title

Lecture 5 - GDA & Naive Bayes | Stanford CS229: Machine Learning Andrew Ng (Autumn 2018)

description

For more information about Stanfordâ€™s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3GfTLkU
Andrew Ng
Adjunct Professor of Computer Science
https://www.andrewng.org/
To follow along with the course schedule and syllabus, visit:
http://cs229.stanford.edu/syllabus-autumn2018.html

detail

{'title': 'Lecture 5 - GDA & Naive Bayes | Stanford CS229: Machine Learning Andrew Ng (Autumn 2018)', 'heatmap': [{'end': 302.182, 'start': 236.636, 'weight': 0.714}, {'end': 1588.736, 'start': 1416.072, 'weight': 0.739}, {'end': 1661.012, 'start': 1603.434, 'weight': 0.823}, {'end': 1993.013, 'start': 1940.644, 'weight': 0.791}, {'end': 2319.387, 'start': 2266.964, 'weight': 0.703}, {'end': 3550.326, 'start': 3497.141, 'weight': 0.752}, {'end': 4221.145, 'start': 4165.221, 'weight': 0.974}, {'end': 4552.251, 'start': 4435.698, 'weight': 0.806}], 'summary': 'The lecture covers topics such as gaussian discriminant analysis (gda), naive bayes, gaussian density, maximum likelihood estimation, and algorithm comparisons, discussing their application in machine learning and their performance with small datasets, emphasizing the efficiency and potential issues of the algorithms.', 'chapters': [{'end': 62.24, 'segs': [{'end': 33.635, 'src': 'embed', 'start': 4.5, 'weight': 2, 'content': [{'end': 5.56, 'text': 'Hey, morning everyone.', 'start': 4.5, 'duration': 1.06}, {'end': 6.441, 'text': 'Welcome back.', 'start': 5.921, 'duration': 0.52}, {'end': 16.145, 'text': 'Um, so last week you heard about, uh, logistic regression and, um, uh, generalized linear models.', 'start': 7.121, 'duration': 9.024}, {'end': 22.768, 'text': "And it turns out all of the learning algorithms we've been learning about so far are called discriminative learning algorithms,", 'start': 16.826, 'duration': 5.942}, {'end': 24.569, 'text': 'which is one big bucket of learning algorithms.', 'start': 22.768, 'duration': 1.801}, {'end': 30.412, 'text': "And today, um, what I'd like to do is share with you how generative learning algorithms work.", 'start': 24.849, 'duration': 5.563}, {'end': 33.635, 'text': 'Um, in particular, you learn about Gaussian discriminant analysis.', 'start': 30.832, 'duration': 2.803}], 'summary': 'Introduction to discriminative and generative learning algorithms, focusing on gaussian discriminant analysis.', 'duration': 29.135, 'max_score': 4.5, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS04500.jpg'}, {'end': 69.025, 'src': 'embed', 'start': 40.922, 'weight': 0, 'content': [{'end': 47.968, 'text': 'GDA is actually a um simpler and maybe more computationally efficient algorithm to implement uh in some cases.', 'start': 40.922, 'duration': 7.046}, {'end': 54.314, 'text': 'So, um, and it sometimes works better if you have, uh, very small datasets, sometimes with some caveats.', 'start': 48.108, 'duration': 6.206}, {'end': 60.338, 'text': "Um and we'll talk about comparison between generative learning algorithms, which is a new concept of algorithms you hear about today,", 'start': 54.954, 'duration': 5.384}, {'end': 62.24, 'text': 'versus discriminative learning algorithms.', 'start': 60.338, 'duration': 1.902}, {'end': 69.025, 'text': "And then we'll talk about Naive Bayes and how you can use that to, uh, build a span filter, for example.", 'start': 62.8, 'duration': 6.225}], 'summary': 'Gda is a simpler, more efficient algorithm, suited for small datasets, compared to generative learning algorithms.', 'duration': 28.103, 'max_score': 40.922, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS040922.jpg'}], 'start': 4.5, 'title': 'Introduction to generative learning algorithms', 'summary': 'Introduces gaussian discriminant analysis (gda) as a computationally efficient algorithm for classification, particularly effective with small datasets, and compares generative and discriminative learning algorithms.', 'chapters': [{'end': 62.24, 'start': 4.5, 'title': 'Introduction to generative learning algorithms', 'summary': 'Introduces generative learning algorithms, focusing on gaussian discriminant analysis (gda) as a simpler and more computationally efficient algorithm for classification compared to logistic regression, particularly effective with small datasets, and discusses the comparison between generative and discriminative learning algorithms.', 'duration': 57.74, 'highlights': ['Gaussian discriminant analysis (GDA) is a simpler and more computationally efficient algorithm for classification compared to logistic regression, especially effective with small datasets, sometimes with some caveats.', 'Generative learning algorithms, such as GDA, are introduced as a new concept, and a comparison is made with discriminative learning algorithms.', 'The learning algorithms covered so far, including logistic regression and generalized linear models, fall under the category of discriminative learning algorithms.']}], 'duration': 57.74, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS04500.jpg', 'highlights': ['Gaussian discriminant analysis (GDA) is a simpler and more computationally efficient algorithm for classification compared to logistic regression, especially effective with small datasets, sometimes with some caveats.', 'Generative learning algorithms, such as GDA, are introduced as a new concept, and a comparison is made with discriminative learning algorithms.', 'The learning algorithms covered so far, including logistic regression and generalized linear models, fall under the category of discriminative learning algorithms.']}, {'end': 717.508, 'segs': [{'end': 107.721, 'src': 'embed', 'start': 84.619, 'weight': 1, 'content': [{'end': 94.672, 'text': 'then what a discriminative learning algorithm like logistic regression would do is use gradient descent to search for a line that separates the positive and negative examples right?', 'start': 84.619, 'duration': 10.053}, {'end': 101.617, 'text': 'So if you round it and randomly initialized parameters, maybe starts with some uh decision boundary like that.', 'start': 94.732, 'duration': 6.885}, {'end': 107.721, 'text': 'And over the course of gradient descent, you know the line migrates or evolves until you get maybe a line like that.', 'start': 101.757, 'duration': 5.964}], 'summary': 'Logistic regression uses gradient descent to find a separating line for positive and negative examples.', 'duration': 23.102, 'max_score': 84.619, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS084619.jpg'}, {'end': 169.429, 'src': 'embed', 'start': 141.531, 'weight': 0, 'content': [{'end': 147.856, 'text': 'This is called a generative learning algorithm, which is Rather than looking at two classes and trying to find the separation.', 'start': 141.531, 'duration': 6.325}, {'end': 150.64, 'text': 'instead, the algorithm is going to look at the classes one at a time.', 'start': 147.856, 'duration': 2.784}, {'end': 159.331, 'text': "First, we'll look at all of the malignant tumors, right, in the cancer example, and try to build a model for what malignant tumors looks like.", 'start': 151.241, 'duration': 8.09}, {'end': 169.429, 'text': 'So you might say, oh, it looks like all the malignant tumors, um, roughly, all the malignant tumors roughly live in that ellipse.', 'start': 159.351, 'duration': 10.078}], 'summary': 'Generative learning algorithm builds model for malignant tumors.', 'duration': 27.898, 'max_score': 141.531, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0141531.jpg'}, {'end': 227.714, 'src': 'embed', 'start': 204.094, 'weight': 2, 'content': [{'end': 214.651, 'text': 'So, um, rather than uh, looking at both classes simultaneously and searching for a way to separate them, a generative learning algorithm, uh,', 'start': 204.094, 'duration': 10.557}, {'end': 221.253, 'text': 'instead builds a model of what each of the classes looks like, kind of almost in isolation, you know, with some details.', 'start': 214.651, 'duration': 6.602}, {'end': 222.113, 'text': "we'll learn about later.", 'start': 221.253, 'duration': 0.86}, {'end': 227.714, 'text': 'And then, at test time, uh, it evaluates a new example against the benign model,', 'start': 222.613, 'duration': 5.101}], 'summary': 'Generative learning algorithm builds isolated models for each class.', 'duration': 23.62, 'max_score': 204.094, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0204094.jpg'}, {'end': 302.182, 'src': 'heatmap', 'start': 236.636, 'weight': 0.714, 'content': [{'end': 250.059, 'text': 'Um, a discriminative learning algorithm learns P of y, given x right?', 'start': 236.636, 'duration': 13.423}, {'end': 268.73, 'text': 'Um or uh or- or it learns um right, some mapping from X to Y directly, you know the learn- or all you can learn.', 'start': 250.799, 'duration': 17.931}, {'end': 271.191, 'text': 'I think, uh, Anand briefly talked about the perceptron algorithm.', 'start': 268.75, 'duration': 2.441}, {'end': 272.712, 'text': 'He talked about support vector machines later.', 'start': 271.211, 'duration': 1.501}, {'end': 276.714, 'text': 'Um, learns the function mapping from X to the labels directly.', 'start': 273.452, 'duration': 3.262}, {'end': 280.976, 'text': "So that's a discriminative learning algorithm where you're trying to discriminate between positive and negative classes.", 'start': 276.754, 'duration': 4.222}, {'end': 302.182, 'text': 'In contrast, a generative learning algorithm, it learns, P of, um, X given Y.', 'start': 282.697, 'duration': 19.485}], 'summary': 'Discriminative learning algorithm learns p of y, given x. anand discussed perceptron and support vector machines.', 'duration': 65.546, 'max_score': 236.636, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0236636.jpg'}, {'end': 302.182, 'src': 'embed', 