is either 1 for an email or -1 for not an email.', 'Explanation of feature extraction as the first step in linear prediction, emphasizing the relevance of input properties for predicting the output, setting the stage for the learning process.']}, {'end': 752.199, 'start': 395.456, 'title': 'Feature extraction in machine learning', 'summary': 'Explains the process of feature extraction in machine learning, including the concept of feature vectors and weight vectors, with examples of feature names, values, and their impact on prediction scores.', 'duration': 356.743, 'highlights': ['Feature extraction involves distilling complex objects into lists of numbers, which serves as the basis for machine learning algorithms. Feature extraction is the process of distilling complex objects, such as strings or images, into lists of numbers, which are used as the foundation for machine learning algorithms.', 'Feature vectors are lists of numbers representing the properties of the input, while weight vectors are interpreted as the contribution of each feature to the prediction. Feature vectors represent the properties of the input as lists of numbers, while weight vectors indicate the contribution of each feature to the prediction.', "The score for a prediction is calculated using the dot product of the weight vector and the feature vector, with each feature's value multiplied by its corresponding weight and then summed up. The prediction score is determined by calculating the dot product of the weight vector and the feature vector, where each feature's value is multiplied by its corresponding weight and then summed.", 'Feature extraction involves the implementation of a function, either manually or automatically, to process examples and generate feature vectors. The process of feature extraction involves the implementation of a function, which can be manually written in code to process examples and generate feature vectors.']}], 'duration': 508.241, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw243958.jpg', 'highlights': ['Introduction of a binary classification problem for predicting email addresses, where the input is a string and the output is either 1 for an email or -1 for not an email.', 'Feature extraction involves distilling complex objects into lists of numbers, which serves as the basis for machine learning algorithms.', 'The predictor produced by the learning algorithm is a function that maps input x to output y, representing the modeling and inference paradigm in the context of machine learning.', 'Feature extraction involves the implementation of a function, either manually or automatically, to process examples and generate feature vectors.', "The score for a prediction is calculated using the dot product of the weight vector and the feature vector, with each feature's value multiplied by its corresponding weight and then summed up."]}, {'end': 1061.567, 'segs': [{'end': 814.689, 'src': 'embed', 'start': 753.443, 'weight': 0, 'content': [{'end': 756.028, 'text': "Later we'll see how you can actually learn features as well.", 'start': 753.443, 'duration': 2.585}, {'end': 761.899, 'text': "So you can slowly start to do less of the manual effort, but we're gonna hold off until next time for that.", 'start': 756.048, 'duration': 5.851}, {'end': 772.025, 'text': 'Question And I know that in certain types of regressions like uh the weights being uh a percentage change of this variable leads to a percentage change in the outcome.', 'start': 762.26, 'duration': 9.765}, {'end': 774.467, 'text': "It doesn't- it doesn't mean this here, right? Yeah.", 'start': 772.105, 'duration': 2.362}, {'end': 777.409, 'text': 'So the question is about interpretation of weights.', 'start': 774.487, 'duration': 2.922}, {'end': 780.03, 'text': 'Sometimes weights can have a more precise meaning.', 'start': 777.769, 'duration': 2.261}, {'end': 791.398, 'text': "In general, um, you can- you- you can try to read the tea leaves, but it's- I don't think there is maybe, uh, in general, mathematically, uh,", 'start': 780.611, 'duration': 10.787}, {'end': 794.12, 'text': 'precise thing you can say about the meaning of individual weights.', 'start': 791.398, 'duration': 2.722}, {'end': 799.662, 'text': 'But intuitively and- and the intuition is important is that you should think about each feature.', 'start': 794.58, 'duration': 5.082}, {'end': 803.364, 'text': "as you know, a little person that's gonna make a vote on this prediction right?", 'start': 799.662, 'duration': 3.702}, {'end': 805.305, 'text': "So you're voting either plus yay or nay.", 'start': 803.384, 'duration': 1.921}, {'end': 814.689, 'text': 'And uh, the weight of a particular feature is- specifies both the direction of the vote, whether, if positive weight means that um,', 'start': 806.205, 'duration': 8.484}], 'summary': 'Discussion on interpreting weights in regression and learning features for less manual effort.', 'duration': 61.246, 'max_score': 753.443, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw753443.jpg'}, {'end': 948.342, 'src': 'embed', 'start': 898.752, 'weight': 3, 'content': [{'end': 902.335, 'text': "Um, later we'll see that the magnitude of weight does, uh, tell you, you know, something.", 'start': 898.752, 'duration': 3.583}, {'end': 912.046, 'text': "Okay, So- so, just to summarize, it's important to note that the- the weight vector there's only one weight vector, right?", 'start': 904.938, 'duration': 7.108}, {'end': 915.629, 'text': 'You have to find one set of parameters for every- everybody.', 'start': 912.066, 'duration': 3.563}, {'end': 918.613, 'text': 'Um, but the feature vector is per example.', 'start': 916.37, 'duration': 2.243}, {'end': 920.695, 'text': 'So for every input, you get a new feature vector.', 'start': 918.753, 'duration': 1.942}, {'end': 926.461, 'text': 'So- and the dot product of those two weighted combination of features is this, uh, is the score.', 'start': 920.715, 'duration': 5.746}, {'end': 938.939, 'text': "Okay, So so now let's try to put the pieces together and define um uh of the actual predictor, right?", 'start': 929.635, 'duration': 9.304}, {'end': 943.56, 'text': 'So remember we had this uh box with an f in it, which takes x and returns y.', 'start': 938.959, 'duration': 4.601}, {'end': 948.342, 'text': "So what is inside that box? Um, and I've hopefully given you some intuition.", 'start': 943.56, 'duration': 4.782}], 'summary': "Weight vector and feature vector are crucial for the predictor's score.", 'duration': 49.59, 'max_score': 898.752, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw898752.jpg'}, {'end': 1002.271, 'src': 'embed', 'start': 973.348, 'weight': 1, 'content': [{'end': 981.193, 'text': 'Um, so a linear classifier, um, denoted f of w.', 'start': 973.348, 'duration': 7.845}, {'end': 983.475, 'text': "So f is what we're gonna use to denote predictors.", 'start': 981.193, 'duration': 2.282}, {'end': 987.318, 'text': 'W just means that this predictor depends on a particular set of weights.', 'start': 983.975, 'duration': 3.343}, {'end': 994.665, 'text': 'And this predictor is, uh, going to look at the score and return the sign of that score.', 'start': 988.519, 'duration': 6.146}, {'end': 1002.271, 'text': "So what is a sign? The sign looks at the score and says, is it a positive number? If it's positive, then we're gonna return plus 1.", 'start': 994.705, 'duration': 7.566}], 'summary': 'Linear classifier f(w) predicts based on score sign.', 'duration': 28.923, 'max_score': 973.348, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw973348.jpg'}], 'start': 753.443, 'title': 'Interpreting weights in regression models and understanding linear classifiers', 'summary': 'Discusses interpreting weights in regression models, emphasizing their influence on predictions. it also focuses on understanding linear classifiers, covering the dot product, role of weights, sign function in classification, and geometric intuition behind them.', 'chapters': [{'end': 836.741, 'start': 753.443, 'title': 'Interpreting weights in regression models', 'summary': 'Discusses the interpretation of weights in regression models, emphasizing that weights represent the direction and strength of influence of features on predictions, with an example of percentage change and voting analogy.', 'duration': 83.298, 'highlights': ["The weight of a feature in regression models specifies both the direction (positive or negative) of the feature's influence on the prediction and the strength of that influence, with an analogy to a little person voting with a positive or negative weight.", 'Interpreting weights in regressions can be challenging, as there may not be a precise mathematical meaning for individual weights, but intuition and understanding the influence of each feature is important for interpretation.', 'Example of weights in regressions explained with a scenario where a percentage change in a variable leads to a percentage change in the outcome, highlighting the varying influence of different features on predictions.']}, {'end': 1061.567, 'start': 837.501, 'title': 'Understanding linear classifiers', 'summary': 'Focuses on understanding linear classifiers, discussing the dot product, the role of weights, the significance of the sign function in classification, and the geometric intuition behind linear classifiers.', 'duration': 224.066, 'highlights': ['The significance of the sign function in classification: The sign function determines the class by returning +1 for positive scores, -1 for negative scores, and is indifferent to 0.', 'The role of weights: The weights do not need to add up to something, with the magnitude of weights providing valuable information.', 'The dot product and score calculation: The score is calculated as the dot product of the weight vector and the feature vector, providing a real number that is then used in classification.']