title

Gaussian Mixture Models - The Math of Intelligence (Week 7)

description

We're going to predict customer churn using a clustering technique called the Gaussian Mixture Model! This is a probability distribution that consists of multiple Gaussian distributions, very cool. I also have something important but unrelated to say in the beginning of the video.
Code for this video:
https://github.com/llSourcell/Gaussian_Mixture_Models
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More learning resources:
http://yulearning.blogspot.nl/2014/11/einsteins-most-famous-equation-is-emc2.html
http://web.iitd.ac.in/~sumeet/GMM_said_crv10_tutorial.pdf
https://brilliant.org/wiki/gaussian-mixture-model/
http://www.vlfeat.org/overview/gmm.html
http://www.informatica.uniroma2.it/upload/2009/IM/mixture-tutorial.pdf
http://cs.nyu.edu/~dsontag/courses/ml12/slides/lecture21.pdf
http://statweb.stanford.edu/~tibs/stat315a/LECTURES/em.pdf
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{'title': 'Gaussian Mixture Models - The Math of Intelligence (Week 7)', 'heatmap': [{'end': 463.635, 'start': 432.902, 'weight': 0.732}, {'end': 554.656, 'start': 479.983, 'weight': 0.717}, {'end': 690.184, 'start': 591.658, 'weight': 0.742}, {'end': 986.2, 'start': 914.896, 'weight': 0.791}, {'end': 1417.588, 'start': 1395.573, 'weight': 0.71}, {'end': 1583.291, 'start': 1528.14, 'weight': 0.812}, {'end': 1899.71, 'start': 1852.095, 'weight': 0.819}], 'summary': 'Covers topics such as predicting customer churn, community impact, parameter estimation, anomaly detection, user behavior classification, and the expectation maximization algorithm in the context of gaussian mixture models, which are used for unsupervised learning and data analysis.', 'chapters': [{'end': 84.796, 'segs': [{'end': 33.066, 'src': 'embed', 'start': 0.109, 'weight': 0, 'content': [{'end': 1.43, 'text': "Hello world, it's Siraj.", 'start': 0.109, 'duration': 1.321}, {'end': 8.794, 'text': "And imagine that you've built a game and you want to predict whether or not your players are going to continue playing next month or not.", 'start': 1.57, 'duration': 7.224}, {'end': 13.656, 'text': 'You want to classify your players as going to churn or not going to churn.', 'start': 9.154, 'duration': 4.502}, {'end': 20.52, 'text': "And you've got a single data point, and that is the amount of money that that user has spent in the game this month,", 'start': 14.097, 'duration': 6.423}, {'end': 27.504, 'text': 'either withdrawn or deposited to buy some in-game currency or digital gold or some kind of items, right?', 'start': 20.52, 'duration': 6.984}, {'end': 33.066, 'text': 'And based on that data point alone, you want to predict whether or not the user is going to continue playing the game or not.', 'start': 28.004, 'duration': 5.062}], 'summary': 'Predict player churn based on monthly spending.', 'duration': 32.957, 'max_score': 0.109, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg109.jpg'}, {'end': 69.924, 'src': 'embed', 'start': 40.91, 'weight': 1, 'content': [{'end': 42.61, 'text': "You'd want to use a bunch of different features.", 'start': 40.91, 'duration': 1.7}, {'end': 49.353, 'text': "But for this simple one dimensional example, we're just going to use that because what matters is the model that we're going to learn today.", 'start': 42.971, 'duration': 6.382}, {'end': 52.775, 'text': 'And the model is a Gaussian mixture model.', 'start': 49.754, 'duration': 3.021}, {'end': 60.439, 'text': "That's what the model is called, and it is a universally used model for generative unsupervised learning or clustering,", 'start': 53.295, 'duration': 7.144}, {'end': 61.419, 'text': "which is what we're going to do.", 'start': 60.439, 'duration': 0.98}, {'end': 69.924, 'text': "It's also called EM clustering or expectation maximization clustering based on the optimization strategy that we're going to use,", 'start': 62.44, 'duration': 7.484}], 'summary': 'Introduction to gaussian mixture model for generative unsupervised learning and clustering.', 'duration': 29.014, 'max_score': 40.91, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg40910.jpg'}], 'start': 0.109, 'title': 'Predicting customer churn with gaussian mixture model', 'summary': 'Introduces using a single data point to predict customer churn using a gaussian mixture model, a universally used model for generative unsupervised learning or clustering.', 'chapters': [{'end': 84.796, 'start': 0.109, 'title': 'Predicting customer churn with gaussian mixture model', 'summary': 'Introduces using a single data point - the amount of money spent by a user in a game - to predict customer churn using a gaussian mixture model, a universally used model for generative unsupervised learning or clustering.', 'duration': 84.687, 'highlights': ['Introducing the use of a single data point - amount of money spent by a user in a game - to predict customer churn using a Gaussian mixture model. Single data point prediction, Gaussian mixture model application, potential impact on customer churn prediction accuracy.', 'Explanation of Gaussian mixture model as a universally used model for generative unsupervised learning or clustering. Gaussian mixture model overview, application in unsupervised learning, clustering, and generative modeling.']}], 'duration': 84.687, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg109.jpg', 'highlights': ['Introducing the use of a single data point - amount of money spent by a user in a game - to predict customer churn using a Gaussian mixture model.', 'Explanation of Gaussian mixture model as a universally used model for generative unsupervised learning or clustering.']}, {'end': 748.802, 'segs': [{'end': 131.222, 'src': 'embed', 'start': 84.876, 'weight': 1, 'content': [{'end': 92.162, 'text': 'And before we start with this amazing, amazing example and code, I want to say one thing, okay? This is a message from Siraj.', 'start': 84.876, 'duration': 7.286}, {'end': 92.823, 'text': 'This is the message.', 'start': 92.182, 'duration': 0.641}, {'end': 96.745, 'text': 'The message is, I had a, this is a 30 second message.', 'start': 93.243, 'duration': 3.502}, {'end': 99.787, 'text': 'I went and I met subscribers for this channel.', 'start': 97.165, 'duration': 2.622}, {'end': 100.727, 'text': 'I met the community.', 'start': 99.847, 'duration': 0.88}, {'end': 103.468, 'text': 'Here in Amsterdam, I met 15 or so people.', 'start': 101.087, 'duration': 2.381}, {'end': 107.07, 'text': 'I went to London this past weekend and I met about 15 or so people.', 'start': 103.748, 'duration': 3.322}, {'end': 112.713, 'text': 'And I was just blown away by the quality of people that have subscribed to this channel.', 'start': 108.251, 'duration': 4.462}, {'end': 116.554, 'text': 'The community that we have built is incredible, seriously.', 'start': 112.733, 'duration': 3.821}, {'end': 118.956, 'text': 'There are people working for the United Nations.', 'start': 116.895, 'duration': 2.061}, {'end': 124.398, 'text': 'There are people who I have met who are working to create a machine learning community in Tunisia.', 'start': 119.216, 'duration': 5.182}, {'end': 131.222, 'text': 'There are people who have apps with 500, 000 plus users that are trying to stop smoking.', 'start': 124.718, 'duration': 6.504}], 'summary': "Siraj met 15 people in amsterdam and london, impressed by subscribers' quality and impact, including un workers, ml community builders, and app developers with 500,000+ users.", 'duration': 46.346, 'max_score': 84.876, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg84876.jpg'}, {'end': 207.829, 'src': 'embed', 'start': 184.743, 'weight': 0, 'content': [{'end': 192.271, 'text': "I'm gonna do a world tour at some point, but anyway, It's a very exciting time to be in this field and we are the real change makers.", 'start': 184.743, 'duration': 7.528}, {'end': 195.194, 'text': "okay?. We're the ones who are gonna solve these problems.", 'start': 192.271, 'duration': 2.923}, {'end': 199.759, 'text': "So it's amazing that we exist and we are growing at a rate of 500 to 800 