'start': 271.211, 'weight': 3, 'content': [{'end': 272.712, 'text': 'He talked about support vector machines later.', 'start': 271.211, 'duration': 1.501}, {'end': 276.714, 'text': 'Um, learns the function mapping from X to the labels directly.', 'start': 273.452, 'duration': 3.262}, {'end': 280.976, 'text': "So that's a discriminative learning algorithm where you're trying to discriminate between positive and negative classes.", 'start': 276.754, 'duration': 4.222}, {'end': 302.182, 'text': 'In contrast, a generative learning algorithm, it learns, P of, um, X given Y.', 'start': 282.697, 'duration': 19.485}], 'summary': 'Discussed support vector machines for discriminative learning.', 'duration': 30.971, 'max_score': 271.211, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0271211.jpg'}, {'end': 400.373, 'src': 'embed', 'start': 347.148, 'weight': 5, 'content': [{'end': 348.509, 'text': 'Right?, Before you see any features.', 'start': 347.148, 'duration': 1.361}, {'end': 362.687, 'text': "Okay?. And so, using Bayes' rule, if you can build a model for P of X given Y and for P of Y, um,", 'start': 349.03, 'duration': 13.657}, {'end': 371.795, 'text': "if you know if you can calculate numbers for both of these quantities, then, using Bayes' rule, when you have a new test example with features X,", 'start': 362.687, 'duration': 9.108}, {'end': 385.746, 'text': 'you can then calculate the chance of Y being equal to 1 as this right.', 'start': 371.795, 'duration': 13.951}, {'end': 400.373, 'text': 'uh, where P of x by the-, okay?', 'start': 385.746, 'duration': 14.627}], 'summary': "Using bayes' rule, you can calculate the chance of y being equal to 1 based on the model for p(x|y) and p(y).", 'duration': 53.225, 'max_score': 347.148, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0347148.jpg'}, {'end': 565.851, 'src': 'embed', 'start': 539.614, 'weight': 7, 'content': [{'end': 553.585, 'text': "And the key assumption in Gaussian discriminant analysis is we're going to assume that P of X, given Y, is distributed Gaussian right?", 'start': 539.614, 'duration': 13.971}, {'end': 556.927, 'text': 'In other words, condition on the tumor as being malignant.', 'start': 553.645, 'duration': 3.282}, {'end': 559.108, 'text': 'the distribution of the features is Gaussian.', 'start': 556.927, 'duration': 2.181}, {'end': 565.851, 'text': 'You know, the feature is like the size of the- size of the tumor, the- the cell adhesion, whatever features you use to measure a tumor.', 'start': 559.588, 'duration': 6.263}], 'summary': 'Gaussian discriminant analysis assumes gaussian distribution of features in tumor classification.', 'duration': 26.237, 'max_score': 539.614, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0539614.jpg'}, {'end': 645.527, 'src': 'embed', 'start': 608.119, 'weight': 8, 'content': [{'end': 617.241, 'text': 'So, um, if Z, the strategic Gaussian with some mean vector Mu and some covariance matrix Sigma.', 'start': 608.119, 'duration': 9.122}, {'end': 629.464, 'text': 'Um, so if Z is, uh, in Rn, then Mu would be Rn as well, and Sigma the covariance matrix will be n by n.', 'start': 618.081, 'duration': 11.383}, {'end': 633.005, 'text': 'So Z is two-dimensional, Mu is two-dimensional, and Sigma is two-dimensional.', 'start': 629.464, 'duration': 3.541}, {'end': 645.527, 'text': 'And the expected value of Z is equal to, um, the mean, and the, um, covariance of Z.', 'start': 633.825, 'duration': 11.702}], 'summary': 'In a two-dimensional space, z with mean vector mu and covariance matrix sigma has two-dimensional properties.', 'duration': 37.408, 'max_score': 608.119, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0608119.jpg'}], 'start': 62.8, 'title': 'Naive bayes and generative learning', 'summary': 'Explores the differences between discriminative and generative learning algorithms, using logistic regression as an example. it discusses generative learning algorithms, p(x|y), p(y), and gaussian discriminant analysis in rn space.', 'chapters': [{'end': 302.182, 'start': 62.8, 'title': 'Naive bayes and generative vs. discriminative learning', 'summary': 'Discusses the differences between discriminative and generative learning algorithms using logistic regression as an example, highlighting how generative learning algorithms build a model for each class and evaluate new examples based on similarity, contrasting with discriminative algorithms that search for a decision boundary to separate classes.', 'duration': 239.382, 'highlights': ['Generative learning algorithms build a model for each class separately, such as creating models for malignant and benign tumors in medical diagnosis.', 'Logistic regression is an example of a discriminative learning algorithm that searches for a decision boundary to separate positive and negative examples using gradient descent.', 'Generative learning algorithms evaluate new examples by comparing them to the models of each class to determine the closest match.', 'Discriminative learning algorithms learn the function mapping from X to the labels directly, aiming to discriminate between positive and negative classes.', 'Generative learning algorithms learn the probability of X given Y, focusing on modeling the conditional distribution of features given the class label.']}, {'end': 489.348, 'start': 302.182, 'title': 'Generative learning algorithms', 'summary': "Discusses generative learning algorithms, explaining the concept of p(x|y), p(y), and using bayes' rule to calculate the chance of y being equal to 1, with examples for continuous and discrete features.", 'duration': 187.166, 'highlights': ["The chapter explains the concept of P(x|y) and P(y), which are used to calculate the chance of y being equal to 1 using Bayes' rule.", 'It mentions two examples of generative learning algorithms: one for continuous value features like tumor classification and one for discrete features like building an email spam filter.', 'The algorithms can be used for tasks such as tumor classification, email spam filtering, or sentiment analysis on social media.', 'The framework for generative learning algorithms involves learning P(x|y) and P(y) to calculate the chance that the tumor is malignant for a new patient with features x.']}, {'end': 717.508, 'start': 490.954, 'title': 'Gaussian distributed analysis', 'summary': 'Discusses gaussian discriminant analysis, assuming continuous features x, and explains the multivariate gaussian distribution with mean vector mu and covariance matrix sigma in rn space.', 'duration': 226.554, 'highlights': ['Gaussian discriminant analysis assumes P of X, given Y, is distributed Gaussian, and discusses the multivariate Gaussian distribution with mean vector Mu and covariance matrix Sigma in Rn space.', 'Explains the multivariate Gaussian distribution with mean vector Mu and covariance matrix Sigma in Rn space.', 'Discusses the generalization of the familiar bell-shaped curve over a one-dimensional random variable to multiple random variables at the same time.']}], 'duration': 654.708, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS062800.jpg', 'highlights': ['Generative learning algorithms build separate models for each class, e.g., malignant and benign tumors.', 'Logistic regression is a discriminative learning algorithm that uses gradient descent to find a decision boundary.', 'Generative learning algorithms evaluate new examples by comparing them to class models.', 'Discriminative learning algorithms learn the function mapping from X to labels directly.', 'Generative learning algorithms learn the probability of X given Y, focusing on modeling the conditional distribution.', "The chapter explains P(x|y) and P(y) used to calculate the chance of y being equal to 1 using Bayes' rule.", 'Generative learning algorithms can be used for tasks like tumor classification and email spam filtering.', 'Gaussian discriminant analysis assumes P of X, given Y, is distributed Gaussian in Rn space.', 'The chapter discusses the multivariate Gaussian distribution with mean vector Mu and covariance matrix Sigma in Rn space.']}, {'end': 1045.244, 'segs': [{'end': 789.007, 'src': 'embed', 'start': 717.608, 'weight': 2, 'content': [{'end': 720.09, 'text': 'But when you use it enough, you, you, you end up memorizing it.', 'start': 717.608, 'duration': 2.482}, {'end': 728.221, 'text': 'Uh, but let me show you some pictures of what this looks like since I think that would, that might be more useful.', 'start': 721.211, 'duration': 7.01}, {'end': 733.163, 'text': 'So the multivariate Gaussian density has two parameters, mu and sigma.', 'start': 728.881, 'duration': 4.282}, {'end': 742.866, 'text': 'They control the mean and the variance of this density, okay? So this is a picture of the Gaussian density.', 'start': 733.563, 'duration': 9.303}, {'end': 745.727, 'text': 'Um, this is a two-dimensional Gaussian bump.', 'start': 743.566, 'duration': 2.161}, {'end': 750.468, 'text': "And for now, I've set the mean parameter to 0.", 'start': 746.627, 'duration': 3.841}, {'end': 752.129, 'text': 'So mu is the two-dimensional parameter.', 'start': 750.468, 'duration': 1.661}, {'end': 756.25, 'text': 'This is a 0, 0, which is why this Gaussian bump is, uh, centered.', 'start': 752.229, 'duration': 4.021}, {'end': 768.397, 'text': 'at 0, um, and the covariance matrix Sigma is the identity, um, is the identity matrix.', 'start': 757.35, 'duration': 11.047}, {'end': 772.74, 'text': 'So, uh, so you know, so- so you have this standard.', 'start': 768.657, 'duration': 4.083}, {'end': 777.883, 'text': 'this is also called the standard Gaussian distribution, which means- means 0, and covariance equals to the identity.', 'start': 772.74, 'duration': 5.143}, {'end': 784.945, 'text': "Now, I'm gonna take the covariance matrix and shrink