}], 'duration': 308.124, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw753443.jpg', 'highlights': ["The weight of a feature in regression models specifies both the direction (positive or negative) of the feature's influence on the prediction and the strength of that influence, with an analogy to a little person voting with a positive or negative weight.", 'The significance of the sign function in classification: The sign function determines the class by returning +1 for positive scores, -1 for negative scores, and is indifferent to 0.', 'Interpreting weights in regressions can be challenging, as there may not be a precise mathematical meaning for individual weights, but intuition and understanding the influence of each feature is important for interpretation.', 'The role of weights: The weights do not need to add up to something, with the magnitude of weights providing valuable information.', 'Example of weights in regressions explained with a scenario where a percentage change in a variable leads to a percentage change in the outcome, highlighting the varying influence of different features on predictions.', 'The dot product and score calculation: The score is calculated as the dot product of the weight vector and the feature vector, providing a real number that is then used in classification.']}, {'end': 1981.884, 'segs': [{'end': 1346.549, 'src': 'embed', 'start': 1316.267, 'weight': 1, 'content': [{'end': 1319.808, 'text': 'where the classification is positive versus negative.', 'start': 1316.267, 'duration': 3.541}, {'end': 1329.897, 'text': "Okay, And in this case um it's- it separates because, uh it's-, we have linear classifiers,", 'start': 1321.374, 'duration': 8.523}, {'end': 1335.019, 'text': "the decision boundary is straight and we're just separating the- the space into, you know, two halves.", 'start': 1329.897, 'duration': 5.122}, {'end': 1346.549, 'text': 'Um, if you were in three dimensions, um, this vector would still be just, uh, you know, a vector, but this decision, um, boundary would be a plane.', 'start': 1336.54, 'duration': 10.009}], 'summary': 'Linear classifiers separate space into two halves based on positive versus negative classification.', 'duration': 30.282, 'max_score': 1316.267, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1316267.jpg'}, {'end': 1455.91, 'src': 'heatmap', 'start': 1402.529, 'weight': 0.933, 'content': [{'end': 1405.15, 'text': "Okay So let's move on.", 'start': 1402.529, 'duration': 2.621}, {'end': 1406.61, 'text': 'Any questions about linear predictors?', 'start': 1405.21, 'duration': 1.4}, {'end': 1410.692, 'text': "So, so far, what we've done is we haven't done any learning, right?", 'start': 1406.65, 'duration': 4.042}, {'end': 1417.574, 'text': "Uh, if you've uh, you know noticed, we've just simply defined the set of predictors that we're interested in.", 'start': 1410.932, 'duration': 6.642}, {'end': 1421.795, 'text': 'So we have feature vector, we have wave vectors, multiply them together,', 'start': 1417.674, 'duration': 4.121}, {'end': 1429.137, 'text': 'get a score um and then you can send them through a sine function and you get, uh, these linear classifiers right?', 'start': 1421.795, 'duration': 7.342}, {'end': 1431.478, 'text': "There- there's no specification of uh data yet.", 'start': 1429.177, 'duration': 2.301}, {'end': 1437.154, 'text': "Okay So now let's actually turn to do some learning.", 'start': 1433.251, 'duration': 3.903}, {'end': 1448.724, 'text': 'So remember this framework, learning needs to take some data and return a predictor, and our predictors are, uh, specified by a wave vector.', 'start': 1438.776, 'duration': 9.948}, {'end': 1455.91, 'text': 'So you can equivalently think about the learning algorithm as outputting, uh, a wave vector if you want for linear classifiers.', 'start': 1448.784, 'duration': 7.126}], 'summary': 'Introduction to linear predictors and transition to learning algorithms.', 'duration': 53.381, 'max_score': 1402.529, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1402529.jpg'}, {'end': 1548.943, 'src': 'heatmap', 'start': 1488.413, 'weight': 0.742, 'content': [{'end': 1501.221, 'text': 'And this modularity is actually really really powerful um and and it allows people to go ahead and work on different types of uh criteria for and different types of models,', 'start': 1488.413, 'duration': 12.808}, {'end': 1504.543, 'text': 'separately from the people who actually develop general purpose algorithms.', 'start': 1501.221, 'duration': 3.322}, {'end': 1507.607, 'text': 'Um, and this has served to kind of the field of machine learning quite well.', 'start': 1505.143, 'duration': 2.464}, {'end': 1512.695, 'text': "Okay So let's start with optimization problem.", 'start': 1509.75, 'duration': 2.945}, {'end': 1517.301, 'text': "So there's an important concept, um, called a loss function.", 'start': 1513.356, 'duration': 3.945}, {'end': 1525.24, 'text': "And this is a super general idea that's used in the machine learning and statistics.", 'start': 1520.558, 'duration': 4.682}, {'end': 1534.505, 'text': 'So a loss function takes a particular example x, y, and a weight vector, um, and returns a number.', 'start': 1526.421, 'duration': 8.084}, {'end': 1546.792, 'text': 'And this number represents how unhappy we would be if we use the predictor given by w to make a prediction on x when the correct output is y.', 'start': 1534.965, 'duration': 11.827}, {'end': 1548.943, 'text': "Okay, So it's a little bit of a mouthful.", 'start': 1547.622, 'duration': 1.321}], 'summary': 'Modularity in machine learning allows separate work on models and algorithms, benefiting the field.', 'duration': 60.53, 'max_score': 1488.413, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1488413.jpg'}, {'end': 1534.505, 'src': 'embed', 'start': 1501.221, 'weight': 0, 'content': [{'end': 1504.543, 'text': 'separately from the people who actually develop general purpose algorithms.', 'start': 1501.221, 'duration': 3.322}, {'end': 1507.607, 'text': 'Um, and this has served to kind of the field of machine learning quite well.', 'start': 1505.143, 'duration': 2.464}, {'end': 1512.695, 'text': "Okay So let's start with optimization problem.", 'start': 1509.75, 'duration': 2.945}, {'end': 1517.301, 'text': "So there's an important concept, um, called a loss function.", 'start': 1513.356, 'duration': 3.945}, {'end': 1525.24, 'text': "And this is a super general idea that's used in the machine learning and statistics.", 'start': 1520.558, 'duration': 4.682}, {'end': 1534.505, 'text': 'So a loss function takes a particular example x, y, and a weight vector, um, and returns a number.', 'start': 1526.421, 'duration': 8.084}], 'summary': 'Machine learning utilizes loss functions for optimization problem solving.', 'duration': 33.284, 'max_score': 1501.221, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1501221.jpg'}, {'end': 1579.261, 'src': 'embed', 'start': 1551.864, 'weight': 2, 'content': [{'end': 1559.988, 'text': 'you know, if you handed me a classifier and I go onto this example and try to classify it, is it gonna get it right or is it gonna get it wrong??', 'start': 1551.864, 'duration': 8.124}, {'end': 1561.429, 'text': 'So, high loss is bad.', 'start': 1560.369, 'duration': 1.06}, {'end': 1564.831, 'text': "uh, you don't wanna lose, and low loss is good.", 'start': 1561.429, 'duration': 3.402}, {'end': 1568.793, 'text': 'So normally, zero loss is the- the best you can kind of hope for.', 'start': 1565.211, 'duration': 3.582}, {'end': 1576.258, 'text': "Okay So let's do- figure out the loss function for binary classification here.", 'start': 1571.112, 'duration': 5.146}, {'end': 1579.261, 'text': 'Um, so just some notation.', 'start': 1577.139, 'duration': 2.122}], 'summary': 'Classifier aims for low loss, with zero being the best.', 'duration': 27.397, 'max_score': 1551.864, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1551864.jpg'}, {'end': 1645.287, 'src': 'heatmap', 'start': 1593.196, 'weight': 0.72, 'content': [{'end': 1595.238, 'text': "and let's look at this example.", 'start': 1593.196, 'duration': 2.042}, {'end': 1601.886, 'text': 'So w equals 2 minus 1 phi of x equals 2, 0 and y equals minus 1.', 'start': 1595.338, 'duration': 6.548}, {'end': 1614.19, 'text': 'Okay? So we already defined the score as, um, one example is, uh, w dot phi of x, which is, um, how co- confident we are predicting my plus 1.', 'start': 1601.886, 'duration': 12.304}, {'end': 1616.251, 'text': "That's a way to, uh, you know, interpret this.", 'start': 1614.19, 'duration': 2.061}, {'end': 1621.053, 'text': "Okay?. So, um, what's the score of the- for this particular example?", 'start': 1617.292, 'duration': 3.761}, {'end': 1623.786, 'text': "again?, it's 4, right?", 'start': 1621.053, 'duration': 2.733}, {'end': 1630.01, 'text': "Um, which means that you know we're kind of- kind of positive, that it's, uh, you know, a plus 1..", 'start': 1624.366, 'duration': 5.644}, {'end': 1630.51, 'text': 'Yeah, question.', 'start': 1630.01, 'duration': 0.5}, {'end': 1637.897, 'text': 'Uh, I was just wondering, is the loss function generally one-dimensional or- or the output of the loss function is? Yeah.', 'start': 1630.771, 'duration': 7.126}, {'end': 1642.483, 'text': 'So the, the question is whether the output of loss function is usually a single number or not.', 'start': 1637.937, 'duration': 4.546}, {'end': 