subscribers a day.", 'start': 195.274, 'duration': 4.485}, {'end': 203.424, 'text': 'Reply to people in the comments.', 'start': 202.162, 'duration': 1.262}, {'end': 206.588, 'text': 'Ask people for questions in the Slack channel.', 'start': 203.864, 'duration': 2.724}, {'end': 207.829, 'text': 'We are growing.', 'start': 207.168, 'duration': 0.661}], 'summary': 'Exciting time in the field, growing at 500-800 subscribers/day, engaging with audience.', 'duration': 23.086, 'max_score': 184.743, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg184743.jpg'}, {'end': 304.59, 'src': 'embed', 'start': 279.325, 'weight': 4, 'content': [{'end': 284.527, 'text': 'The frequencies go up as the scores go up, and then it has a peak value, and then it goes down again.', 'start': 279.325, 'duration': 5.202}, {'end': 289.748, 'text': 'And we can represent this using a bell curve, otherwise known as a Gaussian distribution.', 'start': 284.627, 'duration': 5.121}, {'end': 297.78, 'text': 'And a Gaussian distribution is a type of distribution where half the data falls on the left of it and the other half falls on the right of it.', 'start': 290.268, 'duration': 7.512}, {'end': 299.863, 'text': "So it's an even distribution.", 'start': 298.06, 'duration': 1.803}, {'end': 304.59, 'text': "And you can notice just by the thought of it intuitively that it's very mathematically convenient.", 'start': 299.883, 'duration': 4.707}], 'summary': 'Scores and frequencies follow a bell curve, a gaussian distribution.', 'duration': 25.265, 'max_score': 279.325, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg279325.jpg'}, {'end': 479.283, 'src': 'heatmap', 'start': 432.902, 'weight': 3, 'content': [{'end': 438.825, 'text': 'which is the data point minus the mean squared over two times the standard deviation squared.', 'start': 432.902, 'duration': 5.923}, {'end': 449.011, 'text': 'So this is a function of a continuous random variable whose integral across a interval gives the probability that the value of the variable lies within the same interval.', 'start': 439.026, 'duration': 9.985}, {'end': 450.211, 'text': 'So we have some interval.', 'start': 449.271, 'duration': 0.94}, {'end': 454.873, 'text': "So that's a Gaussian distribution, and that's the formula for one.", 'start': 451.632, 'duration': 3.241}, {'end': 463.635, 'text': 'So what is a Gaussian mixture model? Sometimes our data has multiple distributions or it has multiple peaks.', 'start': 455.034, 'duration': 8.601}, {'end': 466.917, 'text': "It doesn't always just have one peak and we can notice that.", 'start': 463.855, 'duration': 3.062}, {'end': 471.939, 'text': 'We can look at our data set and we can say, well it looks like there are multiple peaks happening here.', 'start': 467.697, 'duration': 4.242}, {'end': 479.283, 'text': 'There are two peak points and the data seems to be going up and down and up and down twice or maybe three times or four times.', 'start': 471.959, 'duration': 7.324}], 'summary': 'Gaussian distribution explained, gaussian mixture model for data with multiple peaks.', 'duration': 46.381, 'max_score': 432.902, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg432902.jpg'}, {'end': 554.656, 'src': 'heatmap', 'start': 479.983, 'weight': 0.717, 'content': [{'end': 485.046, 'text': 'But if we think that there are multiple distributions Gaussian distributions that can represent this data,', 'start': 479.983, 'duration': 5.063}, {'end': 488.628, 'text': "then we can build what's called a Gaussian mixture model.", 'start': 485.786, 'duration': 2.842}, {'end': 491.53, 'text': 'And what this is, it is a probability distribution.', 'start': 488.688, 'duration': 2.842}, {'end': 492.771, 'text': "It's more a probability.", 'start': 491.571, 'duration': 1.2}, {'end': 501.338, 'text': 'you can think of it as just a probability distribution that consists of multiple probability distributions and that are multiple Gaussians.', 'start': 492.771, 'duration': 8.567}, {'end': 508.187, 'text': 'So for d dimensions, where d are the number of features in our data set.', 'start': 502.563, 'duration': 5.624}, {'end': 515.653, 'text': 'the Gaussian distribution of a vector x, where x equals the number of data points that we have, is defined by the following equation', 'start': 508.187, 'duration': 7.466}, {'end': 522.773, 'text': 'And So you can see how you can substitute D for the number of features we have.', 'start': 517.054, 'duration': 5.719}, {'end': 530.516, 'text': "This is the for the mean, and so Sigma represents the covariance matrix of the Gaussian, and so you notice how we're not using the standard deviation.", 'start': 522.773, 'duration': 7.743}, {'end': 537.498, 'text': "instead, we're using the covariance matrix when it comes to the Gaussian mixture model, and this is what it would look like, right.", 'start': 530.516, 'duration': 6.982}, {'end': 546.073, 'text': 'so in the case of two dimensions, it would look like this it would give us a a curve for all of our possible Data points.', 'start': 537.498, 'duration': 8.575}, {'end': 547.473, 'text': 'and so why do we use the covariance?', 'start': 546.073, 'duration': 1.4}, {'end': 554.656, 'text': 'well, the covariance is a measure of how changes in one variable are? Associated with changes in a second variable.', 'start': 547.473, 'duration': 7.183}], 'summary': 'Gaussian mixture model consists of multiple gaussian distributions for representing data, using covariance matrix instead of standard deviation, and providing a probability distribution for multiple features.', 'duration': 74.673, 'max_score': 479.983, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg479983.jpg'}, {'end': 690.184, 'src': 'heatmap', 'start': 577.136, 'weight': 5, 'content': [{'end': 587.996, 'text': 'the covariance matrix, as opposed to the standard deviation when we plug it in here, gives us a better, more accurate result.', 'start': 577.136, 'duration': 10.86}, {'end': 591.658, 'text': 'And so the way we compute the covariance matrix.', 'start': 588.876, 'duration': 2.782}, {'end': 596.061, 'text': 'I talked about this before when we talked about eigenvectors and eigenvalue pairs,', 'start': 591.658, 'duration': 4.403}, {'end': 602.284, 'text': 'but the parameters that it uses are the number of scores in each of the data sets, the variance,', 'start': 596.061, 'duration': 6.223}, {'end': 609.709, 'text': 'the covariance and where C is the size of the number of columns in the data, right?', 'start': 602.284, 'duration': 7.425}, {'end': 611.63, 'text': "It's a column by column matrix.", 'start': 609.749, 'duration': 1.881}, {'end': 614.243, 'text': "And we'll compute this in a second.", 'start': 613.103, 'duration': 1.14}, {'end': 623.906, 'text': 'But the probability given in a mixture of k Gaussians, where k is the number of distributions that we believe that there are.', 'start': 614.883, 'duration': 9.023}, {'end': 626.526, 'text': 'in our case, we believe that there are going to be two.', 'start': 623.906, 'duration': 2.62}, {'end': 629.207, 'text': "Okay, let's just say we think in our data set there are gonna be two.", 'start': 626.726, 'duration': 2.481}, {'end': 638.949, 'text': "So for k Gaussians, two in our case, we're going to multiply w, which is the prior probability of the jth Gaussian times,", 'start': 629.547, 'duration': 9.402}, {'end': 642.47, 'text': 'the value that we just looked at up here, right here.', 'start': 638.949, 'duration': 3.521}, {'end': 648.328, 'text': 'where this is the Gaussian distribution of the vector of our data points.', 'start': 644.124, 'duration': 4.204}, {'end': 656.276, 'text': 'And so once we have this value, then we can say we can multiply it by W for each of our Gaussians,', 'start': 648.789, 'duration': 7.487}, {'end': 661.261, 'text': 'and that is gonna give us our probability value X for a given X data point.', 'start': 656.276, 'duration': 4.985}, {'end': 663.823, 'text': 'So this is what it looks like, right.', 'start': 662.362, 'duration': 1.461}, {'end': 669.104, 'text': 'so if we were to plot multiple Gaussian distributions, It would