it, right? So take the covariance matrix and multiply it by a number less than 1.", 'start': 778.641, 'duration': 6.304}, {'end': 789.007, 'text': 'That should shrink the variance, reduce the variability in distributions.', 'start': 784.945, 'duration': 4.062}], 'summary': 'Multivariate gaussian density with parameters mu and sigma controls mean and variance. shrinking covariance matrix reduces variability.', 'duration': 71.399, 'max_score': 717.608, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0717608.jpg'}, {'end': 834.738, 'src': 'embed', 'start': 810.66, 'weight': 1, 'content': [{'end': 817.011, 'text': 'Um, but it also makes it taller as a result because, you know, the area under the curve must integrate to 1.', 'start': 810.66, 'duration': 6.351}, {'end': 819.172, 'text': "Now let's make it fatter.", 'start': 817.011, 'duration': 2.161}, {'end': 822.353, 'text': "uh, let's make the covariance two times the identity.", 'start': 819.172, 'duration': 3.181}, {'end': 831.097, 'text': 'then you end up with a wider distribution, where the values of um I guess the axis here this would be the Z1 and the Z2 axis,', 'start': 822.353, 'duration': 8.744}, {'end': 834.738, 'text': 'the two dimensions of the Gaussian density right increases the variance of the density.', 'start': 831.097, 'duration': 3.641}], 'summary': 'Increasing covariance by 2 widens gaussian distribution, increasing variance.', 'duration': 24.078, 'max_score': 810.66, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0810660.jpg'}, {'end': 939.643, 'src': 'embed', 'start': 913.088, 'weight': 0, 'content': [{'end': 921.235, 'text': 'And if you increase the off-diagonal excuse me, then it looks like that and increase it further to 0.8, 0.8, it looks like that, okay?', 'start': 913.088, 'duration': 8.147}, {'end': 931.599, 'text': 'Uh, where now most of the probability, mass-, most probability density function places value on um, Z1 and Z2 being positively correlated, okay?', 'start': 921.595, 'duration': 10.004}, {'end': 939.643, 'text': "Um, next let's look at uh, what happens if we set the off diagonal elements to negative values right?", 'start': 932.279, 'duration': 7.364}], 'summary': 'Increasing off-diagonal elements shows positive correlation, then negative values are observed.', 'duration': 26.555, 'max_score': 913.088, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0913088.jpg'}], 'start': 717.608, 'title': 'Gaussian density and distribution', 'summary': 'Delves into the parameters mu and sigma, demonstrating their impact on the two-dimensional gaussian density and explains the effects of covariance matrix modifications on variance, density function, correlation, and principal axes.', 'chapters': [{'end': 772.74, 'start': 717.608, 'title': 'Multivariate gaussian density', 'summary': 'Explains the parameters mu and sigma that control the mean and variance of the two-dimensional gaussian density, with mu set to 0 and the covariance matrix sigma as the identity matrix.', 'duration': 55.132, 'highlights': ['The parameters mu and sigma control the mean and variance of the Gaussian density, with mu set to 0.', 'The covariance matrix Sigma is the identity matrix, leading to a standard two-dimensional Gaussian bump centered at 0.']}, {'end': 1045.244, 'start': 772.74, 'title': 'Gaussian distribution and covariance', 'summary': 'Explains how modifying the covariance matrix affects the gaussian distribution, demonstrating the impact on variance, density function, correlation, and principal axes.', 'duration': 272.504, 'highlights': ['Modifying the covariance matrix by multiplying it with a number less than 1 shrinks the variance and reduces the spread of the Gaussian density.', 'Increasing the covariance matrix to two times the identity results in a wider distribution and increases the variance of the density.', 'Increasing the off-diagonal entries in the covariance matrix leads to a change in the shape of the Gaussian density, indicating positive correlation between Z1 and Z2.']}], 'duration': 327.636, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS0717608.jpg', 'highlights': ['Increasing the off-diagonal entries in the covariance matrix leads to a change in the shape of the Gaussian density, indicating positive correlation between Z1 and Z2.', 'Increasing the covariance matrix to two times the identity results in a wider distribution and increases the variance of the density.', 'Modifying the covariance matrix by multiplying it with a number less than 1 shrinks the variance and reduces the spread of the Gaussian density.', 'The covariance matrix Sigma is the identity matrix, leading to a standard two-dimensional Gaussian bump centered at 0.', 'The parameters mu and sigma control the mean and variance of the Gaussian density, with mu set to 0.']}, {'end': 1707.35, 'segs': [{'end': 1166.703, 'src': 'embed', 'start': 1064.737, 'weight': 2, 'content': [{'end': 1069.9, 'text': 'And so by varying the value of mu, you could also shift the center of the Gaussian density around.', 'start': 1064.737, 'duration': 5.163}, {'end': 1080.479, 'text': 'Okay, So hope this gives you a sense of um as you vary the parameters, the mean and the covariance matrix of the 2D Gaussian density, um,', 'start': 1070.592, 'duration': 9.887}, {'end': 1085.902, 'text': 'the source of probability- probability density functions you can get as a result of changing Mu and Sigma.', 'start': 1080.479, 'duration': 5.423}, {'end': 1093.828, 'text': 'Okay Um, any other questions about this? Cool.', 'start': 1086.543, 'duration': 7.285}, {'end': 1131.128, 'text': 'So here is the GDA.', 'start': 1104.199, 'duration': 26.929}, {'end': 1136.647, 'text': 'right, model.', 'start': 1135.947, 'duration': 0.7}, {'end': 1142.131, 'text': "Um, and, and, uh, let's see.", 'start': 1137.008, 'duration': 5.123}, {'end': 1153.151, 'text': 'So, um, Remember for GDA, we need to model P of X given Y, right, instead of P of Y given X.', 'start': 1143.672, 'duration': 9.479}, {'end': 1158.156, 'text': "So I'm gonna write this separately in two separate equations, P of X given Y equals 0.", 'start': 1153.151, 'duration': 5.005}, {'end': 1166.703, 'text': "So what's the chance, what's the, uh, probability density of the features if it's a benign tumor? Um, I'm gonna assume it's Gaussian.", 'start': 1158.156, 'duration': 8.547}], 'summary': 'Varying mu shifts gaussian density center. gda models p(x|y), assumes gaussian features.', 'duration': 101.966, 'max_score': 1064.737, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01064737.jpg'}, {'end': 1597.411, 'src': 'heatmap', 'start': 1416.072, 'weight': 0, 'content': [{'end': 1428.581, 'text': 'let me define the likelihood of the parameters to be equal to the product.', 'start': 1416.072, 'duration': 12.509}, {'end': 1433.804, 'text': 'from i equals 1 through m, of p, of x, i, y i.', 'start': 1428.581, 'duration': 5.223}, {'end': 1438.668, 'text': 'you know, parameterized by um, the parameters.', 'start': 1433.804, 'duration': 4.864}, {'end': 1463.293, 'text': "Um and I'm- I'm just gonna drop the parameters here right to simplify the notation a little bit, okay?", 'start': 1447.987, 'duration': 15.306}, {'end': 1472.437, 'text': 'And the big difference between um, a generative learning algorithm like this, compared to a discriminative learning algorithm,', 'start': 1463.313, 'duration': 9.124}, {'end': 1482.138, 'text': 'is that the cost function you maximize is this joint likelihood, which is P, of x, comma y.', 'start': 1472.437, 'duration': 9.701}, {'end': 1490.562, 'text': 'Whereas for a discriminative learning algorithm, we were maximizing, um, this other thing.', 'start': 1482.138, 'duration': 8.424}, {'end': 1504.887, 'text': 'uh, which is sometimes also called the conditional likelihood.', 'start': 1502.446, 'duration': 2.441}, {'end': 1518.732, 'text': 'Okay, So the big difference between the- these two cost functions is that for logistic regression or linear regression or generalized linear models.', 'start': 1509.849, 'duration': 8.883}, {'end': 1524.834, 'text': 'um, you are trying to choose parameters data that maximize P of y given x.', 'start': 1518.732, 'duration': 6.102}, {'end': 1533.334, 'text': "But for generative learning algorithms, we're gonna try to choose parameters that maximize P of x and y or P of x comma y, right? Okay.", 'start': 1524.834, 'duration': 8.5}, {'end': 1588.736, 'text': 'So So if you use, um, maximum likelihood estimation, um, so you choose the parameters phi, mu 0, mu 1, and sigma that maximize the log likelihood.', 'start': 1536.339, 'duration': 52.397}, {'end': 1597.411, 'text': 'right, where this you define as, you know, log of the likelihood that we defined out there.', 'start': 1591.448, 'duration': 5.963}], 'summary': 'Generative learning maximizes joint likelihood, discriminative learning maximizes conditional likelihood.', 'duration': 72.577, 'max_score': 1416.072, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01416072.jpg'}, {'end': 1707.35, 'src': 'heatmap', 'start': 1603.434, 'weight': 1, 'content': [{'end': 1609.137, 'text': 'But so the way you maximize this is um, look at that formula for the likelihood.', 'start': 1603.434, 'duration': 5.703}, {'end': 1612.958, 'text': 'take logs, take derivatives of this thing, set the derivatives equal to 0,', 'start': 1609.137, 'duration': 3.821}, {'end': 1615.819, 'text': 'and then solve for the values of the parameters that maximize this whole thing.', 'start': 1612.958, 'duration': 2.861}, {'end': 1626.361, 'text': "And I'll- I'll just tell you the answers you're supposed to get uh, but- but you still have to do the derivation right?", 'start': 1616.459, 'duration': 9.902}, {'end': 1632.983, 'text': 'Um, the value of Phi that maximizes this is, you know, not that surprisingly.', 