1645.287, 'text': 'Um, in most cases, it is.', 'start': 1643.044, 'duration': 2.243}], 'summary': 'W=2, phi(x)=2,0, y=-1, score=4, loss function is usually a single number.', 'duration': 52.091, 'max_score': 1593.196, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1593196.jpg'}, {'end': 1838.744, 'src': 'heatmap', 'start': 1690.094, 'weight': 0.903, 'content': [{'end': 1692.355, 'text': "So let's, let's actually do this.", 'start': 1690.094, 'duration': 2.261}, {'end': 1696.437, 'text': "So we're talking about classification.", 'start': 1694.676, 'duration': 1.761}, {'end': 1698.939, 'text': "I'm gonna sneak regression in, in a bit.", 'start': 1696.918, 'duration': 2.021}, {'end': 1703.041, 'text': 'So score is w dot phi of x.', 'start': 1699.639, 'duration': 3.402}, {'end': 1706.202, 'text': 'This is how confident we are about plus 1.', 'start': 1703.041, 'duration': 3.161}, {'end': 1712.516, 'text': 'Um, and the margin, is the score, uh, times y.', 'start': 1706.202, 'duration': 6.314}, {'end': 1716.978, 'text': 'Um, and this relies on y being plus 1 or minus 1.', 'start': 1712.516, 'duration': 4.462}, {'end': 1722.34, 'text': "So this might seem a little bit mysterious, but let's try to, you know, decipher that, um, here.", 'start': 1716.978, 'duration': 5.362}, {'end': 1728.522, 'text': 'Um, so in this example, the score is 4.', 'start': 1723.66, 'duration': 4.862}, {'end': 1742.352, 'text': "So what's the margin? you multiply by minus 1, so the margin is, uh, minus 4, right? And the margins interpretation is how correct we are.", 'start': 1728.522, 'duration': 13.83}, {'end': 1751.853, 'text': "Right? So imagine, uh, the correct answer is, uh, if- if the score and the margin have the same sign, then you're gonna get positive numbers.", 'start': 1743.789, 'duration': 8.064}, {'end': 1755.716, 'text': 'And then the- the confident- the more confident you are, then- then the more correct you are.', 'start': 1752.274, 'duration': 3.442}, {'end': 1768.343, 'text': "Um, but if y is minus 1 and the score is positive, then the margin is gonna be negative, which means that, uh, you're gonna be confidently wrong.", 'start': 1756.596, 'duration': 11.747}, {'end': 1770.324, 'text': 'um, which is bad.', 'start': 1768.343, 'duration': 1.981}, {'end': 1776.129, 'text': "Okay So just to see if we kind of understand what's going on.", 'start': 1773.027, 'duration': 3.102}, {'end': 1785.534, 'text': "Um, so when does a binary classifier make a mistake on a given example? Um, so I'm gonna ask for a kind of a show of hands.", 'start': 1776.529, 'duration': 9.005}, {'end': 1792.615, 'text': "How many people think it's- it's when the margin is, uh, less than 0? Okay.", 'start': 1785.914, 'duration': 6.701}, {'end': 1794.277, 'text': 'I guess we can kind of stop there.', 'start': 1792.876, 'duration': 1.401}, {'end': 1802.125, 'text': "Um, um, I used to do these online quizzes where it wasn't anonymous, but we're not doing that this year.", 'start': 1795.358, 'duration': 6.767}, {'end': 1805.509, 'text': 'Okay So yes, the margin is less than 0.', 'start': 1802.546, 'duration': 2.963}, {'end': 1812.116, 'text': "Um, when the margin is less than 0, that means y and the score are different signs, which means that you're making a mistake.", 'start': 1805.509, 'duration': 6.607}, {'end': 1817.888, 'text': 'Okay So now we have, uh, the notion of a margin.', 'start': 1815.566, 'duration': 2.322}, {'end': 1821.17, 'text': "Let's define, uh, something called the 0-1 loss.", 'start': 1817.968, 'duration': 3.202}, {'end': 1823.692, 'text': "And it's called 0-1 because it returns either a 0 or 1.", 'start': 1821.29, 'duration': 2.402}, {'end': 1826.134, 'text': 'Okay Very creative name.', 'start': 1823.692, 'duration': 2.442}, {'end': 1836.722, 'text': 'Um, so the loss function is, uh, simply, did you make a mistake or not? Okay.', 'start': 1827.475, 'duration': 9.247}, {'end': 1838.744, 'text': "So this notation, let's try to decipher a bit.", 'start': 1836.742, 'duration': 2.002}], 'summary': 'Understanding classification, margin, and 0-1 loss in machine learning.', 'duration': 148.65, 'max_score': 1690.094, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1690094.jpg'}], 'start': 1061.647, 'title': 'Linear classifiers and loss functions', 'summary': 'Introduces the geometric interpretation of linear classifiers and their decision boundary, and explains the role of loss functions in characterizing the performance of classifiers, emphasizing their importance in optimization problems for learning algorithms. it also discusses the concept of loss function, margin, and the 0-1 loss function incurring a loss of 1 for a margin less than or equal to 0 and a loss of 0 for a margin greater than 0.', 'chapters': [{'end': 1394.913, 'start': 1061.647, 'title': 'Geometric interpretation of linear classifiers', 'summary': 'Introduces the geometric interpretation of linear classifiers, demonstrating how a decision boundary separates the space into positive and negative classifications based on the angle with the weight vector, and explains that the magnitude of the weight only matters during learning.', 'duration': 333.266, 'highlights': ['The decision boundary separates the space into positive and negative classifications based on the angle with the weight vector, with points to the right classified as positive and points to the left classified as negative.', 'The magnitude of the weight does not affect the decision boundary, only the direction matters for making predictions.', 'The geometric interpretation of linear classifiers is explained, showing how the weight vector determines the decision boundary in separating the space into positive and negative classifications.', 'The concept of the decision boundary is introduced, serving as the separation between regions of space where the classification is positive versus negative, and is applicable not just for linear classifiers but also for any sort of classifier.', 'The observation that the magnitude of the weight only matters during learning, as it affects the process of making predictions, is noted.']}, {'end': 1630.01, 'start': 1394.913, 'title': 'Loss functions in machine learning', 'summary': 'Introduces the concept of loss functions in machine learning, emphasizing their role in characterizing the performance of classifiers and their importance in optimization problems for learning algorithms.', 'duration': 235.097, 'highlights': ['The concept of loss functions in machine learning is introduced, which are used to quantify the performance of classifiers by measuring the discrepancy between predicted and actual outputs, aiding in optimization problems for learning algorithms.', 'The learning algorithm is based on optimization, with the separation of defining an optimization problem to specify desired classifier properties and the subsequent development of algorithms to achieve these properties, showcasing the modularity and power of this approach within machine learning.', 'The definition and interpretation of loss functions are discussed, where a higher loss indicates poorer classifier performance and a lower loss signifies better performance, with zero loss being the optimal outcome, providing a clear understanding of the significance of loss functions in evaluating classifiers.', 'The process of deriving the loss function for binary classification is explained, utilizing the notation of correct and predicted labels, as well as the calculation of scores for specific examples, offering a practical illustration of applying loss functions in assessing classifier performance.']}, {'end': 1981.884, 'start': 1630.01, 'title': 'Loss function and margin in machine learning', 'summary': 'Explains the concept of loss function and margin in machine learning, where the loss function outputs a single number, and the margin determines the correctness of the prediction, with the 0-1 loss function incurring a loss of 1 for a margin less than or equal to 0 and a loss of 0 for a margin greater than 0.', 'duration': 351.874, 'highlights': ['The loss function outputs a single number in most practical cases, and the margin determines the correctness of the prediction, with a 0-1 loss function incurring a loss of 1 for a margin less than or equal to 0 and a loss of 0 for a margin greater than 0.', 'The concept of margin is discussed, where the margin is the score multiplied by y, relying on y being plus 1 or minus 1, and the interpretation of the margin is how correct the prediction is.', 'The class focuses on one-dimensional loss functions, although there are cases of multi-objective optimization, and the 0-1 loss function returns either a 0 or 1 based on whether a mistake was made.']}], 'duration': 920.237, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1061647.jpg', 'highlights': ['The concept of loss functions in machine learning is introduced, which are used to quantify the performance of classifiers by measuring the discrepancy between predicted and actual outputs, aiding in optimization problems for learning algorithms.', 'The geometric interpretation of linear classifiers is explained, showing how the weight vector determines the decision boundary in separating the space into positive and negative classifications.', 'The process of deriving the loss function for binary classification is explained, utilizing the notation of correct and predicted labels, as well as the calculation of scores for specific examples, offering a practical illustration of applying loss functions in assessing classifier performance.']