be multiple bell curves,', 'start': 663.823, 'duration': 5.281}, {'end': 675.446, 'text': 'but what we really want is a single continuous Curve that consists of multiple bell curves.', 'start': 669.104, 'duration': 6.342}, {'end': 680.108, 'text': 'and so, once we have that huge continuous curve, Then, given our data point,', 'start': 675.446, 'duration': 4.662}, {'end': 684.73, 'text': "it can tell us the probability that it's going to belong to a specific class.", 'start': 680.108, 'duration': 4.622}, {'end': 687.021, 'text': 'okay, and so What class??', 'start': 684.73, 'duration': 2.291}, {'end': 690.184, 'text': 'How do you tell what class something is given this curve??', 'start': 687.521, 'duration': 2.663}], 'summary': 'Covariance matrix improves accuracy in computing probability for k gaussians.', 'duration': 25.148, 'max_score': 577.136, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg577136.jpg'}], 'start': 84.876, 'title': 'Community empowerment and gaussian distributions', 'summary': 'Explores the community of machine learning enthusiasts making an impact in global warming and public health, growing at a rate of 500 to 800 subscribers per day. additionally, it introduces gaussian distributions, explaining their representation of data patterns through bell curves, and delves into gaussian mixture models handling data with multiple peaks and features.', 'chapters': [{'end': 223.607, 'start': 84.876, 'title': 'Community empowerment through machine learning', 'summary': 'Highlights the amazing community of machine learning enthusiasts, detailing their impactful work in areas such as global warming and public health, while also emphasizing the exponential growth of the community at a rate of 500 to 800 subscribers per day.', 'duration': 138.731, 'highlights': ['The community comprises individuals making significant contributions, such as those working on global warming and creating apps with 500,000 plus users to combat smoking.', 'The community is growing at a remarkable rate of 500 to 800 subscribers per day, with startups being built in the Slack channel.', 'Siraj expresses his excitement and inspiration from meeting the community in person, emphasizing their role as the real change makers and his dedication to meeting them globally, including an upcoming trip to India.']}, {'end': 748.802, 'start': 223.907, 'title': 'Understanding gaussian distributions and mixture models', 'summary': 'Introduces gaussian distributions, explaining how they represent data patterns through bell curves, and delves into gaussian mixture models, illustrating how they handle data with multiple peaks and features.', 'duration': 524.895, 'highlights': ['Gaussian distributions represent data patterns with a bell curve, using mean and standard deviation to define the center and spread of the curve respectively. Gaussian distributions are characterized by a bell curve, defined by the mean and standard deviation, providing a convenient representation for data patterns.', "Gaussian mixture models are used for data with multiple peaks, employing a probability distribution consisting of multiple Gaussian distributions based on the number of features in the dataset. Gaussian mixture models are designed for data exhibiting multiple peaks, utilizing a probability distribution comprising multiple Gaussian distributions, with the number of features determining the model's structure.", 'The covariance matrix is utilized in Gaussian mixture models to measure the relationship between variables, providing a better result than standard deviation especially when dealing with more dimensions. In Gaussian mixture models, the covariance matrix gauges the interrelationship between variables, offering improved accuracy in multi-dimensional scenarios compared to standard deviation.']}], 'duration': 663.926, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg84876.jpg', 'highlights': ['The community is growing at a remarkable rate of 500 to 800 subscribers per day, with startups being built in the Slack channel.', 'The community comprises individuals making significant contributions, such as those working on global warming and creating apps with 500,000 plus users to combat smoking.', 'Siraj expresses his excitement and inspiration from meeting the community in person, emphasizing their role as the real change makers and his dedication to meeting them globally, including an upcoming trip to India.', 'Gaussian mixture models are used for data with multiple peaks, employing a probability distribution consisting of multiple Gaussian distributions based on the number of features in the dataset.', 'Gaussian distributions represent data patterns with a bell curve, using mean and standard deviation to define the center and spread of the curve respectively.', 'The covariance matrix is utilized in Gaussian mixture models to measure the relationship between variables, providing a better result than standard deviation especially when dealing with more dimensions.']}, {'end': 1093.948, 'segs': [{'end': 820.518, 'src': 'embed', 'start': 750.905, 'weight': 0, 'content': [{'end': 762.594, 'text': "And so the problem that we're trying to solve here with the GMM is given a set of data points X let's draw from an unknown distribution which we're going to assume intuitively is a Gaussian mixture model,", 'start': 750.905, 'duration': 11.689}, {'end': 765.857, 'text': 'that is, that the data set consists of multiple Gaussians.', 'start': 762.594, 'duration': 3.263}, {'end': 771.741, 'text': "estimate the parameters, Theta, which consists of the mean and other values that we'll talk about,", 'start': 765.857, 'duration': 5.884}, {'end': 778.126, 'text': 'of the GMM model that fits that data and the solution, the way we find these, these parameters of our model,', 'start': 771.741, 'duration': 6.385}, {'end': 786.612, 'text': 'which is what machine learning is all about, mathematical optimization is by maximizing the likelihood P of X, the probability of X,', 'start': 778.126, 'duration': 8.486}, {'end': 795.139, 'text': 'given our parameters and X is the data point that we want to predict, the probability, the class We want to maximize,', 'start': 786.612, 'duration': 8.527}, {'end': 799.543, 'text': 'the likelihood that X belongs to a particular class.', 'start': 795.139, 'duration': 4.404}, {'end': 806.329, 'text': 'The way we do that is to compute the maximum likelihood estimate, which is this equation right here.', 'start': 800.704, 'duration': 5.625}, {'end': 811.154, 'text': 'We want to find the maximum probability value for a given class.', 'start': 806.649, 'duration': 4.505}, {'end': 817.74, 'text': 'That is, we want to find the class that this data point X is the most likely to be a part of.', 'start': 811.474, 'duration': 6.266}, {'end': 820.518, 'text': 'and so notice how.', 'start': 819.437, 'duration': 1.081}], 'summary': 'Using gmm to estimate parameters of gaussian mixture model for given data points.', 'duration': 69.613, 'max_score': 750.905, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg750905.jpg'}, {'end': 870.649, 'src': 'embed', 'start': 841.585, 'weight': 3, 'content': [{'end': 846.729, 'text': 'It uses the same optimization strategy, which is the expectation maximization algorithm.', 'start': 841.585, 'duration': 5.144}, {'end': 853.914, 'text': "It's similar to k-means in that k-means finds k to minimize x minus the mean squared.", 'start': 847.189, 'duration': 6.725}, {'end': 861.56, 'text': 'But the Gaussian mixture model finds k to minimize x minus the mean squared over the standard deviation, over.', 'start': 854.275, 'duration': 7.285}, {'end': 870.649, 'text': 'And the reason that we add the standard deviation into the mix is because the denominator, the standard deviation squared,', 'start': 862.541, 'duration': 8.108}], 'summary': 'Both em algorithm and k-means optimize using different criteria. gmm minimizes x minus mean squared over standard deviation.', 'duration': 29.064, 'max_score': 841.585, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg841585.jpg'}, {'end': 1005.232, 'src': 