'start': 1626.962, 'duration': 6.021}, {'end': 1638.956, 'text': 'So- so, Phi, is the estimate of uh probability of y being equal to 1, right?', 'start': 1634.023, 'duration': 4.933}, {'end': 1645.481, 'text': "So what's the chance, when the next patient walks into your uh doctor's office, that they have a a malignant tumor?", 'start': 1639.036, 'duration': 6.445}, {'end': 1651.345, 'text': "And so the mass molecular estimate for phi is um, it's just of all of your training examples.", 'start': 1646.101, 'duration': 5.244}, {'end': 1654.227, 'text': "what's the fraction with label y equals 1, right?", 'start': 1651.345, 'duration': 2.882}, {'end': 1661.012, 'text': 'So the mass molecular of the uh bias of the coin toss is just well, count of the fraction of heads you got, okay?', 'start': 1654.287, 'duration': 6.725}, {'end': 1661.872, 'text': 'So this is it.', 'start': 1661.072, 'duration': 0.8}, {'end': 1675.448, 'text': 'Um, and one other way to write this is, um, sum from i equals 1 through m, indicate, uh, okay.', 'start': 1662.433, 'duration': 13.015}, {'end': 1684.538, 'text': "Right Um, let's see.", 'start': 1682.155, 'duration': 2.383}, {'end': 1687.481, 'text': 'So actually, software indicates a notation on Wednesday.', 'start': 1684.718, 'duration': 2.763}, {'end': 1692.68, 'text': 'Did you? Uh, did you talk- did you talk about indicator notation Wednesday? No.', 'start': 1687.501, 'duration': 5.179}, {'end': 1698.083, 'text': 'Okay, Oh so, um, uh, this notation is an indicator function.', 'start': 1692.78, 'duration': 5.303}, {'end': 1702.446, 'text': 'uh, where um indicator y i equals 1, is uh.', 'start': 1698.083, 'duration': 4.363}, {'end': 1705.909, 'text': 'uh returns 0 or 1, depending on whether the thing inside is true, right?', 'start': 1702.446, 'duration': 3.463}, {'end': 1707.35, 'text': "So there's an indicator notation.", 'start': 1705.929, 'duration': 1.421}], 'summary': 'Maximize likelihood by taking derivatives and solving for parameters to estimate probability of y being 1.', 'duration': 61.249, 'max_score': 1603.434, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01603434.jpg'}], 'start': 1045.244, 'title': 'Gaussian density analysis model and generative learning algorithms', 'summary': 'Explains how the 2d gaussian density can be shifted by varying the parameters mu and covariance matrix, introduces the gda model for modeling p of x given y and p of y, and covers the notation for a bernoulli random variable, the process of fitting parameters for p of x and y, and the use of maximum likelihood estimation to find the estimate of probability of y being equal to 1.', 'chapters': [{'end': 1268.877, 'start': 1045.244, 'title': 'Gaussian density analysis model', 'summary': 'Explains how the 2d gaussian density can be shifted by varying the parameters mu and covariance matrix, and introduces the gda model for modeling p of x given y and p of y.', 'duration': 223.633, 'highlights': ['The 2D Gaussian density can be shifted by varying the parameters mu and covariance matrix.', 'Introduction of the GDA model for modeling P of X given Y and P of Y.']}, {'end': 1707.35, 'start': 1268.877, 'title': 'Generative learning algorithms', 'summary': 'Explains the notation for a bernoulli random variable, the process of fitting parameters for p of x and y, and the use of maximum likelihood estimation to find the estimate of probability of y being equal to 1.', 'duration': 438.473, 'highlights': ['The estimate of Phi is the probability of y being equal to 1, and the mass molecular estimate for phi is the fraction of training examples with label y equals 1.', 'Indicator notation is used to indicate whether the condition is true or false, returning 0 or 1 accordingly.', 'The cost function for generative learning algorithms is the joint likelihood, which is P of x and y, and the process involves maximizing the log likelihood to find the values of the parameters.']}], 'duration': 662.106, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01045243.jpg', 'highlights': ['The process of fitting parameters for P of X and Y involves maximizing the log likelihood to find the values of the parameters', 'The estimate of Phi is the probability of Y being equal to 1, and the mass molecular estimate for Phi is the fraction of training examples with label Y equals 1', 'The 2D Gaussian density can be shifted by varying the parameters mu and covariance matrix', 'Introduction of the GDA model for modeling P of X given Y and P of Y', 'Indicator notation is used to indicate whether the condition is true or false, returning 0 or 1 accordingly']}, {'end': 2472.394, 'segs': [{'end': 1775.361, 'src': 'embed', 'start': 1750.502, 'weight': 4, 'content': [{'end': 1755.965, 'text': 'what do you think is the maximum likelihood estimate of the mean of all of the uh features for the benign tumors?', 'start': 1750.502, 'duration': 5.463}, {'end': 1760.327, 'text': 'right?. Well, what you do is you take all the benign tumors in your training set and just take the average.', 'start': 1755.965, 'duration': 4.362}, {'end': 1761.668, 'text': 'That seems like a very reasonable way.', 'start': 1760.427, 'duration': 1.241}, {'end': 1763.889, 'text': 'Just look at- look at your training set.', 'start': 1762.088, 'duration': 1.801}, {'end': 1764.83, 'text': 'look at all of the um.', 'start': 1763.889, 'duration': 0.941}, {'end': 1771.019, 'text': "look at all of the benign tumors, all the O's, I guess, and then just take the mean of these.", 'start': 1766.297, 'duration': 4.722}, {'end': 1775.361, 'text': 'and that you know seems like a pretty reasonable way to estimate mu 0, right?', 'start': 1771.019, 'duration': 4.342}], 'summary': 'Maximum likelihood estimate of mean for benign tumors is found by averaging all features in the training set.', 'duration': 24.859, 'max_score': 1750.502, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01750502.jpg'}, {'end': 1915.776, 'src': 'embed', 'start': 1882.189, 'weight': 3, 'content': [{'end': 1903.551, 'text': "Okay? Um, and then, right, maximum likelihood for mu 1, no surprises, is sort of kind of what you'd expect.", 'start': 1882.189, 'duration': 21.362}, {'end': 1909.094, 'text': 'Sum up all of the positive examples and divide by the total number of positive examples and get their mean.', 'start': 1904.212, 'duration': 4.882}, {'end': 1912.915, 'text': "So that's maximum likelihood for mu 1.", 'start': 1909.134, 'duration': 3.781}, {'end': 1915.776, 'text': "Um, and then I'll just write this out.", 'start': 1912.915, 'duration': 2.861}], 'summary': 'Maximum likelihood for mu 1 involves summing up positive examples and dividing by the total number.', 'duration': 33.587, 'max_score': 1882.189, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01882189.jpg'}, {'end': 1993.013, 'src': 'heatmap', 'start': 1940.644, 'weight': 0.791, 'content': [{'end': 1941.124, 'text': 'Yeah, okay.', 'start': 1940.644, 'duration': 0.48}, {'end': 1942.625, 'text': "Don't worry too much about that.", 'start': 1941.644, 'duration': 0.981}, {'end': 1946.726, 'text': 'Uh, you can unpack the details in the lecture notes or- or in the homeworks.', 'start': 1943.205, 'duration': 3.521}, {'end': 1956.474, 'text': 'Okay, Um, but the covariance matrix basically tries to, you know, fit contours to the ellipse right? like we saw.', 'start': 1948.167, 'duration': 8.307}, {'end': 1959.921, 'text': 'uh so- so try to fit a Gaussian to both of these with these corresponding means.', 'start': 1956.474, 'duration': 3.447}, {'end': 1962.787, 'text': 'but you want one covariance matrix to both of these.', 'start': 1959.921, 'duration': 2.866}, {'end': 1971.138, 'text': 'Okay, Um, so these are the- so-, so-, so the way- so the way I motivated this was, you know, I said well,', 'start': 1963.473, 'duration': 7.665}, {'end': 1976.201, 'text': 'if you want to estimate the mean of a coin toss, just count the fraction of coin tosses, the Km of heads, uh.', 'start': 1971.138, 'duration': 5.063}, {'end': 1980.925, 'text': 'and then it seems like the mean for mu 0, mu 1, you just look at these examples and pick the mean right?', 'start': 1976.201, 'duration': 4.724}, {'end': 1984.027, 'text': 'So that- that was the intuitive explanation for how you get these formulas.', 'start': 1980.945, 'duration': 3.082}, {'end': 1993.013, 'text': 'But the mathematically sound way to get these formulas is not via this intuitive argument that I just gave is instead to look at the likelihood.', 'start': 1984.567, 'duration': 8.446}], 'summary': 'The lecture discusses fitting a covariance matrix to gaussian contours and the mathematically sound approach to obtaining formulas for means.', 'duration': 52.369, 'max_score': 1940.644, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01940644.jpg'}, {'end': 1971.138, 'src': 'embed', 'start': 1948.167, 'weight': 0, 'content': [{'end': 1956.474, 'text': 'Okay, Um, but the covariance matrix basically tries to, you know, fit contours to the ellipse right? like we saw.', 'start': 1948.167, 'duration': 8.307}, {'end': 1959.921, 'text': 'uh so- so try to fit a Gaussian to both of these with these corresponding means.', 'start': 1956.474, 'duration': 3.447}, {'end': 1962.787, 'text': 'but you want one covariance matrix to both of these.', 'start': 1959.921, 'duration': 2.866}, {'end': 1971.138, 'text': 'Okay, Um, so these are the- so-, so-, so the way- so the way I motivated this was, you know, I said well,', 'start': 1963.473, 'duration': 7.665}], 'summary': 'Covariance matrix fits contours to ellipse, aiming for one matrix for both gaussian distributions.', 'duration': 22.971, 'max_score': 1948.167, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01948167.jpg'}, {'end': 2228.676, 'src': 'embed', 'start': 2188.561, 'weight': 1, 'content': [{'end': 2192.264, 