}, {'end': 2544.213, 'segs': [{'end': 2068.98, 'src': 'embed', 'start': 2018.64, 'weight': 0, 'content': [{'end': 2033.887, 'text': "Um, uh, um, And- and the reason I'm doing this is that loss minimization is such a powerful and general framework and it transcends, you know,", 'start': 2018.64, 'duration': 15.247}, {'end': 2036.968, 'text': 'all of these, uh, you know linear classifiers, regressions setups.', 'start': 2033.887, 'duration': 3.081}, {'end': 2040.87, 'text': 'So I want to kind of emphasize the overall- overall- overall story.', 'start': 2037.188, 'duration': 3.682}, {'end': 2046.432, 'text': "So I'm gonna give you a bunch of different examples um classification, regression side-by-side,", 'start': 2041.21, 'duration': 5.222}, {'end': 2053.534, 'text': 'so we can actually see how they compare and hopefully the- the common denominator will kind of emerge more um clearly from that.', 'start': 2046.432, 'duration': 7.102}, {'end': 2058.533, 'text': 'Okay, So we talked a little bit about linear regression in the last lecture, right?', 'start': 2055.051, 'duration': 3.482}, {'end': 2068.98, 'text': 'So linear regression in some sense is simpler than classification, because if you have a linear uh, uh, predictor, um and you get the score w, dot,', 'start': 2058.592, 'duration': 10.388}], 'summary': 'Loss minimization transcends linear classifiers and regressions, aiming to emphasize its power through various examples.', 'duration': 50.34, 'max_score': 2018.64, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2018640.jpg'}, {'end': 2160.103, 'src': 'embed', 'start': 2126.364, 'weight': 1, 'content': [{'end': 2127.005, 'text': 'you know the target.', 'start': 2126.364, 'duration': 0.641}, {'end': 2131.073, 'text': 'Okay So this is, this is a difference.', 'start': 2129.189, 'duration': 1.884}, {'end': 2138.789, 'text': 'Um, and if you square the difference, you get something called, uh, the squared loss.', 'start': 2131.414, 'duration': 7.375}, {'end': 2144.239, 'text': 'So this is something we mentioned last lecture.', 'start': 2142.259, 'duration': 1.98}, {'end': 2147.88, 'text': 'Um, residual can be either negative or positive.', 'start': 2144.259, 'duration': 3.621}, {'end': 2153.722, 'text': "Um, but errors, either if you're very positive or very negative, that's bad.", 'start': 2148.78, 'duration': 4.942}, {'end': 2160.103, 'text': "And squaring it makes it so that you're gonna, you know, suffer equally for, um, errors in both, you know, directions.", 'start': 2154.122, 'duration': 5.981}], 'summary': 'Using squared loss to penalize errors in both directions evenly.', 'duration': 33.739, 'max_score': 2126.364, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2126364.jpg'}, {'end': 2303.862, 'src': 'embed', 'start': 2277.943, 'weight': 2, 'content': [{'end': 2284.249, 'text': 'The, the salient points here are that the absolute deviation loss is kind of has this kink here.', 'start': 2277.943, 'duration': 6.306}, {'end': 2287.271, 'text': "Um, and so it's not smooth.", 'start': 2285.009, 'duration': 2.262}, {'end': 2289.193, 'text': 'Sometimes it makes it harder to optimize.', 'start': 2287.632, 'duration': 1.561}, {'end': 2296.798, 'text': "Um, But the square loss also has this kind of thing that blows up, which means that it's um.", 'start': 2289.854, 'duration': 6.944}, {'end': 2303.862, 'text': "uh, it really doesn't like having outliers or, uh, really large values, because it's gonna- you're- you're gonna pay a lot for it.", 'start': 2296.798, 'duration': 7.064}], 'summary': 'Absolute deviation loss is not smooth, making optimization harder. square loss dislikes outliers and large values.', 'duration': 25.919, 'max_score': 2277.943, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2277943.jpg'}, {'end': 2467.111, 'src': 'heatmap', 'start': 2415.984, 'weight': 0.944, 'content': [{'end': 2421.366, 'text': "So let's just say we want to minimize the average loss over all the examples, okay?", 'start': 2415.984, 'duration': 5.382}, {'end': 2428.368, 'text': "So, once we have these loss functions, if you average over the training set, you get something which we're gonna call the train loss.", 'start': 2421.406, 'duration': 6.962}, {'end': 2431.329, 'text': "um, and that's a function of w right?", 'start': 2428.368, 'duration': 2.961}, {'end': 2433.73, 'text': 'So loss is on a particular example.', 'start': 2431.87, 'duration': 1.86}, {'end': 2435.471, 'text': 'train loss is on the entire dataset.', 'start': 2433.73, 'duration': 1.741}, {'end': 2452.783, 'text': 'Okay? So any questions about this, uh, so far? Okay.', 'start': 2441.857, 'duration': 10.926}, {'end': 2457.766, 'text': "So there is this, uh, discussion about which regression loss to use, which I'm gonna skip.", 'start': 2452.823, 'duration': 4.943}, {'end': 2460.768, 'text': "Um, you can feel free to read it in the notes if you're interested.", 'start': 2458.106, 'duration': 2.662}, {'end': 2467.111, 'text': 'The punchline is that if you want things that look like the mean square loss, if you want things that look like the median use,', 'start': 2461.248, 'duration': 5.863}], 'summary': 'Minimize average loss over examples, train loss is function of w, regression loss discussed.', 'duration': 51.127, 'max_score': 2415.984, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2415984.jpg'}, {'end': 2504.649, 'src': 'embed', 'start': 2467.111, 'weight': 4, 'content': [{'end': 2468.172, 'text': 'absolute deviation loss.', 'start': 2467.111, 'duration': 1.061}, {'end': 2470.093, 'text': "Um, but I'll skip that for now.", 'start': 2468.712, 'duration': 1.381}, {'end': 2480.881, 'text': 'Uh, when do people start thinking of regression like in terms of loss minimization?', 'start': 2476.497, 'duration': 4.384}, {'end': 2483.724, 'text': 'Uh so, regression has least squares.', 'start': 2480.901, 'duration': 2.823}, {'end': 2486.026, 'text': 'regression is from like the early 1800s.', 'start': 2483.724, 'duration': 2.302}, {'end': 2494.073, 'text': "Um, so it's been around for is, you know, kind of, you could call it the first machine learning that was ever done, um, if you- if you want.", 'start': 2486.046, 'duration': 8.027}, {'end': 2504.649, 'text': "Um, I guess the loss minimization framework is, um, it's hard to kind of pinpoint a particular point in time.", 'start': 2494.093, 'duration': 10.556}], 'summary': "Regression's loss minimization dates back to 1800s.", 'duration': 37.538, 'max_score': 2467.111, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2467111.jpg'}], 'start': 1986.431, 'title': 'Linear regression, classification, and loss functions', 'summary': 'Covers binary classification, linear predictors, loss minimization, linear regression, and loss functions, emphasizing the powerful framework of loss minimization and decision-making involved in minimizing average loss over all examples.', 'chapters': [{'end': 2068.98, 'start': 1986.431, 'title': 'Binary classification and linear regression', 'summary': 'Covers the concepts of binary classification, linear predictors, and loss minimization, emphasizing the powerful and general framework of loss minimization in transcending linear classifiers and regression setups.', 'duration': 82.549, 'highlights': ['The chapter emphasizes the powerful and general framework of loss minimization in transcending linear classifiers and regression setups.', 'Linear regression is simpler than classification, as it involves a linear predictor and a score w, dot.']}, {'end': 2544.213, 'start': 2068.98, 'title': 'Linear regression and loss functions', 'summary': 'Explains linear regression and the concept of loss functions, including the calculation of residual, squared loss, and absolute deviation loss, as well as the trade-offs and responsible decision-making involved in minimizing the average loss over all examples in the dataset.', 'duration': 475.233, 'highlights': ['The residual is the difference between the true value and the predicted value, and the squared loss is the square of the residual, serving as a measure of how much the prediction overshoots the target (e.g., residual of 5 leads to a squared loss of 25).', 'The chapter discusses different loss functions, including the squared loss and absolute deviation loss, highlighting the trade-offs involved in minimizing the average loss over all examples in the dataset.', 'Regression has been around since the early 1800s, and the loss minimization framework is a pedagogical tool to organize different methods in machine learning.']}], 'duration': 557.782, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw1986431.jpg', 'highlights': ['The chapter emphasizes the powerful and general framework of loss minimization in transcending linear classifiers and regression setups.', 'The residual is the difference between the true value and the predicted value, and the squared loss is the square of the residual, serving as a measure of how much the prediction overshoots the target (e.g., residual of 5 leads to a squared loss of 25).', 'The chapter discusses different loss functions, including the squared loss and absolute deviation loss, highlighting the trade-offs involved in minimizing the average loss over all examples in the dataset.', 'Linear regression is simpler than classification, as it involves a linear predictor and a score w, dot.', 'Regression has been around since the early 1800s, and the loss minimization framework is a pedagogical tool to organize different methods in machine learning.']