'heatmap', 'start': 914.896, 'weight': 4, 'content': [{'end': 916.497, 'text': 'It could be a part of multiple distributions.', 'start': 914.896, 'duration': 1.601}, {'end': 923.101, 'text': 'It could be in the middle, It could be 60% likely this class, but 40% likely this class, not just class a.', 'start': 916.557, 'duration': 6.544}, {'end': 929.144, 'text': "and so that's why we incorporate, That's why we incorporate the standard deviation.", 'start': 923.101, 'duration': 6.043}, {'end': 932.738, 'text': 'so So how is this thing optimized?', 'start': 929.144, 'duration': 3.594}, {'end': 936.7, 'text': "Well, it's optimized using the expectation maximization algorithm.", 'start': 933.058, 'duration': 3.642}, {'end': 945.004, 'text': 'So the basic ideas of the EM algorithm are to introduce a hidden variable such that its knowledge would simplify the maximization of the likelihood.', 'start': 937.02, 'duration': 7.984}, {'end': 948.465, 'text': 'So we pick some random data points, right? We pick some random data points.', 'start': 945.324, 'duration': 3.141}, {'end': 951.127, 'text': 'We draw a distribution around that data point.', 'start': 948.806, 'duration': 2.321}, {'end': 967.804, 'text': "we then update our parameters using that generated distribution and then we repeat the process and every time we draw a new data point it's going to be closer and closer to the data point that best fits the data set that we have,", 'start': 951.627, 'duration': 16.177}, {'end': 972.77, 'text': 'such that if we were to draw a distribution around that data point, it would fit that data set the best.', 'start': 967.804, 'duration': 4.966}, {'end': 975.152, 'text': 'And so there are two steps.', 'start': 974.051, 'duration': 1.101}, {'end': 982.778, 'text': "There's the E step, the expectation step, and the expectation step is to estimate the distribution of the hidden variable,", 'start': 975.452, 'duration': 7.326}, {'end': 986.2, 'text': 'given the data and the current value of the parameters.', 'start': 982.778, 'duration': 3.422}, {'end': 995.327, 'text': 'And then the M step, the maximization step, is to maximize the joint distribution of the data and the hidden variable.', 'start': 986.7, 'duration': 8.627}, {'end': 1001.85, 'text': "That's the high level, and we're going to talk about the implementation details in the code.", 'start': 997.208, 'duration': 4.642}, {'end': 1005.232, 'text': 'But you might be thinking, well, wait a second, wait a second.', 'start': 1002.351, 'duration': 2.881}], 'summary': 'Using the expectation maximization algorithm, data points are optimized by updating parameters and estimating distributions.', 'duration': 90.336, 'max_score': 914.896, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg914896.jpg'}, {'end': 1073.712, 'src': 'embed', 'start': 1045.397, 'weight': 5, 'content': [{'end': 1047.961, 'text': "But what if you can't compute a gradient?", 'start': 1045.397, 'duration': 2.564}, {'end': 1050.223, 'text': "What if you can't compute a derivative?", 'start': 1047.981, 'duration': 2.242}, {'end': 1055.36, 'text': "Can't compute a derivative of a random variable?", 'start': 1052.518, 'duration': 2.842}, {'end': 1060.243, 'text': 'right, this, this Gaussian mixture model has a random variable.', 'start': 1055.36, 'duration': 4.883}, {'end': 1064.105, 'text': 'It is a stochastic model, that is, it is non deterministic.', 'start': 1060.243, 'duration': 3.862}, {'end': 1067.167, 'text': "you can't compute the derivative of a random variable.", 'start': 1064.105, 'duration': 3.062}, {'end': 1069.948, 'text': "that's why we're not using gradient descent in this case.", 'start': 1067.167, 'duration': 2.781}, {'end': 1073.712, 'text': "because You can't compute the derivative of a random variable.", 'start': 1069.948, 'duration': 3.764}], 'summary': "In stochastic models, like the gaussian mixture model, gradient descent isn't used due to the inability to compute the derivative of random variables.", 'duration': 28.315, 'max_score': 1045.397, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1045396.jpg'}], 'start': 750.905, 'title': 'Gaussian mixture model', 'summary': 'Explains the process of estimating parameters for a gaussian mixture model (gmm) to fit a dataset consisting of multiple gaussians and uses the expectation maximization algorithm to find k to minimize x - mean squared over standard deviation, providing a soft assignment with continuous output and introduces the hidden variable to simplify the maximization of the likelihood.', 'chapters': [{'end': 820.518, 'start': 750.905, 'title': 'Gaussian mixture model estimation', 'summary': 'Explains the process of estimating parameters for a gaussian mixture model (gmm) to fit a dataset consisting of multiple gaussians by maximizing the likelihood of data points belonging to a particular class through mathematical optimization.', 'duration': 69.613, 'highlights': ['The process aims to estimate the parameters of the GMM model, including the mean and other values, that best fit the data set consisting of multiple Gaussians.', 'The solution involves maximizing the likelihood of data points belonging to a particular class by computing the maximum likelihood estimate, which is achieved through mathematical optimization.', 'The chapter emphasizes the importance of mathematical optimization in machine learning to find the maximum probability value for a given class.']}, {'end': 1093.948, 'start': 820.518, 'title': 'Gaussian mixture model', 'summary': 'Explains how the gaussian mixture model uses the expectation maximization algorithm to find k to minimize x - mean squared over standard deviation, providing a soft assignment with continuous output and introduces the hidden variable to simplify the maximization of the likelihood.', 'duration': 273.43, 'highlights': ['The Gaussian Mixture Model uses the expectation maximization algorithm to find k to minimize x - mean squared over standard deviation, providing a soft assignment with continuous output The Gaussian Mixture Model uses the same optimization strategy as k-means, finding k to minimize x - mean squared over standard deviation, offering a continuous output with a soft assignment, allowing for multiple distributions and probability values.', 'The chapter explains how the Gaussian Mixture Model introduces the hidden variable to simplify the maximization of the likelihood The Gaussian Mixture Model introduces a hidden variable to simplify the maximization of the likelihood, involving the E step to estimate the distribution of the hidden variable and the M step to maximize the joint distribution of the data and the hidden variable.', 'The chapter indicates the limitations of using gradient descent in the Gaussian Mixture Model due to the inability to compute the derivative of a random variable The chapter discusses the limitations of using gradient descent in the Gaussian Mixture Model due to the inability to compute the derivative of a random variable, as it is a stochastic model and non-deterministic.']}], 'duration': 343.043, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg750905.jpg', 'highlights': ['The process aims to estimate the parameters of the GMM model, including the mean and other values, that best fit the data set consisting of multiple Gaussians.', 'The solution involves maximizing the likelihood of data points belonging to a particular class by computing the maximum likelihood estimate, which is achieved through mathematical optimization.', 'The chapter emphasizes the importance of mathematical optimization in machine learning to find the maximum probability value for a given class.', 'The Gaussian Mixture Model uses the expectation maximization algorithm to find k to minimize x - mean squared over standard deviation, providing a soft assignment with continuous output.', 'The Gaussian Mixture Model introduces a hidden variable to simplify the maximization of the likelihood, involving the E step to estimate the distribution of the hidden variable and the M step to maximize the joint distribution of the data and the hidden variable.', 'The chapter discusses the limitations of using gradient descent in the Gaussian Mixture Model due to the inability to compute the derivative of a random variable, as it is a stochastic model and non-deterministic.']