'text': 'But if you actually need a probability, then you have to normalize the probability.', 'start': 2188.561, 'duration': 3.703}, {'end': 2209.238, 'text': "Okay So let's examine what the algorithm is doing.", 'start': 2198.029, 'duration': 11.209}, {'end': 2217.826, 'text': 'All right.', 'start': 2217.506, 'duration': 0.32}, {'end': 2220.689, 'text': "So let's look at the same dataset and, uh,", 'start': 2217.926, 'duration': 2.763}, {'end': 2226.775, 'text': 'compare and contrast what a discriminative learning algorithm versus a generative learning algorithm will do on this dataset.', 'start': 2220.689, 'duration': 6.086}, {'end': 2228.676, 'text': 'All right.', 'start': 2226.795, 'duration': 1.881}], 'summary': 'Analyzing algorithms on a dataset to compare discriminative and generative learning.', 'duration': 40.115, 'max_score': 2188.561, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02188561.jpg'}, {'end': 2337.016, 'src': 'heatmap', 'start': 2266.964, 'weight': 2, 'content': [{'end': 2273.829, 'text': "And after about 20 iterations they'll converge to that pretty decent discriminative boundary, okay?", 'start': 2266.964, 'duration': 6.865}, {'end': 2278.053, 'text': "So that's logistic regression, really searching for a line that separates positive and negative examples.", 'start': 2273.849, 'duration': 4.204}, {'end': 2281.035, 'text': 'How about the generative learning algorithm?', 'start': 2279.274, 'duration': 1.761}, {'end': 2287.816, 'text': 'What it does is the following which is fit, uh, with Gaussian distribution analysis.', 'start': 2282.011, 'duration': 5.805}, {'end': 2293.507, 'text': "what we'll do is fit Gaussians to the positive and negative examples right?", 'start': 2287.816, 'duration': 5.691}, {'end': 2296.029, 'text': 'And- and just one-, one- one technical detail.', 'start': 2293.747, 'duration': 2.282}, {'end': 2300.152, 'text': 'Um, I described this as if we look at the two classes separately,', 'start': 2296.309, 'duration': 3.843}, {'end': 2303.755, 'text': 'because we use the same covariance matrix sigma for the positive and negative classes.', 'start': 2300.152, 'duration': 3.603}, {'end': 2306.137, 'text': "We actually don't quite look at them totally separately.", 'start': 2303.835, 'duration': 2.302}, {'end': 2310.28, 'text': 'But we do fit two Gaussian densities to the positive and negative examples.', 'start': 2306.517, 'duration': 3.763}, {'end': 2319.387, 'text': "Um, and then what we do is for each point, try to decide, uh, what is this class label using Bayes' rule, using that formula.", 'start': 2310.86, 'duration': 8.527}, {'end': 2324.149, 'text': 'And it turns out that this implies the following decision boundary right?', 'start': 2319.807, 'duration': 4.342}, {'end': 2330.013, 'text': 'So points to the upper right of this decision boundary that- that straight line I just drew.', 'start': 2324.209, 'duration': 5.804}, {'end': 2332.454, 'text': 'you are closer to the negative class.', 'start': 2330.013, 'duration': 2.441}, {'end': 2337.016, 'text': 'you end up classifying them as negative examples and points to the lower left of that line.', 'start': 2332.454, 'duration': 4.562}], 'summary': 'Logistic regression finds discriminative boundary; generative learning fits gaussians to separate classes.', 'duration': 70.052, 'max_score': 2266.964, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02266964.jpg'}], 'start': 1708.09, 'title': 'Maximum likelihood estimates and gaussian discriminant analysis', 'summary': "Discusses maximum likelihood estimates for benign and malignant tumors' features and introduces covariance matrices. it also explains gaussian discriminant analysis, the process of making predictions, and the comparison between discriminative and generative learning algorithms.", 'chapters': [{'end': 1971.138, 'start': 1708.09, 'title': 'Maximum likelihood estimates and covariance matrices', 'summary': "Discusses the maximum likelihood estimates for the mean of benign and malignant tumors' features, providing a formula for both estimates and explaining the calculation process, and introduces the concept of covariance matrices for fitting contours to ellipses.", 'duration': 263.048, 'highlights': ["The maximum likelihood estimate for the mean of all benign tumors' features is obtained by taking the average of all the benign tumors in the training set, providing a reasonable way to estimate mu 0.", 'The numerator in the formula sums up all the feature vectors for all the examples that are benign, while the denominator counts up the number of examples that have benign tumors in the training set.', 'The maximum likelihood estimate for mu 1 involves summing up all the positive examples and dividing by the total number of positive examples to get their mean.', 'The concept of covariance matrices is introduced, aiming to fit contours to ellipses and fit a Gaussian to both benign and malignant tumors with a single covariance matrix.']}, {'end': 2472.394, 'start': 1971.138, 'title': 'Gaussian discriminant analysis', 'summary': 'Explains the intuition behind estimating means for gaussian discriminant analysis, the process of making predictions, and the comparison between discriminative and generative learning algorithms in the context of logistic regression and gda.', 'duration': 501.256, 'highlights': ['The chapter explains the intuition behind estimating means for Gaussian Discriminant Analysis.', "The process of making predictions using Bayes' rule is discussed.", 'Comparison between discriminative and generative learning algorithms is explored in the context of logistic regression and GDA.']}], 'duration': 764.304, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS01708090.jpg', 'highlights': ['The concept of covariance matrices is introduced, aiming to fit contours to ellipses and fit a Gaussian to both benign and malignant tumors with a single covariance matrix.', 'Comparison between discriminative and generative learning algorithms is explored in the context of logistic regression and GDA.', "The process of making predictions using Bayes' rule is discussed.", 'The maximum likelihood estimate for mu 1 involves summing up all the positive examples and dividing by the total number of positive examples to get their mean.', "The maximum likelihood estimate for the mean of all benign tumors' features is obtained by taking the average of all the benign tumors in the training set, providing a reasonable way to estimate mu 0."]}, {'end': 2893.062, 'segs': [{'end': 2577.123, 'src': 'embed', 'start': 2475.615, 'weight': 2, 'content': [{'end': 2489.15, 'text': "And, um, for a fixed set of parameters, Right? So let's say you've learned some set of parameters.", 'start': 2475.615, 'duration': 13.535}, {'end': 2503.922, 'text': "Um, I'm going to do an exercise where we're going to plot P of y equals 1, given x, you know,", 'start': 2490.151, 'duration': 13.771}, {'end': 2509.607, 'text': 'parameterized by all these things right as a function of x.', 'start': 2503.922, 'duration': 5.685}, {'end': 2517.683, 'text': "Um, so I'm gonna do this little exercise in a second.", 'start': 2515.302, 'duration': 2.381}, {'end': 2524.186, 'text': 'But what this means is um well, this formula, this is equal to p of x.', 'start': 2518.343, 'duration': 5.843}, {'end': 2531.409, 'text': 'given y equals 1, you know which is parameterized by right.', 'start': 2524.186, 'duration': 7.223}, {'end': 2534.13, 'text': 'well, the various parameters times.', 'start': 2531.409, 'duration': 2.721}, {'end': 2541.813, 'text': 'p of y equals 1, is parameterized by phi, divided by p of x, which depends on all the parameters, I guess.', 'start': 2534.13, 'duration': 7.683}, {'end': 2555.934, 'text': "So, uh, by Bayes' rule, you know, this formula is equal to this little thing.", 'start': 2549.312, 'duration': 6.622}, {'end': 2560.555, 'text': 'And uh, just as we saw earlier, I guess right,', 'start': 2556.314, 'duration': 4.241}, {'end': 2565.536, 'text': "once you have fixed all the parameters that's just a number you compute by evaluating the Gaussian density.", 'start': 2560.555, 'duration': 4.981}, {'end': 2570.577, 'text': 'Um, this is a Bernoulli probability.', 'start': 2566.476, 'duration': 4.101}, {'end': 2574.538, 'text': 'So actually P of y equals 1 parameterized by 5, this is just equal to 5 is that second term.', 'start': 2570.657, 'duration': 3.881}, {'end': 2577.123, 'text': 'and you similarly calculate the denominator.', 'start': 2575.242, 'duration': 1.881}], 'summary': "Using bayes' rule, we calculate p(y=1|x) parameterized by phi and x, involving gaussian and bernoulli probabilities.", 'duration': 101.508, 'max_score': 2475.615, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02475615.jpg'}, {'end': 2818.018, 'src': 'embed', 'start': 2788.705, 'weight': 3, 'content': [{'end': 2796.33, 'text': 'Now it turns out that if you repeat this exercise uh, sweeping from left to right for many, many points on the x-axis,', 'start': 2788.705, 'duration': 7.625}, {'end': 2804.916, 'text': 'you find that for points far to the left, the chance of this coming from uh, the y equals 1 class is very small.', 'start': 2796.33, 'duration': 8.586}, {'end': 2812.372, 'text': 'And as you approach this midpoint, it increases to 0.5 and then surpasses 0.5.', 'start': 2805.768, 'duration': 6.604}, {'end': 2818.018, 'text': 'And then beyond a certain point, it becomes very, very close to 1.', 'start': 2812.372, 'duration': 5.646}], 'summary': 'Sweeping exercise shows increasing chance of y=1 as x-axis moves right.', 'duration': 29.313, 'max_score': 2788.705, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02788705.jpg'}, {'end': 2893.062, 'src': 'embed', 'start': 2840.754, 'weight': 0, 'content': [{'end': 2843.856, 'text': 'The shape