}, {'end': 2996.569, 'segs': [{'end': 2622.637, 'src': 'embed', 'start': 2592.895, 'weight': 1, 'content': [{'end': 2595.116, 'text': 'How- how do you actually optimize these objectives??', 'start': 2592.895, 'duration': 2.221}, {'end': 2597.71, 'text': 'So remember, the learner is going.', 'start': 2595.987, 'duration': 1.723}, {'end': 2602.597, 'text': 'uh so now we talked about the optimization problem, which is minimizing the training loss.', 'start': 2597.71, 'duration': 4.887}, {'end': 2604.9, 'text': "Um, we'll come back to that next lecture.", 'start': 2603.318, 'duration': 1.582}, {'end': 2608.546, 'text': "Um, and then now we're gonna talk about optimization algorithm.", 'start': 2604.92, 'duration': 3.626}, {'end': 2617.814, 'text': "Okay? So what is the optimization problem? Now, remember last time we said, okay, let's just abstract away from the details a little bit.", 'start': 2609.448, 'duration': 8.366}, {'end': 2622.637, 'text': "Let's not worry about if it's, uh, the square loss or, you know, some other loss.", 'start': 2617.834, 'duration': 4.803}], 'summary': 'Optimizing objectives includes minimizing training loss and discussing optimization algorithms.', 'duration': 29.742, 'max_score': 2592.895, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2592895.jpg'}, {'end': 2657.812, 'src': 'embed', 'start': 2631.082, 'weight': 0, 'content': [{'end': 2636.786, 'text': 'You have a single weight, and for each weight, you have a number which is your loss on your training examples.', 'start': 2631.082, 'duration': 5.704}, {'end': 2639.368, 'text': 'Okay? And you want to find this point.', 'start': 2637.507, 'duration': 1.861}, {'end': 2644.469, 'text': 'So in two dimensions, um, it looks something like this.', 'start': 2640.668, 'duration': 3.801}, {'end': 2649.63, 'text': "And let me try and actually draw this because I think it'll, uh, be, um, useful in a bit.", 'start': 2644.729, 'duration': 4.901}, {'end': 2650.831, 'text': 'So let me pull this up.', 'start': 2649.75, 'duration': 1.081}, {'end': 2657.812, 'text': 'Okay So in two dimensions, um, what optimization looks like is as follows.', 'start': 2653.371, 'duration': 4.441}], 'summary': 'Optimization in two dimensions involves finding the point for a single weight and its corresponding training loss.', 'duration': 26.73, 'max_score': 2631.082, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2631082.jpg'}, {'end': 2790.302, 'src': 'embed', 'start': 2761.422, 'weight': 2, 'content': [{'end': 2769.668, 'text': 'So the gradient is going to point in this direction that says, hey, in this direction is where the function is increasing the most dramatically.', 'start': 2761.422, 'duration': 8.246}, {'end': 2778.634, 'text': 'Um, and gradient descent says, um, takes- goes in the opposite direction, right? Because remember, we want to minimize loss.', 'start': 2770.749, 'duration': 7.885}, {'end': 2790.302, 'text': "Um, so I'm gonna go here and, um, now I'm hopefully reduce my, uh, function value, not necessarily, but, um, we hope that's- that's the case.", 'start': 2779.675, 'duration': 10.627}], 'summary': 'Gradient descent minimizes loss by moving in opposite direction of function increase.', 'duration': 28.88, 'max_score': 2761.422, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2761422.jpg'}, {'end': 2905.822, 'src': 'embed', 'start': 2878.207, 'weight': 3, 'content': [{'end': 2884.21, 'text': 'Um, so the training loss for least squares regression is this.', 'start': 2878.207, 'duration': 6.003}, {'end': 2892.455, 'text': "So remember it's average over the loss of individual examples and the loss of a particular example is the residual squared.", 'start': 2884.29, 'duration': 8.165}, {'end': 2893.896, 'text': "So that's this expression.", 'start': 2892.795, 'duration': 1.101}, {'end': 2897.978, 'text': 'Um, and then all we have to do is compute the gradient.', 'start': 2895.436, 'duration': 2.542}, {'end': 2903.221, 'text': "And, you know, if you remember your calculus, it's just, uh, use the chain rule.", 'start': 2898.678, 'duration': 4.543}, {'end': 2905.822, 'text': 'Um. so this 2 comes down here.', 'start': 2904.141, 'duration': 1.681}], 'summary': 'Training loss for least squares regression involves computing the gradient and applying the chain rule.', 'duration': 27.615, 'max_score': 2878.207, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2878207.jpg'}], 'start': 2544.213, 'title': 'Loss functions and optimization', 'summary': 'Discusses loss functions for regression and classification, optimization problems, and visual representation of optimization in two dimensions to find the minimum point. it also explains gradient descent, least squares regression, training loss, chain rule, and derivative of the residual squared.', 'chapters': [{'end': 2734.697, 'start': 2544.213, 'title': 'Loss functions and optimization', 'summary': 'Discusses loss functions for regression and classification in machine learning, optimization problems, and visual representation of optimization in two dimensions, aiming to find the minimum point of the loss function.', 'duration': 190.484, 'highlights': ['The chapter discusses loss functions for regression and classification in machine learning This section highlights the focus on different loss functions for regression and classification in machine learning.', 'Visual representation of optimization in two dimensions, aiming to find the minimum point of the loss function The visual representation of optimization in two dimensions and the aim to find the minimum point of the loss function is a key point in understanding the optimization process.', 'Optimization problems and the goal of minimizing the training loss Emphasizing the objective of minimizing the training loss and addressing optimization problems is crucial in machine learning.']}, {'end': 2996.569, 'start': 2740.019, 'title': 'Gradient descent and optimization', 'summary': 'Explains the concept of gradient descent, where the gradient is computed to minimize the loss function, with a focus on least squares regression and its training loss, involving a chain rule and the derivative of the residual squared.', 'duration': 256.55, 'highlights': ['The gradient descent method involves computing the gradient that points in the direction of the most dramatic increase in the function, and then moving in the opposite direction to minimize the loss function.', 'The training loss for least squares regression is computed using the average over the loss of individual examples, with the loss of a particular example being the residual squared, and the gradient is computed using the chain rule and the derivative of the residual squared.', 'In one dimension, the computation of the gradient is similar to taking derivatives, but when dealing with vectors, caution is required to ensure the gradient version matches the single-dimensional version, with a focus on the prediction minus target as the driving force for the gradient.', 'The objective functions need to be written down to ensure that the gradient descent method works effectively, especially when the prediction equals the target, resulting in a gradient of 0.']}], 'duration': 452.356, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2544213.jpg', 'highlights': ['The visual representation of optimization in two dimensions and the aim to find the minimum point of the loss function is a key point in understanding the optimization process.', 'Emphasizing the objective of minimizing the training loss and addressing optimization problems is crucial in machine learning.', 'The gradient descent method involves computing the gradient that points in the direction of the most dramatic increase in the function, and then moving in the opposite direction to minimize the loss function.', 'The training loss for least squares regression is computed using the average over the loss of individual examples, with the loss of a particular example being the residual squared, and the gradient is computed using the chain rule and the derivative of the residual squared.']}, {'end': 4209.948, 'segs': [{'end': 3044.31, 'src': 'embed', 'start': 3013.877, 'weight': 0, 'content': [{'end': 3018.76, 'text': 'is it sensible to update when the gradient or then when the prediction equals the target?', 'start': 3013.877, 'duration': 4.883}, {'end': 3021.682, 'text': 'Okay,', 'start': 3021.422, 'duration': 0.26}, {'end': 3030.128, 'text': "So so let's um, take the code that we have from last time and I'm going to um expand on it a little bit, um,", 'start': 3021.762, 'duration': 8.366}, {'end': 3033.43, 'text': 'and hopefully set the stage for doing stochastic gradient.', 'start': 3030.128, 'duration': 3.302}, {'end': 3035.892, 'text': 'Um, okay.', 'start': 3034.13, 'duration': 1.762}, {'end': 3042.228, 'text': 'So so, last time we had gradient descent, Okay?', 'start': 3036.032, 'duration': 6.196}, {'end': 3044.31, 'text': 'So remember, last time we defined a set of points.', 'start': 3042.248, 'duration': 2.062}], 'summary': 'Discussing expanding code for stochastic gradient descent.', 'duration': 30.433, 'max_score': 3013.877, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw3013877.jpg'}, {'end': 3460.29, 'src': 'embed', 'start': 3435.197, 'weight': 1, 'content': [{'end': 3441.28, 'text': "So, you know, this is not hard proof, but it's kind of evidence that this, uh, learning algorithm is actually kind of doing the right thing.", 'start': 3435.197, 'duration': 6.083}, {'end': 3444.982, 'text': 'Um, okay.', 'start': 3443.922, 'duration': 1.06}, {'end': 3448.984, 'text': "So now let's see if, uh, I add, you know, more points.", 'start': 3445.022, 'duration': 3.962}, {'end': 3451.726, 'text': 'So I now have 100, 000 points.', 'start': 3450.005, 'duration': 1.721}, {'end': 3460.29, 'text': "Now, you know, obviously it gets, you know, slower, um, and it'll, you know, hopefully