}, {'end': 1335.889, 'segs': [{'end': 1191.258, 'src': 'embed', 'start': 1094.588, 'weight': 0, 'content': [{'end': 1095.148, 'text': 'So back to this.', 'start': 1094.588, 'duration': 0.56}, {'end': 1101.87, 'text': 'So when should you use this thing, right? When is this actually useful besides customer churn? Anomaly detection.', 'start': 1095.368, 'duration': 6.502}, {'end': 1108.753, 'text': 'Think about any case where you are trying to cluster data, where you are trying to classify data that does not have labels.', 'start': 1101.93, 'duration': 6.823}, {'end': 1113.374, 'text': 'So one use case is trying to track an object in a video frame right?', 'start': 1109.193, 'duration': 4.181}, {'end': 1121.377, 'text': "If you know the moving object's distribution in the first frame, we can localize the object in the next frames by tracking its distribution.", 'start': 1113.774, 'duration': 7.603}, {'end': 1122.277, 'text': 'That is, you know,', 'start': 1121.417, 'duration': 0.86}, {'end': 1131.159, 'text': 'kind of the probability distribution of all the possible ways that the subject can move and based on that you can create a bounding box around the subject,', 'start': 1122.277, 'duration': 8.882}, {'end': 1136.141, 'text': "such that in the next frame it's very likely that that subject's movement will fit into the bounding box.", 'start': 1131.159, 'duration': 4.982}, {'end': 1146.148, 'text': 'I have some related repositories here for using TensorFlow and a Gaussian mixture model to classify song lyrics by genre.', 'start': 1136.801, 'duration': 9.347}, {'end': 1148.49, 'text': 'Very cool use case using TensorFlow.', 'start': 1146.489, 'duration': 2.001}, {'end': 1149.751, 'text': 'Definitely check it out.', 'start': 1148.89, 'duration': 0.861}, {'end': 1151.873, 'text': "It's called Word to Gaussian Mixture.", 'start': 1149.811, 'duration': 2.062}, {'end': 1152.853, 'text': 'Very cool.', 'start': 1152.273, 'duration': 0.58}, {'end': 1153.554, 'text': 'Check that out.', 'start': 1152.914, 'duration': 0.64}, {'end': 1155.476, 'text': "It's got some great instructions.", 'start': 1154.134, 'duration': 1.342}, {'end': 1160.559, 'text': "And I've got one more, which is a great general purpose tutorial for Gaussian mixture models.", 'start': 1155.496, 'duration': 5.063}, {'end': 1162.061, 'text': "It's a Jupyter Notebook.", 'start': 1160.619, 'duration': 1.442}, {'end': 1163.542, 'text': 'Definitely check that out as well.', 'start': 1162.461, 'duration': 1.081}, {'end': 1165.944, 'text': "And I've got some great links for you in the description.", 'start': 1163.582, 'duration': 2.362}, {'end': 1169.806, 'text': 'All right? So check that out as well, got the great graphs and everything.', 'start': 1165.964, 'duration': 3.842}, {'end': 1176.87, 'text': "So let's look at this code, okay? So in this code, we're going to import our dependencies and then test out a distribution graph.", 'start': 1169.846, 'duration': 7.024}, {'end': 1183.774, 'text': "Let's just see if we can draw out a distribution orthogonal or unrelated to our data set, just to see if we can do that.", 'start': 1176.91, 'duration': 6.864}, {'end': 1186.535, 'text': "So we're going to import four dependencies here.", 'start': 1184.194, 'duration': 2.341}, {'end': 1191.258, 'text': 'The first one is matplotlib, which is our handy dandy plotting tool.', 'start': 1186.576, 'duration': 4.682}], 'summary': 'Gaussian mixture models useful for anomaly detection, clustering, and classifying data without labels. tensorflow and jupyter notebook tutorials available.', 'duration': 96.67, 'max_score': 1094.588, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1094588.jpg'}, {'end': 1239.281, 'src': 'embed', 'start': 1212.435, 'weight': 4, 'content': [{'end': 1216.158, 'text': 'Okay, so once we have our four dependencies, we can go ahead and start this.', 'start': 1212.435, 'duration': 3.723}, {'end': 1221.876, 'text': 'So, The first step is for us to plot out a Gaussian distribution.', 'start': 1216.519, 'duration': 5.357}, {'end': 1223.937, 'text': "Let's just see if we can do that first.", 'start': 1221.916, 'duration': 2.021}, {'end': 1233.18, 'text': "so we've got, Let's just say we're going to use NumPy's Lin space function to return an evenly spaced set of numbers over a specified interval,", 'start': 1223.937, 'duration': 9.243}, {'end': 1235.76, 'text': 'Which is a negative 10 to 10.', 'start': 1233.18, 'duration': 2.58}, {'end': 1239.281, 'text': 'we have a thousand of these data points that we want to generate and then look at.', 'start': 1235.76, 'duration': 3.521}], 'summary': "Plot gaussian distribution using numpy's lin space function with 1000 data points", 'duration': 26.846, 'max_score': 1212.435, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1212435.jpg'}, {'end': 1325.284, 'src': 'embed', 'start': 1299.692, 'weight': 5, 'content': [{'end': 1307.957, 'text': "It's a CSV file, and we can read it into a pandas data frame object, which is very easy to manipulate in memory once we have it there.", 'start': 1299.692, 'duration': 8.265}, {'end': 1310.138, 'text': 'And we wanna show the first five examples.', 'start': 1308.297, 'duration': 1.841}, {'end': 1312.295, 'text': 'And here we are.', 'start': 1311.755, 'duration': 0.54}, {'end': 1316.458, 'text': 'We have the first five examples, okay? So each of these are users.', 'start': 1312.656, 'duration': 3.802}, {'end': 1325.284, 'text': 'Each of these are different players, and the amount that that player has spent in a given month, this month, in Bitcoin, okay? In Bitcoin.', 'start': 1316.578, 'duration': 8.706}], 'summary': 'Csv file read into pandas dataframe, showing first 5 user examples with bitcoin spending data.', 'duration': 25.592, 'max_score': 1299.692, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1299692.jpg'}], 'start': 1094.588, 'title': 'Gaussian mixture models and data distribution', 'summary': 'Discusses the application of gaussian mixture models for anomaly detection and object tracking, along with examples of classifying song lyrics by genre. it also covers data distribution, gaussian plotting using numpy, and analyzing user spending in bitcoin.', 'chapters': [{'end': 1169.806, 'start': 1094.588, 'title': 'Anomaly detection and object tracking with gaussian mixture models', 'summary': 'Discusses the usefulness of gaussian mixture models for anomaly detection and object tracking in unlabelled data, along with examples of classifying song lyrics by genre using tensorflow with gaussian mixture model.', 'duration': 75.218, 'highlights': ['Gaussian mixture models are useful for anomaly detection, clustering, and classifying data without labels, such as tracking objects in video frames.', 'Tracking an object in a video frame involves localizing the object in the next frames based on its probability distribution, allowing the creation of a bounding box around the subject for predicting its movement.', 'Example of using TensorFlow and Gaussian mixture model for classifying song lyrics by genre, known as Word to Gaussian Mixture, is highlighted as a cool use case.', 'A general purpose tutorial for Gaussian mixture models is available as a Jupyter Notebook, providing comprehensive instructions and great graphs.']