of that turns out to be exactly a shape sigmoid function.', 'start': 2840.754, 'duration': 3.102}, {'end': 2847.499, 'text': 'And you proved this in the problem sets as well, right?', 'start': 2843.956, 'duration': 3.543}, {'end': 2867.616, 'text': 'Um, so, um, both logistic regression and Gaussian discriminant analysis actually end up using a sigmoid function to calculate.', 'start': 2849.142, 'duration': 18.474}, {'end': 2868.857, 'text': 'you know, p of y equals 1.', 'start': 2867.616, 'duration': 1.241}, {'end': 2873.14, 'text': 'given x, or-, or- or the-, the-, the outcome ends up being a sigmoid function.', 'start': 2868.857, 'duration': 4.283}, {'end': 2876.843, 'text': 'I guess the mechanics is you actually use this calculation rather than compute a sigmoid function.', 'start': 2873.16, 'duration': 3.683}, {'end': 2884.057, 'text': 'Right But, um, the specific choice of the parameters they end up choosing are quite different.', 'start': 2877.813, 'duration': 6.244}, {'end': 2888.559, 'text': 'And you saw when I was projecting the results on the display just now in PowerPoint.', 'start': 2884.137, 'duration': 4.422}, {'end': 2893.062, 'text': 'uh, that the two algorithms actually come up with two different decision boundaries.', 'start': 2888.559, 'duration': 4.503}], 'summary': 'Logistic regression and gaussian discriminant analysis use sigmoid function to calculate p(y=1); different decision boundaries', 'duration': 52.308, 'max_score': 2840.754, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02840754.jpg'}], 'start': 2475.615, 'title': "Bayes' rule exercise and gaussian discriminant analysis", 'summary': "Covers an exercise on plotting p(y=1|x) using bayes' rule, involving gaussian density and bernoulli probability. it also discusses the process of calculating the probability of y equals 1 given x using gaussian discriminant analysis, leading to the discovery of a sigmoid function, and compares decision boundaries between logistic regression and gaussian discriminant analysis.", 'chapters': [{'end': 2577.123, 'start': 2475.615, 'title': "Bayes' rule exercise", 'summary': "Covers an exercise on plotting p(y=1|x) given a fixed set of parameters and explains the formula using bayes' rule, involving gaussian density and bernoulli probability.", 'duration': 101.508, 'highlights': ['The exercise involves plotting P(y=1|x) given a fixed set of parameters, showcasing the application of the learned parameters.', "The formula is explained using Bayes' rule, involving parameters, Gaussian density, and Bernoulli probability.", 'The calculation of P(y=1|x) parameterized by phi is discussed as equal to phi, highlighting the computational aspect of the exercise.']}, {'end': 2893.062, 'start': 2577.203, 'title': 'Gaussian discriminant analysis and logistic regression', 'summary': 'Discusses the process of calculating the probability of y equals 1 given x using gaussian discriminant analysis, leading to the discovery of a sigmoid function, as well as the comparison of decision boundaries between logistic regression and gaussian discriminant analysis.', 'duration': 315.859, 'highlights': ['The process of calculating the probability of y equals 1 given x using Gaussian discriminant analysis leads to the discovery of a sigmoid function, which is exactly the shape of the curve obtained by evaluating the formula for a dense grid on the x-axis, proving that both logistic regression and Gaussian discriminant analysis end up using a sigmoid function for the calculation.', 'The comparison of decision boundaries between logistic regression and Gaussian discriminant analysis reveals that the two algorithms come up with different decision boundaries, as demonstrated in the display of results in PowerPoint.', 'The chance of y equals 1 given x varies across the x-axis, with the probability increasing from very small for points far to the left, reaching 0.5 at the midpoint, surpassing 0.5, and eventually becoming very close to 1 for points far to the right.']}], 'duration': 417.447, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02475615.jpg', 'highlights': ['The comparison of decision boundaries between logistic regression and Gaussian discriminant analysis reveals different decision boundaries.', 'The process of calculating the probability of y equals 1 given x using Gaussian discriminant analysis leads to the discovery of a sigmoid function.', 'The exercise involves plotting P(y=1|x) given a fixed set of parameters, showcasing the application of the learned parameters.', 'The chance of y equals 1 given x varies across the x-axis, with the probability increasing from very small for points far to the left, reaching 0.5 at the midpoint, surpassing 0.5, and eventually becoming very close to 1 for points far to the right.', "The formula is explained using Bayes' rule, involving parameters, Gaussian density, and Bernoulli probability.", 'The calculation of P(y=1|x) parameterized by phi is discussed as equal to phi, highlighting the computational aspect of the exercise.']}, {'end': 3524.376, 'segs': [{'end': 3147.188, 'src': 'embed', 'start': 3082.907, 'weight': 0, 'content': [{'end': 3091.149, 'text': 'So if you assume P of y equals 1, given x, is governed by a logistic function, by- by this shape, this does not in any way, shape or form,', 'start': 3082.907, 'duration': 8.242}, {'end': 3093.89, 'text': 'assume that x, given y, is Gaussian.', 'start': 3091.149, 'duration': 2.741}, {'end': 3096.251, 'text': 'uh, uh, x, given y, equals 0, is Gaussian.', 'start': 3093.89, 'duration': 2.361}, {'end': 3097.491, 'text': 'x, given y, 1 is Gaussian.', 'start': 3096.251, 'duration': 1.24}, {'end': 3114.736, 'text': 'So what this means is that GDA, the generative learning algorithm, in this case, this makes a stronger set of assumptions and, which is, regression,', 'start': 3099.75, 'duration': 14.986}, {'end': 3127.841, 'text': 'makes a weaker set of assumptions, because you could prove these assumptions from these assumptions, okay?', 'start': 3114.736, 'duration': 13.105}, {'end': 3134.841, 'text': "Um, And, by the way, as as uh as as uh, let's see.", 'start': 3127.861, 'duration': 6.98}, {'end': 3140.384, 'text': 'And so what you see in a lot of learning algorithms is that, um,', 'start': 3135.761, 'duration': 4.623}, {'end': 3147.188, 'text': 'if you make stronger modeling assumptions and if your modeling assumptions are roughly correct, then your model will do better,', 'start': 3140.384, 'duration': 6.804}], 'summary': 'Gda makes stronger assumptions than regression for better model performance.', 'duration': 64.281, 'max_score': 3082.907, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03082907.jpg'}, {'end': 3323.934, 'src': 'embed', 'start': 3296.832, 'weight': 1, 'content': [{'end': 3300.617, 'text': 'if you make weaker assumptions, as in logistic regression,', 'start': 3296.832, 'duration': 3.785}, {'end': 3306.424, 'text': "then your algorithm will be more robust to modeling assumptions such as accidentally assuming the data is Gaussian if it's not.", 'start': 3300.617, 'duration': 5.807}, {'end': 3316.372, 'text': 'Uh, but on the flip side, if you have a very small dataset, then, um, using, a model that makes more assumptions will actually allow you to do better.', 'start': 3307.325, 'duration': 9.047}, {'end': 3321.894, 'text': 'Because by making more assumptions, you are just telling the algorithm more truth about the world, which is you know.', 'start': 3316.472, 'duration': 5.422}, {'end': 3323.934, 'text': 'hey, algorithm, the world is Gaussian.', 'start': 3321.894, 'duration': 2.04}], 'summary': 'Logistic regression is more robust with weaker assumptions, but small datasets benefit from models making more assumptions.', 'duration': 27.102, 'max_score': 3296.832, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03296832.jpg'}, {'end': 3402.089, 'src': 'embed', 'start': 3377.286, 'weight': 3, 'content': [{'end': 3383.514, 'text': 'So I think that the whole world has moved toward using bigger and bigger data sets, right? Digitization of society, which is a lot of data.', 'start': 3377.286, 'duration': 6.228}, {'end': 3386.477, 'text': 'And so for a lot of problems, we have a lot of data.', 'start': 3384.014, 'duration': 2.463}, {'end': 3394.507, 'text': 'I would probably use logistic regression because with more data, you could overcome telling the algorithm less about the world.', 'start': 3387.018, 'duration': 7.489}, {'end': 3397.308, 'text': 'Right So- so the algorithm has two sources of knowledge.', 'start': 3394.887, 'duration': 2.421}, {'end': 3400.429, 'text': 'Uh, one source of knowledge is what did you tell it??', 'start': 3397.328, 'duration': 3.101}, {'end': 3402.089, 'text': 'What are the assumptions you told it to make?', 'start': 3400.449, 'duration': 1.64}], 'summary': 'Using logistic regression with big data sets to minimize algorithm knowledge requirement.', 'duration': 24.803, 'max_score': 3377.286, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03377286.jpg'}, {'end': 3441.308, 'src': 'embed', 'start': 3417.168, 'weight': 4, 'content': [{'end': 3425.234, 'text': 'Now, one practical reason why I still use algorithms like uh, GDA, general discriminant analysis or algorithms like this um, uh,', 'start': 3417.168, 'duration': 8.066}, {'end': 3427.416, 'text': "is that it's actually quite computationally efficient.", 'start': 3425.234, 'duration': 2.182}, {'end': 3430.578, 'text': "And so there's actually one use case at landing AI that I'm working on,", 'start': 3427.636, 'duration': 2.942}, {'end': 3435.382, 'text': "where we just need to fit a ton of models and don't have the patience to run logistic regression over and over.", 'start': 3430.578, 'duration': 4.804}, {'end': 3441.308, 'text': 'And it turns out computing mean and