get there, you know, one day, but I'm just gonna kill it.", 'start': 3453.246, 'duration': 7.044}], 'summary': 'Learning algorithm shows potential with 100,000 points, but still needs improvement.', 'duration': 25.093, 'max_score': 3435.197, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw3435197.jpg'}, {'end': 3557.765, 'src': 'embed', 'start': 3529.582, 'weight': 2, 'content': [{'end': 3532.385, 'text': "And same for when you're, um, you know, under-predicting.", 'start': 3529.582, 'duration': 2.803}, {'end': 3534.227, 'text': "Yeah So that's good intuition to have.", 'start': 3532.806, 'duration': 1.421}, {'end': 3541.495, 'text': "Yeah, What's the noise when you generate um black holes?", 'start': 3534.247, 'duration': 7.248}, {'end': 3545.662, 'text': 'What is the effect of the noise?', 'start': 3543.982, 'duration': 1.68}, {'end': 3550.023, 'text': 'Um, the effect of noise, it makes the problem a little bit, you know, harder.', 'start': 3546.142, 'duration': 3.881}, {'end': 3553.124, 'text': 'uh, so that it takes more examples to learn.', 'start': 3550.023, 'duration': 3.101}, {'end': 3557.765, 'text': 'Um, if you shut off the noise then it will, you know, we can try it.', 'start': 3553.864, 'duration': 3.901}], 'summary': 'Noise makes learning harder, requires more examples.', 'duration': 28.183, 'max_score': 3529.582, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw3529582.jpg'}, {'end': 3719.194, 'src': 'embed', 'start': 3687.311, 'weight': 3, 'content': [{'end': 3689.433, 'text': "So, so here's the idea behind stochastic gradient descent.", 'start': 3687.311, 'duration': 2.122}, {'end': 3691.394, 'text': 'So, instead of doing gradient descent,', 'start': 3689.453, 'duration': 1.941}, {'end': 3699.24, 'text': "we're gonna change the algorithm to say for each example in the training set I'm just gonna pick it up and just update.", 'start': 3691.394, 'duration': 7.846}, {'end': 3705.81, 'text': "you know it's- instead of like sitting down and looking at all the- all the training examples and thinking really hard,", 'start': 3700.469, 'duration': 5.341}, {'end': 3708.411, 'text': "I'm just gonna pick up one training example and update right away.", 'start': 3705.81, 'duration': 2.601}, {'end': 3713.413, 'text': "So again, the key idea here is it's not about quality, it's about quantity.", 'start': 3709.131, 'duration': 4.282}, {'end': 3719.194, 'text': "Maybe not the world's best life lesson, but it seems to work in- work in here.", 'start': 3714.093, 'duration': 5.101}], 'summary': 'Stochastic gradient descent updates each training example individually, prioritizing quantity over quality.', 'duration': 31.883, 'max_score': 3687.311, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw3687311.jpg'}, {'end': 3773.875, 'src': 'embed', 'start': 3747.344, 'weight': 4, 'content': [{'end': 3751.365, 'text': "Uh, I mean, there are formulas, but there's no kind of definitive answer.", 'start': 3747.344, 'duration': 4.021}, {'end': 3752.885, 'text': "Here's some general guidance.", 'start': 3751.845, 'duration': 1.04}, {'end': 3757.729, 'text': "Um, so if step size is small, So you're really close to 0.", 'start': 3753.665, 'duration': 4.064}, {'end': 3759.989, 'text': "That means you're taking tiny steps, right?", 'start': 3757.729, 'duration': 2.26}, {'end': 3766.472, 'text': "That means that, uh, it'll take longer to get where you want to go, but you're kind of proceeding cautiously,", 'start': 3760.55, 'duration': 5.922}, {'end': 3770.094, 'text': "so you're- it's less likely you're gonna, you know.", 'start': 3766.472, 'duration': 3.622}, {'end': 3773.875, 'text': "uh, if you mess up and go in the wrong direction, you're not gonna go too far in the wrong direction.", 'start': 3770.094, 'duration': 3.781}], 'summary': 'Small step size leads to cautious progress and longer time to reach the destination.', 'duration': 26.531, 'max_score': 3747.344, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw3747344.jpg'}, {'end': 3872.592, 'src': 'heatmap', 'start': 3818.893, 'weight': 0.835, 'content': [{'end': 3827.198, 'text': 'Um, or you can set it to be decreasing, the intuition being that as you optimize and get closer to the optimum, you kinda wanna slow down right?', 'start': 3818.893, 'duration': 8.305}, {'end': 3830.98, 'text': "Like if you you're coming on the freeway, you're driving really fast, but once you get to your house,", 'start': 3827.238, 'duration': 3.742}, {'end': 3833.622, 'text': "you probably don't wanna be like driving 60 miles an hour.", 'start': 3830.98, 'duration': 2.642}, {'end': 3840.387, 'text': "Okay Um, so actually I didn't implement stochastic gradient.", 'start': 3836.081, 'duration': 4.306}, {'end': 3840.967, 'text': 'So let me do that.', 'start': 3840.407, 'duration': 0.56}, {'end': 3844.992, 'text': "So let's, let's try to get stochastic gradient up and going here.", 'start': 3841.688, 'duration': 3.304}, {'end': 3848.335, 'text': 'Um, Okay.', 'start': 3845.954, 'duration': 2.381}, {'end': 3852.278, 'text': 'So, so the interface to stochastic gradient changes.', 'start': 3848.535, 'duration': 3.743}, {'end': 3860.464, 'text': 'So, right? So the ingredients and all I need is a function and it, it just kind of computes the sum of all the training examples.', 'start': 3852.418, 'duration': 8.046}, {'end': 3866.908, 'text': "Um, so in stochastic gradient, I'm gonna just know S, F for stochastic gradient.", 'start': 3861.664, 'duration': 5.244}, {'end': 3872.592, 'text': "I'm gonna take an index i, um, and I'm going to update on the i-th point only.", 'start': 3867.388, 'duration': 5.204}], 'summary': 'Discussion on optimizing algorithms and implementing stochastic gradient with index updates.', 'duration': 53.699, 'max_score': 3818.893, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw3818893.jpg'}, {'end': 4025.791, 'src': 'embed', 'start': 4000.918, 'weight': 6, 'content': [{'end': 4009.026, 'text': "And, you know, technically speaking, the, the stochastic gradient descent is where you're sampling a random point and then you're updating on it.", 'start': 4000.918, 'duration': 8.108}, {'end': 4015.508, 'text': "Uh, I'm cheating a little bit, um, uh, because I'm iterating over all the points.", 'start': 4009.586, 'duration': 5.922}, {'end': 4020.189, 'text': "You know, in practice, if you have a lot of points and you randomize the order, it's kind of.", 'start': 4016.228, 'duration': 3.961}, {'end': 4021.59, 'text': "you know is is similar, but it's.", 'start': 4020.189, 'duration': 1.401}, {'end': 4025.791, 'text': "uh, there is a kind of a technical difference that I'm trying to hide.", 'start': 4021.59, 'duration': 4.201}], 'summary': 'Stochastic gradient descent involves sampling random points and updating, with a technical difference when iterating over all points.', 'duration': 24.873, 'max_score': 4000.918, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4000918.jpg'}, {'end': 4207.127, 'src': 'heatmap', 'start': 4157.538, 'weight': 0.845, 'content': [{'end': 4160.1, 'text': 'Okay So I do have a version of this code that does work.', 'start': 4157.538, 'duration': 2.562}, {'end': 4163.122, 'text': "So what am I doing here? That's different.", 'start': 4160.861, 'duration': 2.261}, {'end': 4164.301, 'text': 'Okay Have some water.', 'start': 4163.522, 'duration': 0.779}, {'end': 4165.162, 'text': 'Maybe I need some water.', 'start': 4164.322, 'duration': 0.84}, {'end': 4173.712, 'text': 'Okay So this version works.', 'start': 4165.183, 'duration': 8.529}, {'end': 4181.319, 'text': "Yeah Yeah, that's, that's probably good.", 'start': 4174.893, 'duration': 6.426}, {'end': 4182.64, 'text': "That's a good call.", 'start': 4182.02, 'duration': 0.62}, {'end': 4185.163, 'text': 'Yeah Okay.', 'start': 4183.162, 'duration': 2.001}, {'end': 4189.046, 'text': 'All right, now it works.', 'start': 4188.307, 'duration': 0.739}, {'end': 4189.747, 'text': 'Thank you.', 'start': 4189.448, 'duration': 0.299}, {'end': 4195.724, 'text': 'Um, so yeah.', 'start': 4194.864, 'duration': 0.86}, {'end': 4203.166, 'text': "Yeah, this is a good, uh, lesson, um, is that when you're dividing, um, this needs to be one.", 'start': 4196.244, 'duration': 6.922}, {'end': 4207.127, 'text': "Actually in Python 3, this is not a problem, but I'm still on Python 2 for some reason.", 'start': 4203.226, 'duration': 3.901}], 'summary': 'The speaker has a working version of code, mentions needing water, and discusses a lesson on division in python 2 and 3.', 'duration': 49.589, 'max_score': 4157.538, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4157537.jpg'}], 'start': 2996.569, 'title': 'Stochastic gradient descent', 'summary': 'Delves into implementing stochastic gradient descent in python using the numpy library, discussing the impact of noise on learning, emphasizing quantity over quality, and providing insights on improving efficiency in modern machine learning, with evidence of convergence and performance improvement.', 'chapters': [{'end': 3093.975, 'start': 2996.569, 'title': 'Understanding gradient descent', 'summary': 'Discusses the concept of gradient descent, including the computation of gradients, the expansion of code for stochastic gradient, and the relationship between the algorithm and modeling.', 'duration': 97.406, 'highlights': ['The chapter discusses the concept of gradient descent, including the computation of gradients, the expansion of code for stochastic gradient, and the relationship between the algorithm and modeling.', 'Gradient descent depends on a function, a derivative of a function, and the dimensionality, as discussed with the example of d=2.', 'The chapter explores the expansion of code for stochastic gradient and sets the stage for its implementation.']