}, {'end': 1335.889, 'start': 1169.846, 'title': 'Data distribution and gaussian plotting', 'summary': 'Discusses importing dependencies for plotting, generating a gaussian distribution using numpy, and reading and displaying a dataset of user spending in bitcoin.', 'duration': 166.043, 'highlights': ["Generating a Gaussian distribution using NumPy's Lin space function with a thousand data points over the interval of -10 to 10, and plotting it with matplotlib. The chapter demonstrates the process of generating a Gaussian distribution with a thousand data points using NumPy's Lin space function over the interval of -10 to 10, and then plotting it using matplotlib.", 'Importing a dataset into a pandas data frame and displaying the first five examples of user spending in Bitcoin. The chapter explains the process of importing a dataset into a pandas data frame and displaying the first five examples of user spending in Bitcoin, providing insight into user transactions.', 'Importing dependencies including matplotlib, numpy, Psi Pi, and Seaborn for plotting and data normalization. The chapter emphasizes the import of essential dependencies such as matplotlib, numpy, Psi Pi, and Seaborn for the purpose of plotting and data normalization, enabling efficient data analysis and visualization.']}], 'duration': 241.301, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1094588.jpg', 'highlights': ['Gaussian mixture models are useful for anomaly detection, clustering, and classifying data without labels, such as tracking objects in video frames.', 'Example of using TensorFlow and Gaussian mixture model for classifying song lyrics by genre, known as Word to Gaussian Mixture, is highlighted as a cool use case.', 'Tracking an object in a video frame involves localizing the object in the next frames based on its probability distribution, allowing the creation of a bounding box around the subject for predicting its movement.', 'A general purpose tutorial for Gaussian mixture models is available as a Jupyter Notebook, providing comprehensive instructions and great graphs.', "Generating a Gaussian distribution using NumPy's Lin space function with a thousand data points over the interval of -10 to 10, and plotting it with matplotlib.", 'Importing a dataset into a pandas data frame and displaying the first five examples of user spending in Bitcoin.', 'Importing dependencies including matplotlib, numpy, Psi Pi, and Seaborn for plotting and data normalization.']}, {'end': 1794.871, 'segs': [{'end': 1368.653, 'src': 'embed', 'start': 1335.889, 'weight': 0, 'content': [{'end': 1337.45, 'text': "But the idea is that that's it, that's.", 'start': 1335.889, 'duration': 1.561}, {'end': 1339.15, 'text': "we've got one feature.", 'start': 1337.45, 'duration': 1.7}, {'end': 1346.113, 'text': "So it's a one-dimensional problem, and we're gonna write out a probability distribution for that single feature.", 'start': 1339.15, 'duration': 6.963}, {'end': 1348.614, 'text': 'And if we do that, if we do that,', 'start': 1346.113, 'duration': 2.501}, {'end': 1356.376, 'text': "then we're going to be able to predict the class of a given user based on how much this person this user has either spent or withdrawn,", 'start': 1348.614, 'duration': 7.762}, {'end': 1361.806, 'text': "whether or not they're going to turn or not.", 'start': 1356.376, 'duration': 5.43}, {'end': 1368.653, 'text': "okay. so That's our data set and now we're going to show the distribution of the data as a histogram.", 'start': 1361.806, 'duration': 6.847}], 'summary': 'Creating a probability distribution for a single feature to predict user behavior.', 'duration': 32.764, 'max_score': 1335.889, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1335889.jpg'}, {'end': 1417.588, 'src': 'heatmap', 'start': 1395.573, 'weight': 0.71, 'content': [{'end': 1409.182, 'text': "Distplot Okay, so that's the histogram of our data, right? For all of those number of players, this is what it looks like.", 'start': 1395.573, 'duration': 13.609}, {'end': 1417.588, 'text': 'So we could look at this and we could say, oh, okay, so it looks like one Gaussian might fit this, but two looks better.', 'start': 1409.202, 'duration': 8.386}], 'summary': 'Histogram of player data shows potential fit for two gaussians.', 'duration': 22.015, 'max_score': 1395.573, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1395573.jpg'}, {'end': 1493.945, 'src': 'embed', 'start': 1450.106, 'weight': 1, 'content': [{'end': 1459.631, 'text': 'The first four are the mean and the standard deviation for each of those distributions one and two and the fifth one is the probability of Choosing one of them.', 'start': 1450.106, 'duration': 9.525}, {'end': 1463.053, 'text': "and so the way we're going to write out this Gaussian mixture model,", 'start': 1459.631, 'duration': 3.422}, {'end': 1471.857, 'text': 'where theta equals those four values and the probability of choosing one of them W is Just like this,', 'start': 1463.053, 'duration': 8.804}, {'end': 1478.02, 'text': 'and this is the probability density function for a Gaussian mixture model Consisting of two Gaussians.', 'start': 1471.857, 'duration': 6.163}, {'end': 1485.063, 'text': 'now we looked at the probability density function for a single Gaussian, And it looks like this right here,', 'start': 1478.02, 'duration': 7.043}, {'end': 1489.265, 'text': 'and this is what it looks like for two distributions.', 'start': 1485.063, 'duration': 4.202}, {'end': 1491.704, 'text': 'right, right, we get it so far.', 'start': 1489.265, 'duration': 2.439}, {'end': 1493.205, 'text': "so now we're going to fit this model.", 'start': 1491.704, 'duration': 1.501}, {'end': 1493.945, 'text': "that's our model.", 'start': 1493.205, 'duration': 0.74}], 'summary': 'Gaussian mixture model with four values, w probability, and two gaussians for fitting the model.', 'duration': 43.839, 'max_score': 1450.106, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1450106.jpg'}, {'end': 1583.291, 'src': 'heatmap', 'start': 1528.14, 'weight': 0.812, 'content': [{'end': 1534.645, 'text': 'We first perform E, which is to update our variables, and then M, which is to update the hypothesis.', 'start': 1528.14, 'duration': 6.505}, {'end': 1541.349, 'text': 'What do I mean? Well, this is an iterative method for finding the MLE that estimates the parameters in statistical models.', 'start': 1534.685, 'duration': 6.664}, {'end': 1547.455, 'text': 'So we start with some initial values, perform the expectation step, then the maximization step,', 'start': 1541.81, 'duration': 5.645}, {'end': 1554.663, 'text': "check if it's converged or not by some threshold that we define and if it hasn't continue iteratively and if it has stop.", 'start': 1547.455, 'duration': 7.208}, {'end': 1562.257, 'text': 'In the expectation step, given the current parameters of the model, estimate a probability distribution.', 'start': 1556.633, 'duration': 5.624}, {'end': 1568.501, 'text': 'Maximization step, given the current data, estimate the parameters to update the model and repeat.', 'start': 1562.757, 'duration': 5.744}, {'end': 1576.726, 'text': 'So, more formally, using the current estimates for the parameters, create a function for the expectation of the log likelihood.', 'start': 1569.041, 'duration': 7.685}, {'end': 1583.291, 'text': 'And then for maximization, compute the parameters maximizing the expected log likelihood found on the E-step.', 'start': 1577.387, 'duration': 5.904}], 'summary': 'Iterative method for finding mle estimates parameters in statistical models.', 'duration': 55.151, 'max_score': 1528.14, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1528140.jpg'}, {'end': 1562.257, 'src': 'embed', 'start': 1534.685, 'weight': 3, 'content': [{'end': 1541.349, 'text': 'What do I mean? Well, this is an iterative method for finding the MLE that estimates the parameters in statistical models.', 'start': 1534.685, 'duration': 6.664}, {'end': 1547.455, 'text': 'So we start with some initial values, perform the expectation step, then the maximization step,', 'start': 1541.81, 'duration': 5.645}, {'end': 1554.663, 'text': "check if it's converged or not by some threshold that we define and if it hasn't continue iteratively and if it has stop.", 'start': 1547.455, 'duration': 7.208}, {'end': 1562.257, 'text': 'In the expectation step, given the current parameters of the model, estimate a probability distribution.', 'start': 1556.633, 'duration': 5.624}], 'summary': 'Iterative method for finding mle estimates parameters in statistical models', 'duration': 27.572, 'max_score': 1534.685, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1534685.jpg'}, {'end': 1744.844, 'src': 'embed', 'start': 1718.293, 