variances of, um, covariance matrices is very efficient.', 'start': 3435.982, 'duration': 5.326}], 'summary': 'Using gda for computational efficiency at landing ai for fitting ton of models.', 'duration': 24.14, 'max_score': 3417.168, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03417168.jpg'}], 'start': 2895.114, 'title': 'Algorithm comparisons', 'summary': 'Compares the assumptions and performance of generative algorithm (gda) and discriminative algorithm (logistic regression), highlighting that gda makes stronger assumptions and can perform better if assumptions are roughly correct, while logistic regression makes weaker assumptions but can suffer if the assumptions are wrong. it also explores the implications of model assumptions in logistic regression, highlighting its robustness to various data distributions and the trade-offs between making weaker or stronger assumptions, with a focus on the efficiency and performance of logistic regression and gda.', 'chapters': [{'end': 3190.891, 'start': 2895.114, 'title': 'Generative vs. discriminative algorithms', 'summary': 'Compares the assumptions and performance of generative algorithm (gda) and discriminative algorithm (logistic regression), highlighting that gda makes stronger assumptions and can perform better if the assumptions are roughly correct, while logistic regression makes weaker assumptions but can suffer if the assumptions are wrong.', 'duration': 295.777, 'highlights': ['GDA assumes X given Y as Gaussian and Y as Bernoulli, making stronger assumptions than logistic regression, while logistic regression assumes p(y=1|x) is governed by a logistic function, making weaker assumptions.', 'If the assumptions are roughly correct, GDA can perform better, especially with a small dataset, but if the assumptions are wrong, GDA may perform poorly.', 'Making stronger modeling assumptions can lead to better performance if the assumptions are roughly correct, as it provides more information to the algorithm.']}, {'end': 3524.376, 'start': 3191.651, 'title': 'Model assumptions in logistic regression', 'summary': 'Explores the implications of model assumptions in logistic regression, highlighting its robustness to various data distributions and the trade-offs between making weaker or stronger assumptions, with a focus on the efficiency and performance of logistic regression and gda.', 'duration': 332.725, 'highlights': ['Logistic regression is robust to different data distributions, making it suitable for scenarios where the data type is uncertain, ensuring better model performance under varied data assumptions.', 'Leveraging logistic regression becomes advantageous with larger datasets, as it requires fewer assumptions and allows the algorithm to learn from the data, aligning with the trend of utilizing big data in current problem-solving contexts.', 'The computational efficiency of GDA makes it a practical choice for scenarios requiring the fitting of multiple models, providing a faster alternative to logistic regression, despite potential differences in performance.', 'The choice between logistic regression and GDA hinges on the balance between computational efficiency and model performance, with logistic regression offering flexibility in handling diverse data types and larger datasets, while GDA provides computational efficiency but may require stronger assumptions.', "The nature of data distributions and the scale of the dataset are crucial factors in determining the most suitable algorithm, as logistic regression's adaptability to varied data types and sizes contrasts with GDA's efficiency but potential trade-offs in accuracy."]}], 'duration': 629.262, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS02895114.jpg', 'highlights': ['GDA assumes X given Y as Gaussian and Y as Bernoulli, making stronger assumptions than logistic regression.', 'Logistic regression is robust to different data distributions, making it suitable for scenarios where the data type is uncertain.', 'Making stronger modeling assumptions can lead to better performance if the assumptions are roughly correct, as it provides more information to the algorithm.', 'Leveraging logistic regression becomes advantageous with larger datasets, as it requires fewer assumptions and allows the algorithm to learn from the data.', 'The choice between logistic regression and GDA hinges on the balance between computational efficiency and model performance.']}, {'end': 4727.091, 'segs': [{'end': 3574.683, 'src': 'embed', 'start': 3525.398, 'weight': 1, 'content': [{'end': 3535.579, 'text': 'Questions? Yeah.', 'start': 3525.398, 'duration': 10.181}, {'end': 3541.922, 'text': "Is it recommended that you do some statistical test to see if it's Gaussian? Um, I can tell you what's done in practice.", 'start': 3535.679, 'duration': 6.243}, {'end': 3547.285, 'text': 'I think in practice, if you have enough data to do a statistical test and gain conviction,', 'start': 3542.182, 'duration': 5.103}, {'end': 3550.326, 'text': 'you probably have enough data to just use logistic regression.', 'start': 3547.285, 'duration': 3.041}, {'end': 3552.888, 'text': "Um, uh, I- I- I don't know.", 'start': 3550.346, 'duration': 2.542}, {'end': 3554.689, 'text': "Well, no, that's not really fair.", 'start': 3552.948, 'duration': 1.741}, {'end': 3555.189, 'text': "I don't know.", 'start': 3554.709, 'duration': 0.48}, {'end': 3562.813, 'text': 'If a very high dimensional data I- I think what often happens more is people just plot the data and if it looks clearly non-Gaussian,', 'start': 3555.529, 'duration': 7.284}, {'end': 3565.155, 'text': 'then you know that would be a reason to not use GTA.', 'start': 3562.813, 'duration': 2.342}, {'end': 3574.683, 'text': "But what happens often is that, um, uh, uh, sometimes you just have a very small training set and it's just a matter of judgment, right?", 'start': 3565.275, 'duration': 9.408}], 'summary': 'Statistical test for gaussian distribution not always used due to data size and visual analysis.', 'duration': 49.285, 'max_score': 3525.398, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03525398.jpg'}, {'end': 3922.389, 'src': 'embed', 'start': 3896.348, 'weight': 3, 'content': [{'end': 3904.009, 'text': 'We have a piece of text and you want to classify it into one of two categories for spam or non-spam or one of maybe thousands of categories.', 'start': 3896.348, 'duration': 7.661}, {'end': 3907.45, 'text': "If you're trying to take a product description and classify it into one of the classes.", 'start': 3904.029, 'duration': 3.421}, {'end': 3919.187, 'text': 'Um, and so the first question we will have is um, uh, given an email problem, uh, given the email classification problem,', 'start': 3908.562, 'duration': 10.625}, {'end': 3922.389, 'text': 'how do you represent it as a feature vector??', 'start': 3919.187, 'duration': 3.202}], 'summary': 'Text classification involves representing an email problem as a feature vector.', 'duration': 26.041, 'max_score': 3896.348, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03896348.jpg'}, {'end': 4221.145, 'src': 'heatmap', 'start': 4165.221, 'weight': 0.974, 'content': [{'end': 4168.243, 'text': 'because X is a binary vector of this 10, 000 dimensional.', 'start': 4165.221, 'duration': 3.022}, {'end': 4178.888, 'text': 'So if we try to model P of X in the straightforward way, as a multinomial distribution over you know 2 to the 10, 000 possible outcomes,', 'start': 4168.924, 'duration': 9.964}, {'end': 4180.627, 'text': 'then you need right, uh.', 'start': 4178.888, 'duration': 1.739}, {'end': 4184.59, 'text': 'uh, you need you know 2 to the 10, 000 parameters.', 'start': 4180.627, 'duration': 3.963}, {'end': 4186.211, 'text': 'right, which is a lot.', 'start': 4184.59, 'duration': 1.621}, {'end': 4191.973, 'text': 'Uh, or actually technically you need 2 to the 10, 000 minus 1 parameters because they add up to 1, so you save 1 parameter.', 'start': 4186.591, 'duration': 5.382}, {'end': 4199.951, 'text': "Um, but so modeling this without additional assumptions won't- won't work, right? Because, uh, excessive number of parameters.", 'start': 4192.667, 'duration': 7.284}, {'end': 4220.364, 'text': "So, in the Naive Bayes algorithm, we're going to assume that the Xi's are are conditionally independent given.", 'start': 4200.992, 'duration': 19.372}, {'end': 4221.145, 'text': 'y okay?', 'start': 4220.364, 'duration': 0.781}], 'summary': 'Modeling p of x as a multinomial distribution with 2^10,000 parameters is not feasible due to excessive number of parameters.', 'duration': 55.924, 'max_score': 4165.221, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS04165220.jpg'}, {'end': 4552.251, 'src': 'heatmap', 'start': 4435.698, 'weight': 0.806, 'content': [{'end': 4459.787, 'text': "I'm gonna write phi subscript um j given y equals 1, as the probability that xj equals 1, given y equals 1, phi subscript j given y equals 0,", 'start': 4435.698, 'duration': 24.089}, {'end': 4461.448, 'text': 'and then um phi right.', 'start': 4459.787, 'duration': 1.661}, {'end': 4471.534, 'text': "And just to distinguish all these phi's from each other, I'm gonna just call this phi subscript, y okay?", 'start': 4465.971, 'duration': 5.563}, {'end': 4478.618, 'text': "So this parameter says if it's spam email, if y equals 1 is spam, y is 0 is non-spam.", 'start': 4472.594, 'duration': 6.024}, {'end': 4482.8, 'text': "If it's spam email, what's the chance of word j appearing in the email?", 'start': 4479.098, 'duration': 3.702}, {'end': 4486.873, 'text': "Uh, if it's not spam email, what's the chance of where J appearing in the email?", 'start': 4483.63, 'duration': 3.243}, {'end': 4489.195, 'text': "Um, and then also, what's the cost prior?", 'start': 4487.493, 'duration': 1.702}, {'end': 