}, {'end': 3460.29, 'start': 3094.075, 'title': 'Implementing stochastic gradient descent', 'summary': 'Discusses upgrading a code to support vectors in python using the numpy library, implementing stochastic gradient descent, generating artificial data for testing, and training a learning algorithm with evidence of convergence and performance improvement.', 'duration': 366.215, 'highlights': ['The code is upgraded to support vectors using the numpy library in Python. The speaker upgrades the code to support vectors using the numpy library in Python.', 'Artificial data is generated with 100,000 points for testing the learning algorithm. The speaker generates artificial data with 100,000 points to test the learning algorithm.', 'The learning algorithm is trained with 1,000 iterations, showing evidence of convergence and improvement in performance. The learning algorithm is trained with 1,000 iterations, demonstrating evidence of convergence and performance improvement.', 'The implementation of stochastic gradient descent is mentioned as part of the discussion. The speaker mentions the implementation of stochastic gradient descent as part of the discussion.']}, {'end': 3685.83, 'start': 3463.14, 'title': 'Gradient descent and stochastic gradient descent', 'summary': 'Discusses the implementation of gradient descent, the effect of noise on learning, and the concept of stochastic gradient descent, providing insights on improving efficiency in modern machine learning.', 'duration': 222.69, 'highlights': ['The algorithm implements gradient descent to compute the gradient of the training loss, which is the average of all the points, leading to slower computation when dealing with a large number of examples like millions. Implementation of gradient descent, computation of gradient of training loss, impact on computation efficiency', 'The effect of noise on the dataset makes the learning process harder and requires more examples to learn, potentially slowing down the learning process. Effect of noise on learning process, impact on learning speed', 'Introduction of stochastic gradient descent as a potential solution to improve efficiency by not averaging all gradients from the training set, leading to faster computation. Concept of stochastic gradient descent, efficiency improvement, computation speed boost']}, {'end': 3952.694, 'start': 3687.311, 'title': 'Stochastic gradient descent', 'summary': 'Introduces stochastic gradient descent as an alternative to traditional gradient descent, emphasizing the importance of quantity over quality and the impact of step size on convergence, with no definitive formula for setting it.', 'duration': 265.383, 'highlights': ['Stochastic gradient descent focuses on updating the algorithm for each example in the training set, prioritizing quantity over quality. The approach involves picking up one training example and updating right away, emphasizing the importance of quantity over quality.', 'The step size in stochastic gradient descent plays a crucial role, with smaller step sizes leading to cautious progress and larger step sizes causing rapid but potentially erratic movement. The step size significantly impacts the convergence, with smaller steps leading to cautious progress and larger steps potentially causing erratic movement and divergence.', 'Setting the step size in stochastic gradient descent has no definitive formula, but general guidance suggests that smaller step sizes lead to longer convergence time but cautious progress, while larger step sizes lead to faster but potentially erratic movement. There is no definitive formula for setting the step size, but general guidance suggests that smaller step sizes lead to longer convergence time but cautious progress, while larger step sizes lead to faster but potentially erratic movement.', 'Implementing stochastic gradient descent involves updating on each individual example, computing the loss and gradient on the i-th point, and looping over all the points to evaluate the function and compute the gradient. Implementing stochastic gradient descent involves updating on each individual example, computing the loss and gradient on the i-th point, and looping over all the points to evaluate the function and compute the gradient.']}, {'end': 4209.948, 'start': 3952.714, 'title': 'Stochastic gradient descent', 'summary': 'Covers the implementation of stochastic gradient descent with a decreasing step size schedule and discusses the technical difference between stochastic and regular gradient descent, highlighting the need for a specific division in the code.', 'duration': 257.234, 'highlights': ['The chapter covers the implementation of stochastic gradient descent with a decreasing step size schedule. The speaker discusses using a different step size schedule, starting with 1 and then halving it successively, demonstrating the implementation of stochastic gradient descent.', 'The speaker explains the technical difference between stochastic and regular gradient descent. The speaker highlights the technical difference between stochastic gradient descent, where a random point is sampled and updated, and regular gradient descent, where all points are iterated over, emphasizing the need for randomness in stochastic gradient descent.', "The speaker highlights the need for a specific division in the code. The speaker emphasizes the importance of a specific division, mentioning the need for '1.0' divided by the number of updates in the code, and discusses the impact of this division on the code's functionality."]}], 'duration': 1213.379, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw2996569.jpg', 'highlights': ['The chapter explores the expansion of code for stochastic gradient and sets the stage for its implementation.', 'The learning algorithm is trained with 1,000 iterations, demonstrating evidence of convergence and performance improvement.', 'The effect of noise on the dataset makes the learning process harder and requires more examples to learn, potentially slowing down the learning process.', 'Stochastic gradient descent focuses on updating the algorithm for each example in the training set, emphasizing the importance of quantity over quality.', 'The step size significantly impacts the convergence, with smaller steps leading to cautious progress and larger steps potentially causing erratic movement and divergence.', 'The chapter covers the implementation of stochastic gradient descent with a decreasing step size schedule, demonstrating the implementation of stochastic gradient descent.', 'The speaker highlights the technical difference between stochastic gradient descent, where a random point is sampled and updated, and regular gradient descent, emphasizing the need for randomness in stochastic gradient descent.']}, {'end': 4826.46, 'segs': [{'end': 4273.489, 'src': 'embed', 'start': 4242.731, 'weight': 0, 'content': [{'end': 4260.122, 'text': "Remember? Just to kind of compare, um, gradient descent is, um, you run it and after one step it's like not even close, right? Yeah.", 'start': 4242.731, 'duration': 17.391}, {'end': 4264.644, 'text': 'What noise levels do you have to have until gradient descent becomes better?', 'start': 4261.383, 'duration': 3.261}, {'end': 4271.968, 'text': 'Um so, it is true that if you have more noise then gradient descent might be, uh, stochastic.', 'start': 4265.385, 'duration': 6.583}, {'end': 4273.489, 'text': 'gradient descent can be unstable.', 'start': 4271.968, 'duration': 1.521}], 'summary': 'Gradient descent becomes better with lower noise levels.', 'duration': 30.758, 'max_score': 4242.731, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4242731.jpg'}, {'end': 4497.999, 'src': 'heatmap', 'start': 4428.358, 'weight': 1, 'content': [{'end': 4431.36, 'text': "Um, so that's- that's kind of unfortunate.", 'start': 4428.358, 'duration': 3.002}, {'end': 4437.505, 'text': 'So how should we fix this problem? Yeah.', 'start': 4431.721, 'duration': 5.784}, {'end': 4441.222, 'text': "Yeah, let's- let's make the gradient not 0.", 'start': 4439.44, 'duration': 1.782}, {'end': 4441.963, 'text': "Let's skew things.", 'start': 4441.222, 'duration': 0.741}, {'end': 4450.754, 'text': "Um, so there's one loss which I'm gonna introduce called the hinge loss which, uh, does exactly that.", 'start': 4442.704, 'duration': 8.05}, {'end': 4452.937, 'text': 'Um, so let me write the hinge loss down.', 'start': 4451.235, 'duration': 1.702}, {'end': 4464.292, 'text': 'And the hinge loss, um, is basically, uh, is 0 here when the margin is greater or equal 1 and rises linearly.', 'start': 4454.969, 'duration': 9.323}, {'end': 4471.875, 'text': "So if you've gotten it correct by a margin of 1, so you're kind of pretty safely on the side of I'm getting it correct,", 'start': 4464.352, 'duration': 7.523}, {'end': 4473.556, 'text': "then we won't charge you anything.", 'start': 4471.875, 'duration': 1.681}, {'end': 4480.358, 'text': "But as soon as you start, you know, dipping into this area, we're gonna charge you a kind of a linear amount and your loss is gonna grow linearly.", 'start': 4473.996, 'duration': 6.362}, {'end': 4484.767, 'text': "Um, so there's some reasons why this is a good idea.", 'start': 4482.345, 'duration': 2.422}, {'end': 4486.829, 'text': 'So it upper bounds the zero and loss.', 'start': 4484.827, 'duration': 2.002}, {'end': 4493.715, 'text': "Um, it's uh, it has a property called- known as convexity which means that if you actually run the gradient descent,", 'start': 4487.51, 'duration': 6.205}, {'end': 