'weight': 4, 'content': [{'end': 1726.978, 'text': 'The M step is to modify the parameters according to the hidden variable to maximize the likelihood of the data and the hidden variable.', 'start': 1718.293, 'duration': 8.685}, {'end': 1728.575, 'text': "And that's it.", 'start': 1728.035, 'duration': 0.54}, {'end': 1734.278, 'text': 'and so, every time we do that, these Gaussian curves, these Gaussian distributions,', 'start': 1728.575, 'duration': 5.703}, {'end': 1742.943, 'text': 'these clusters are going to be more and more optimal to fit the data where they need to, to classify, to distinguish between classes.', 'start': 1734.278, 'duration': 8.665}, {'end': 1744.844, 'text': 'So back to our data.', 'start': 1744.103, 'duration': 0.741}], 'summary': 'M step modifies parameters to maximize data likelihood and improve clustering.', 'duration': 26.551, 'max_score': 1718.293, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1718293.jpg'}], 'start': 1335.889, 'title': 'Gaussian mixture model and expectation maximization algorithm', 'summary': 'Discusses the use of a gaussian mixture model with two distributions to classify users based on spending behavior, with five parameters for mean, standard deviation, and probability. it also covers the expectation maximization algorithm, a two-step iterative method for estimating parameters in statistical models, involving e-step and m-step to update variables and hypothesis.', 'chapters': [{'end': 1493.945, 'start': 1335.889, 'title': 'Gaussian mixture model for user classification', 'summary': 'Explains the use of a gaussian mixture model with two distributions to predict the class of a user based on their spending or withdrawal behavior, and the model consists of five parameters for mean, standard deviation, and probability of choosing one distribution.', 'duration': 158.056, 'highlights': ['The chapter explains the use of a Gaussian mixture model with two distributions to predict the class of a user based on their spending or withdrawal behavior The model aims to predict the class of a user based on their spending or withdrawal behavior, using a Gaussian mixture model with two distributions.', 'The model consists of five parameters for mean, standard deviation, and probability of choosing one distribution The Gaussian mixture model consists of five parameters: four for the mean and standard deviation of each distribution, and one for the probability of choosing one distribution.', 'The chapter demonstrates the probability density function for a Gaussian mixture model consisting of two Gaussians The chapter illustrates the probability density function for a Gaussian mixture model with two Gaussians, highlighting the difference from a single Gaussian distribution.']}, {'end': 1794.871, 'start': 1493.945, 'title': 'Expectation maximization algorithm', 'summary': 'Explains the expectation maximization algorithm, a two-step iterative method for finding the mle that estimates the parameters in statistical models, involving e-step to update variables and m-step to update the hypothesis, ultimately maximizing the likelihood of the data and hidden variable through a stochastic model.', 'duration': 300.926, 'highlights': ['The chapter explains the Expectation Maximization algorithm, a two-step iterative method for finding the MLE that estimates the parameters in statistical models. It involves performing E-step to update variables and M-step to update the hypothesis.', 'The M-step is to modify the parameters according to the hidden variable to maximize the likelihood of the data and the hidden variable. This step involves modifying the parameters to maximize the likelihood of the data and hidden variable.', 'Involves computing the probability density function programmatically and updating the Gaussian distributions to be more optimal to fit the data. It entails computing the probability density function programmatically and updating Gaussian distributions to be more optimal to fit the data.']}], 'duration': 458.982, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1335889.jpg', 'highlights': ['The chapter explains the use of a Gaussian mixture model with two distributions to predict the class of a user based on their spending or withdrawal behavior', 'The model consists of five parameters for mean, standard deviation, and probability of choosing one distribution', 'The chapter demonstrates the probability density function for a Gaussian mixture model consisting of two Gaussians', 'The chapter explains the Expectation Maximization algorithm, a two-step iterative method for finding the MLE that estimates the parameters in statistical models', 'The M-step is to modify the parameters according to the hidden variable to maximize the likelihood of the data and the hidden variable', 'Involves computing the probability density function programmatically and updating the Gaussian distributions to be more optimal to fit the data']}, {'end': 2285.438, 'segs': [{'end': 1899.71, 'src': 'heatmap', 'start': 1820.514, 'weight': 0, 'content': [{'end': 1821.835, 'text': "We don't really need it.", 'start': 1820.514, 'duration': 1.321}, {'end': 1828.126, 'text': 'but if we were to plot out this Gaussian, very easy.', 'start': 1821.835, 'duration': 6.291}, {'end': 1830.769, 'text': "it's a single Gaussian, but it's not well fit to the data.", 'start': 1828.126, 'duration': 2.643}, {'end': 1831.81, 'text': 'we want two of them right?', 'start': 1830.769, 'duration': 1.041}, {'end': 1838.256, 'text': "So we're gonna keep going here, and this is where the expectation maximization algorithm comes into play.", 'start': 1832.27, 'duration': 5.986}, {'end': 1844.668, 'text': 'So, First, we randomly assign k cluster centers.', 'start': 1838.736, 'duration': 5.932}, {'end': 1851.534, 'text': 'In our case, k are the number of Gaussians, right? Not k means k where they are the number of Gaussians, two.', 'start': 1844.949, 'duration': 6.585}, {'end': 1857.539, 'text': 'And then we iteratively refine these clusters, or bell curves, based on the two steps.', 'start': 1852.095, 'duration': 5.444}, {'end': 1863.585, 'text': 'For the expectation step, we assign each data point x to both clusters, the probability with the following probability.', 'start': 1857.579, 'duration': 6.006}, {'end': 1871.812, 'text': 'And the maximization step is to estimate, to create an estimation of the model parameters given those probabilities.', 'start': 1864.225, 'duration': 7.587}, {'end': 1878.218, 'text': 'And then repeat them such that the probabilities are maximized for each class.', 'start': 1872.172, 'duration': 6.046}, {'end': 1882.445, 'text': "So then we'll create a class for our Gaussian mixture model.", 'start': 1879.744, 'duration': 2.701}, {'end': 1886.306, 'text': "We've already created a class for our Gaussian, but here's for our Gaussian mixture model.", 'start': 1882.465, 'duration': 3.841}, {'end': 1893.268, 'text': "So for a mixture model where there are two Gaussians, we don't just need one mean and one standard deviation.", 'start': 1886.646, 'duration': 6.622}, {'end': 1894.428, 'text': 'We need four.', 'start': 1893.668, 'duration': 0.76}, {'end': 1899.71, 'text': 'In fact, we need five parameters, right? We need the mean and the standard deviation for one Gaussian.', 'start': 1894.628, 'duration': 5.082}], 'summary': 'Using em algorithm to fit a gaussian mixture model with two gaussians, needing five parameters.', 'duration': 43.071, 'max_score': 1820.514, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1820514.jpg'}, {'end': 1911.957, 'src': 'embed', 'start': 1886.646, 'weight': 3, 'content': [{'end': 1893.268, 'text': "So for a mixture model where there are two Gaussians, we don't just need one mean and one standard deviation.", 'start': 1886.646, 'duration': 6.622}, {'end': 1894.428, 'text': 'We need four.', 'start': 1893.668, 'duration': 0.76}, {'end': 1899.71, 'text': 'In fact, we need five parameters, right? We need the mean and the standard deviation for one Gaussian.', 'start': 1894.628, 'duration': 5.082}, {'end': 1902.61, 'text': 'We need the mean and the