4495.74, 'text': "What's the prior probability that the next email you receive in your uh, in your, in your inbox, is spam email?", 'start': 4489.255, 'duration': 6.485}, {'end': 4503.406, 'text': 'And so um.', 'start': 4501.505, 'duration': 1.901}, {'end': 4515.642, 'text': 'to fit the parameters of this model, you would s- similar to Gaussian discriminant analysis write out the joint likelihood.', 'start': 4503.406, 'duration': 12.236}, {'end': 4522.987, 'text': 'So the joint likelihood of these parameters right?', 'start': 4516.023, 'duration': 6.964}, {'end': 4538.156, 'text': 'is the product you know, given these parameters right, similar to what we had for Gaussian discriminant analysis?', 'start': 4522.987, 'duration': 15.169}, {'end': 4541.198, 'text': 'And the maximum likelihood estimates.', 'start': 4539.357, 'duration': 1.841}, {'end': 4545.507, 'text': 'um, if you take this, take logs, take derivatives, set derivatives to 0,', 'start': 4542.225, 'duration': 3.282}, {'end': 4552.251, 'text': "solve for the values that maximize this you'll find that the uh maximum likelihood estimates of the parameters are phi.", 'start': 4545.507, 'duration': 6.744}], 'summary': 'Deriving maximum likelihood estimates for phi parameters in spam classification model.', 'duration': 116.553, 'max_score': 4435.698, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS04435698.jpg'}, {'end': 4691.398, 'src': 'embed', 'start': 4655.577, 'weight': 0, 'content': [{'end': 4658.578, 'text': 'and it turns out that with- with one fix to this algorithm,', 'start': 4655.577, 'duration': 3.001}, {'end': 4665.32, 'text': "which we'll talk about on Wednesday um this is actually- it's actually a not too horrible spam classifier.", 'start': 4658.578, 'duration': 6.742}, {'end': 4672.004, 'text': 'It turns out that if you use logistic regression, uh, for spam classification, you do better than this almost all the time.', 'start': 4666.22, 'duration': 5.784}, {'end': 4674.406, 'text': 'But this is a very efficient algorithm,', 'start': 4672.445, 'duration': 1.961}, {'end': 4680.23, 'text': 'because estimating these parameters is just counting and then computing probabilities is just multiplying a bunch of numbers.', 'start': 4674.406, 'duration': 5.824}, {'end': 4681.931, 'text': "So there's nothing iterative about this.", 'start': 4680.25, 'duration': 1.681}, {'end': 4687.856, 'text': 'So you can fit this model very efficiently and also keep on updating this model even as you get new data, even as you get new,', 'start': 4681.972, 'duration': 5.884}, {'end': 4691.398, 'text': 'new new you know users hits mark a spam or whatever.', 'start': 4687.856, 'duration': 3.542}], 'summary': 'Efficient spam classifier with logistic regression outperforms algorithm, allowing for efficient model fitting and updating.', 'duration': 35.821, 'max_score': 4655.577, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS04655577.jpg'}], 'start': 3525.398, 'title': 'Machine learning algorithms and applications', 'summary': 'Covers practical approaches to gaussian testing, logistic regression, machine learning with small data, and naive bayes algorithm for email spam classification. it emphasizes the significance of algorithms and domain knowledge in decision-making, as well as the efficiency and potential issues of the naive bayes algorithm.', 'chapters': [{'end': 3591.125, 'start': 3525.398, 'title': 'Gaussian testing and logistic regression', 'summary': 'Discusses the practical approach to testing for gaussian distribution and suggests that having enough data for a statistical test may indicate sufficient data for using logistic regression, with the recommendation to visually inspect data for non-gaussian distribution and utilize domain knowledge in decision-making.', 'duration': 65.727, 'highlights': ['The practical approach is to use logistic regression if there is enough data for statistical testing, indicating the potential sufficiency of data for logistic regression (e.g., if you have enough data to do a statistical test and gain conviction, you probably have enough data to just use logistic regression).', 'Visually inspecting data for non-Gaussian distribution is recommended, with the suggestion that if the data looks clearly non-Gaussian, it may be a reason to not use Gaussian testing and to use domain knowledge in decision-making (e.g., people just plot the data and if it looks clearly non-Gaussian, then you know that would be a reason to not use GTA).', 'Utilizing domain knowledge and judgment, such as consulting with domain experts like doctors to assess the distribution, is recommended for small training sets (e.g., if you have 50 examples of healthcare records, then you just have to ask some doctors and ask well, do you think the distribution is rather relatively Gaussian and use domain knowledge like that).']}, {'end': 3858.441, 'start': 3591.125, 'title': 'Machine learning and small data', 'summary': 'Discusses the significance of designing learning algorithms for small data in machine learning, highlighting the greater impact of algorithms and assumptions when dealing with fewer examples, as opposed to large datasets, emphasizing the influence of coding in knowledge when dealing with less data.', 'duration': 267.316, 'highlights': ['The significance of designing learning algorithms for small data', 'Impact of algorithms and assumptions on performance', 'Relevance of coding in knowledge for small data', 'Importance of skill in coding for small data', 'Emphasis on coding knowledge for small data']}, {'end': 4199.951, 'start': 3859.021, 'title': 'Email spam classification', 'summary': 'Discusses the process of classifying emails as spam or non-spam using natural language processing, specifically focusing on representing email as a feature vector and modeling p of x given y in a naive bayes algorithm.', 'duration': 340.93, 'highlights': ["The process of representing an email as a feature vector is explained, where a binary feature vector is created by assigning 1 if a word appears in the email and 0 if it doesn't, using the top 10,000 words from the email training set as the dictionary.", 'The challenge of modeling P of X given Y in a Naive Bayes algorithm due to the excessive number of parameters (2 to the 10,000 possible outcomes) is addressed, necessitating additional assumptions to make the modeling feasible.']}, {'end': 4503.406, 'start': 4200.992, 'title': 'Naive bayes algorithm explanation', 'summary': 'Explains the conditional independence assumption in the naive bayes algorithm, stating that the probability of observing multiple features given a class label can be assumed to be independent, despite not being a mathematically true assumption, which is used to derive the naive bayes model.', 'duration': 302.414, 'highlights': ['The chapter explains the conditional independence assumption in the Naive Bayes algorithm, stating that the probability of observing multiple features given a class label can be assumed to be independent.', 'The assumption is used to derive the Naive Bayes model despite not being a mathematically true assumption.', 'The explanation emphasizes that the assumption is not always true in a mathematical sense but may still be applicable in practice.']}, {'end': 4727.091, 'start': 4503.406, 'title': 'Naive bayes for email spam classification', 'summary': 'Discusses the naive bayes algorithm for email spam classification, highlighting the estimation of parameters and its efficiency, but also pointing out the need for a fix due to potential issues with zero values in equations.', 'duration': 223.685, 'highlights': ['Estimating parameters in Naive Bayes involves counting and computing probabilities, making it a very efficient algorithm.', 'The algorithm needs a fix to address potential issues when encountering zero values in the equations, which will be discussed further in the upcoming session.', 'Using logistic regression for spam classification generally outperforms Naive Bayes, but the latter remains a very efficient algorithm due to its simplicity in parameter estimation and probability computation.']}], 'duration': 1201.693, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/nt63k3bfXS0/pics/nt63k3bfXS03525398.jpg', 'highlights': ['Using logistic regression for spam classification generally outperforms Naive Bayes', 'The practical approach is to use logistic regression if there is enough data for statistical testing', 'Visually inspecting data for non-Gaussian distribution is recommended', 'The process of representing an email as a feature vector is explained', 'Estimating parameters in Naive Bayes involves counting and computing probabilities']}], 'highlights': ['GDA is a simpler and more computationally efficient algorithm for classification compared to logistic regression, especially effective with small datasets, sometimes with some caveats.', 'Generative learning algorithms build separate models for each class, e.g., malignant and benign tumors.', 'Increasing the off-diagonal entries in the covariance matrix leads to a change in the shape of the Gaussian density, indicating positive correlation between Z1 and Z2.', 'The process of fitting parameters for P of X and Y involves maximizing the log likelihood to find the values of the parameters', 'The concept of covariance matrices is introduced, aiming to fit contours to ellipses and fit a Gaussian to both benign and malignant tumors with a single covariance matrix.', 'The comparison of decision boundaries between logistic regression and Gaussian discriminant analysis reveals different decision boundaries.', 'GDA assumes X given Y as Gaussian and Y as Bernoulli, making stronger assumptions than logistic regression.', 'Using logistic regression for spam classification generally outperforms Naive Bayes']}