4495.837, 'text': "you're actually gonna converge to the global optimum.", 'start': 4493.715, 'duration': 2.122}, {'end': 4497.999, 'text': "Um, I'm not gonna get into that.", 'start': 4496.457, 'duration': 1.542}], 'summary': 'Introducing hinge loss to fix problem, charges linearly if margin is less than 1, has properties like convexity.', 'duration': 69.641, 'max_score': 4428.358, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4428358.jpg'}, {'end': 4717.24, 'src': 'embed', 'start': 4672.694, 'weight': 2, 'content': [{'end': 4677.035, 'text': "What's the significance of the margin being one? Um, this is a little bit arbitrary.", 'start': 4672.694, 'duration': 4.341}, {'end': 4679.875, 'text': "You're just kind of sending a non-zero value.", 'start': 4677.055, 'duration': 2.82}, {'end': 4689.757, 'text': 'Um, and, and you know, in uh, support vector machines you set it to one and then you have regularization on the weights and that gives you, uh,', 'start': 4680.836, 'duration': 8.921}, {'end': 4690.657, 'text': 'some interpretation.', 'start': 4689.757, 'duration': 0.9}, {'end': 4695.218, 'text': "So I don't have time to go over that right now, but feel free to ask me later.", 'start': 4690.837, 'duration': 4.381}, {'end': 4697.839, 'text': "There's another Floss function.", 'start': 4696.438, 'duration': 1.401}, {'end': 4700.039, 'text': 'Uh, do you have a question? Yeah.', 'start': 4697.859, 'duration': 2.18}, {'end': 4708.334, 'text': 'Is the, why do we choose the margin as the loss function as opposed to like the squared error or another? Yeah.', 'start': 4701.188, 'duration': 7.146}, {'end': 4709.535, 'text': 'So why do you choose the margin?', 'start': 4708.354, 'duration': 1.181}, {'end': 4715.099, 'text': "So, in classification, we're going to look at the margin, because that tells you how confidently you're predicting.", 'start': 4709.575, 'duration': 5.524}, {'end': 4717.24, 'text': 'uh, you know correctly.', 'start': 4715.099, 'duration': 2.141}], 'summary': 'In classification, a margin of 1 is chosen for support vector machines to indicate confidence in predictions.', 'duration': 44.546, 'max_score': 4672.694, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4672694.jpg'}, {'end': 4764.894, 'src': 'embed', 'start': 4739.659, 'weight': 4, 'content': [{'end': 4745.243, 'text': 'really general and a lot of things that you might have heard of least squares, logistic regression are kind of special cases of this.', 'start': 4739.659, 'duration': 5.584}, {'end': 4750.307, 'text': 'So if you kind of master how to do loss minimization, you kind of, uh, can do it all.', 'start': 4745.303, 'duration': 5.004}, {'end': 4755.11, 'text': "Okay So summary, um, basically what's on the board here.", 'start': 4752.028, 'duration': 3.082}, {'end': 4764.894, 'text': "If you're doing classification, you take the score which comes from w dot phi of x, and you drive it into the sign,", 'start': 4756.405, 'duration': 8.489}], 'summary': 'Mastering loss minimization allows you to handle various cases of regression and classification.', 'duration': 25.235, 'max_score': 4739.659, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4739659.jpg'}, {'end': 4817.177, 'src': 'embed', 'start': 4779.805, 'weight': 5, 'content': [{'end': 4786.368, 'text': "And here's- we only talked about five loss functions, but there's many others, um, especially for a kind of structure prediction or ranking problems.", 'start': 4779.805, 'duration': 6.563}, {'end': 4787.809, 'text': "There's all sorts of different loss functions.", 'start': 4786.408, 'duration': 1.401}, {'end': 4791.51, 'text': "But they're kind of based on these simple ideas of.", 'start': 4788.329, 'duration': 3.181}, {'end': 4799.732, 'text': "you know, you have a hinge that upper bounds to 0, 1 if you're doing classification and um, some sort of square like error, for you know regression.", 'start': 4791.51, 'duration': 8.222}, {'end': 4806.453, 'text': "And then, once you have your loss functions provided it's not 0, 1, you can optimize it using um SGD,", 'start': 4801.072, 'duration': 5.381}, {'end': 4809.314, 'text': 'which turns out to be a lot faster than you know gradient descent.', 'start': 4806.453, 'duration': 2.861}, {'end': 4817.177, 'text': "Okay So next time we're gonna talk about, uh, phi of x, which we've kind of left as, you know, someone just hands it to you.", 'start': 4810.134, 'duration': 7.043}], 'summary': 'Discussed five loss functions and optimization using sgd for faster results.', 'duration': 37.372, 'max_score': 4779.805, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4779805.jpg'}], 'start': 4210.648, 'title': 'Stochastic gradient descent and loss functions', 'summary': 'Discusses the efficiency of stochastic gradient descent compared to gradient descent, introduces the hinge loss function and its gradient computation for classification, discusses the role of margin in classification, residuals in regression, and the general framework of loss minimization, highlighting various loss functions and the optimization process using sgd.', 'chapters': [{'end': 4695.218, 'start': 4210.648, 'title': 'Stochastic gradient descent for classification', 'summary': 'Discusses the speed and efficiency of stochastic gradient descent compared to gradient descent, introducing the hinge loss function and its gradient computation for classification, and the significance of the margin in the context of support vector machines.', 'duration': 484.57, 'highlights': ['The chapter discusses the speed and efficiency of stochastic gradient descent compared to gradient descent Stochastic gradient descent is shown to be significantly faster than gradient descent, converging to results much quicker, especially in the presence of noise levels.', 'Introducing the hinge loss function and its gradient computation for classification The hinge loss function is introduced to address the non-differentiability and inefficiency of the zero-one loss function for stochastic gradient descent in classification, with a focus on its properties and the computation of its gradient.', 'The significance of the margin in the context of support vector machines The significance of the margin being one is discussed, noting its somewhat arbitrary nature and its association with regularization on the weights in support vector machines.']}, {'end': 4826.46, 'start': 4696.438, 'title': 'Loss functions in classification and regression', 'summary': 'Discusses the role of margin in classification, residuals in regression, and the general framework of loss minimization, highlighting various loss functions and the optimization process using sgd.', 'duration': 130.022, 'highlights': ['The importance of margin in classification is emphasized as it indicates the confidence level of predictions.', 'The discussion on loss minimization framework highlights logistic regression as a special case and its relationship with other well-known methods such as least squares.', 'The distinction between margin in classification and residuals in regression is explained as key components in assessing performance.', 'The mention of various loss functions beyond the five discussed, particularly for structure prediction or ranking problems, signifies the wide range of options based on fundamental concepts.', 'The advantage of optimizing loss functions using SGD over gradient descent is mentioned, emphasizing its efficiency in training.']}], 'duration': 615.812, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zrT2qETJilw/pics/zrT2qETJilw4210648.jpg', 'highlights': ['Stochastic gradient descent is significantly faster than gradient descent, especially in the presence of noise levels.', 'The hinge loss function is introduced to address the non-differentiability and inefficiency of the zero-one loss function for stochastic gradient descent in classification.', 'The significance of the margin being one is discussed, noting its somewhat arbitrary nature and its association with regularization on the weights in support vector machines.', 'The importance of margin in classification is emphasized as it indicates the confidence level of predictions.', 'The discussion on loss minimization framework highlights logistic regression as a special case and its relationship with other well-known methods such as least squares.', 'The mention of various loss functions beyond the five discussed signifies the wide range of options based on fundamental concepts.', 'The advantage of optimizing loss functions using SGD over gradient descent is mentioned, emphasizing its efficiency in training.']}], 'highlights': ['The chapter emphasizes the powerful and general framework of loss minimization in transcending linear classifiers and regression setups.', 'The process of deriving the loss function for binary classification is explained, utilizing the notation of correct and predicted labels, as well as the calculation of scores for specific examples, offering a practical illustration of applying loss functions in assessing classifier performance.', "The weight of a feature in regression models specifies both the direction (positive or negative) of the feature's influence on the prediction and the strength of that influence, with an analogy to a little person voting with a positive or negative weight.", 'The gradient descent method involves computing the gradient that points in the direction of the most dramatic increase in the function, and then moving in the opposite direction to minimize the loss function.', 'The chapter introduces different types of models, including reflex models, state-based models, variable-based models, and logic models.']}