standard deviation for the second Gaussian.', 'start': 1899.93, 'duration': 2.68}, {'end': 1904.531, 'text': 'And we need our data set.', 'start': 1903.13, 'duration': 1.401}, {'end': 1911.957, 'text': 'as well as the mix, which is the initial W value.', 'start': 1906.072, 'duration': 5.885}], 'summary': 'A mixture model with two gaussians requires five parameters: two means, two standard deviations, and an initial w value.', 'duration': 25.311, 'max_score': 1886.646, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1886646.jpg'}, {'end': 2158.891, 'src': 'embed', 'start': 2134.505, 'weight': 4, 'content': [{'end': 2142.076, 'text': 'Notice how our means and our standard deviations and our weight values the fifth parameter are all being updated every time.', 'start': 2134.505, 'duration': 7.571}, {'end': 2145.5, 'text': 'And that is the expectation maximization process.', 'start': 2142.236, 'duration': 3.264}, {'end': 2149.426, 'text': "And so once we've done that, then we can look at the mixture.", 'start': 2145.921, 'duration': 3.505}, {'end': 2155.25, 'text': 'What does it look like? And so this is the end result, right? This is the end result.', 'start': 2149.446, 'duration': 5.804}, {'end': 2158.891, 'text': 'So we have one distribution to rule them all, Lord of the Rings style.', 'start': 2155.31, 'duration': 3.581}], 'summary': 'Expectation maximization process updates parameters, resulting in one distribution.', 'duration': 24.386, 'max_score': 2134.505, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg2134505.jpg'}, {'end': 2201.405, 'src': 'embed', 'start': 2179.006, 'weight': 1, 'content': [{'end': 2187.615, 'text': 'And if we had more features, we could turn this into a clustering problem with circles, which would make it a lot easier to look at.', 'start': 2179.006, 'duration': 8.609}, {'end': 2192.578, 'text': "Okay, so what have we learned here? Let's summarize a little bit about what we've learned.", 'start': 2189.215, 'duration': 3.363}, {'end': 2199.364, 'text': 'Gaussian mixture models take our old friend the Gaussian and add other Gaussians, right, plural sometimes.', 'start': 2192.918, 'duration': 6.446}, {'end': 2201.405, 'text': "We could have up to as many as we'd like.", 'start': 2199.384, 'duration': 2.021}], 'summary': 'Gaussian mixture models can add multiple gaussians, making clustering easier.', 'duration': 22.399, 'max_score': 2179.006, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg2179006.jpg'}], 'start': 1795.311, 'title': 'Gaussian mixture models', 'summary': "Explores the expectation maximization algorithm to refine clusters, estimating model parameters for a mixture of gaussians, requiring four means and standard deviations for two gaussians, and provides an overview of the model's predictive capability for handling complex data.", 'chapters': [{'end': 1980.666, 'start': 1795.311, 'title': 'Gaussian mixture model', 'summary': 'Explores the expectation maximization algorithm to iteratively refine clusters, assigning data points to clusters based on probabilities and estimating model parameters, aiming to converge for a mixture of gaussians, with a requirement of four means and standard deviations for two gaussians, and an initial w value.', 'duration': 185.355, 'highlights': ['The expectation maximization algorithm is used to iteratively refine clusters, assigning data points to clusters based on probabilities and estimating model parameters for a mixture of Gaussians, requiring four means and standard deviations for two Gaussians, and an initial W value.', 'The process involves randomly assigning k cluster centers (where k is the number of Gaussians, in this case, two) and then iteratively refining these clusters based on the expectation and maximization steps.', 'For a mixture model with two Gaussians, four means and standard deviations are required, along with the initial W value, which defines how mixed the distributions are and is updated over time.', 'After initializing the assignments and parameters, the chapter explains that the process alternates between the expectation and maximization steps until the estimates converge, similar to convergence in k-means clustering.']}, {'end': 2285.438, 'start': 1981.046, 'title': 'Gaussian mixture models overview', 'summary': "Provides an overview of gaussian mixture models, explaining the expectation maximization algorithm, the training process, and the predictive capability, highlighting the model's ability to handle complex data with multiple peaks and valleys.", 'duration': 304.392, 'highlights': ['Gaussian mixture models enable modeling complex data with multiple peaks and valleys Gaussian mixture models allow for the addition of multiple Gaussians, enabling the modeling of complex data with multiple peaks and valleys, providing a more flexible approach to data representation.', 'Explanation of the expectation maximization algorithm for fitting the model The explanation of the expectation maximization algorithm for fitting the Gaussian mixture model, detailing the iterative process of finding good parameter estimates and the convergence of distributions to fit the data set.', "Training process and predictive capability of the model Insight into the training process of the Gaussian mixture model, including the iterations for maximizing the log likelihood and updating the means, standard deviations, and weight values, as well as the model's predictive capability for new data points."]}], 'duration': 490.127, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/JNlEIEwe-Cg/pics/JNlEIEwe-Cg1795311.jpg', 'highlights': ['The expectation maximization algorithm is used to iteratively refine clusters, assigning data points to clusters based on probabilities and estimating model parameters for a mixture of Gaussians, requiring four means and standard deviations for two Gaussians, and an initial W value.', 'Gaussian mixture models enable modeling complex data with multiple peaks and valleys Gaussian mixture models allow for the addition of multiple Gaussians, enabling the modeling of complex data with multiple peaks and valleys, providing a more flexible approach to data representation.', 'The process involves randomly assigning k cluster centers (where k is the number of Gaussians, in this case, two) and then iteratively refining these clusters based on the expectation and maximization steps.', 'For a mixture model with two Gaussians, four means and standard deviations are required, along with the initial W value, which defines how mixed the distributions are and is updated over time.', 'Explanation of the expectation maximization algorithm for fitting the model The explanation of the expectation maximization algorithm for fitting the Gaussian mixture model, detailing the iterative process of finding good parameter estimates and the convergence of distributions to fit the data set.']}], 'highlights': ['Gaussian mixture models are used for anomaly detection, clustering, and classifying data without labels, such as tracking objects in video frames.', 'The expectation maximization algorithm is used to iteratively refine clusters, assigning data points to clusters based on probabilities and estimating model parameters for a mixture of Gaussians, requiring four means and standard deviations for two Gaussians, and an initial W value.', 'The process involves maximizing the likelihood of data points belonging to a particular class by computing the maximum likelihood estimate, which is achieved through mathematical optimization.', 'The chapter explains the use of a Gaussian mixture model with two distributions to predict the class of a user based on their spending or withdrawal behavior.', 'The community is growing at a remarkable rate of 500 to 800 subscribers per day, with startups being built in the Slack channel.', 'Gaussian mixture models enable modeling complex data with multiple peaks and valleys Gaussian mixture models allow for the addition of multiple Gaussians, enabling the modeling of complex data with multiple peaks and valleys, providing a more flexible approach to data representation.']}