Unsupervised Learning, K Means March 12, 2020 Data Science CSCI - PowerPoint PPT Presentation

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sha1_base64="hwHBCHxlXmNAb1i+1nKjhGPDZ7s=">ACAHicbZDLSgMxFIbP1Fut1EXLtwEi+DGMiOCboSiG5cV7EXaoWTSTBuaZIYkI5RhNr6KGxeKuPUx3Pk2peFtv4Q+PjPOZycP0w408bzvp3C0vLK6lpxvbSxubW94+7uNXScKkLrJOaxaoVYU84krRtmOG0limIRctoMhzfjevORKs1ieW9GCQ0E7ksWMYKNtbruQYiuUCfEKnvI0SkSU27lXbfsVbyJ0CL4MyjDTLWu+9XpxSQVBrCsdZt30tMkGFlGOE0L3VSTRNMhrhP2xYlFlQH2eSAHB1bp4eiWNknDZq4vycyLQeidB2CmwGer42Nv+rtVMTXQYZk0lqCTRVHKkYnROA3UY4oSw0cWMFHM/hWRAVaYGJtZyYbgz5+8CI2ziu9V/LvzcvV6FkcRDuEITsCHC6jCLdSgDgRyeIZXeHOenBfn3fmYthac2cw+/JHz+QOthJUt</latexit> Training with Gradient Descent n ( Y i − ˆ X Y ) 2 = minimize i =1 = ¯ Y − m ¯ b = X Cov ( X, Y ) m = V ar ( X ) 8

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Training with Gradient Descent 12 https://independentseminarblog.com/2018/01/12/moving-below-the-surface-3-gradient-descent-william/

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sha1_base64="q3o/vVOTz7GUx+RiBjGcRGq1f0o=">ACD3icbVDLSgMxFM3UV62vUZdugkVpEctMEXRTKLpx2YJ9SB9DJk3b0CQzJBmhDP0DN/6KGxeKuHXrzr8xbWehrQcu93DOvST3+CGjSjvOt5VaWV1b30hvZra2d3b37P2DugoiUkNByQTR8pwqgNU01I81QEsR9Rhr+6GbqNx6IVDQd3ockg5HA0H7FCNtJM8+rcISbKuIezEtuZNuLCa5e4/Cc5jTdPoJ/Pd4uenXUKzgxwmbgJyYIEFc/+avcCHEiNGZIqZbrhLoTI6kpZmSaUeKhAiP0IC0DBWIE9WJZ/dM4IlRerAfSFNCw5n6eyNGXKkx980kR3qoFr2p+J/XinT/qhNTEUaCDx/qB8xqAM4DQf2qCRYs7EhCEtq/grxEmEtYkwY0JwF09eJvViwXUKbvUiW75O4kiDI3AMcsAFl6AMbkEF1AGj+AZvI368l6sd6tj/loykp2DsEfWJ8/aLmZsg=</latexit> Training with Gradient Descent Helpful equations for following along in the jupyter notebook n X ( Y i − ( mX i + b )) 2 Q = i =1 n ∂ Q X ∂ b = − 2( Y i − mX i − b ) = 0 i =1 n ∂ Q X ∂ m = − 2 X i ( Y i − b − mX i ) = 0 i =1 = Cov ( X, Y ) b = ¯ Y − m ¯ m = X V ar ( X ) 13 https://independentseminarblog.com/2018/01/12/moving-below-the-surface-3-gradient-descent-william/

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 14

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 15

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 16

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 17

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 18

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 19

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 20

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption Today • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 21

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption Today • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 22

Supervised vs. Unsupervised Learning • Supervised: Explicit data labels • Sentiment analysis—review text -> star ratings • Image tagging—image -> caption Tuesday • Unsupervised: No explicit labels • Clustering—find groups similar customers • Dimensionality Reduction—find features that differentiate individuals 23

Oh you thought it was that simple? How cute… • Semi Supervised—Combining large amounts of unlabelled with smaller amounts of labelled (pretraining) • Weakly/Distantly Supervised—using noisy labels or partial labels (bootstrapping, automatically-labeled data) • Reinforcement Learning—label on the result of a sequence of actions, but not on each action (games, robotics) • “Found” Data… (?) 24

Oh you thought it was that simple? How cute… • Semi Supervised—Combining large amounts of unlabelled with smaller amounts of labelled (pretraining) • Weakly/Distantly Supervised—using noisy labels or partial labels (bootstrapping, automatically-labeled data) • Reinforcement Learning—label on the result of a sequence of actions, but not on each action (games, robotics) • “Found” Data… (?) 25

Oh you thought it was that simple? How cute… • Semi Supervised—Combining large amounts of unlabelled with smaller amounts of labelled (pretraining) • Weakly/Distantly Supervised—using noisy labels or partial labels (bootstrapping, automatically-labeled data) • Reinforcement Learning—label on the result of a sequence of actions, but not on each action (games, robotics) • “Found” Data… (?) 26

Oh you thought it was that simple? How cute… • Semi Supervised—Combining large amounts of unlabelled with smaller amounts of labelled (pretraining) • Weakly/Distantly Supervised—using noisy labels or partial labels (bootstrapping, automatically-labeled data) • Reinforcement Learning—label on the result of a sequence of actions, but not on each action (games, robotics) • “Found” Data… (?) 27

Oh you thought it was that simple? How cute… • Semi Supervised—Combining large amounts of unlabelled with smaller amounts of labelled (pretraining) • Weakly/Distantly Supervised—using noisy labels or partial labels (bootstrapping, automatically-labeled data) • Reinforcement Learning—label on the result of a sequence of actions, but not on each action (games, robotics) • “Found” Data… (?) 28

Unsupervised Learning • “Finding structure in data” • In data science, this is typically for “exploratory analysis”. “What the $@%! is this data even?! Enlighten me.” • Or for preprocessing/featurizing—e.g. so you can use article “topics” to predict clicks. • In ML, right now, used extensively for “pretraining” (e.g. autoencoding, dimensionality reduction, language modeling*) 29

Unsupervised Learning • “Finding structure in data” (vs. predicting labels) • In data science, this is typically for “exploratory analysis”. “What the $@%! is this data even?! Enlighten me.” • Or for preprocessing/featurizing—e.g. so you can use article “topics” to predict clicks. • In ML, right now, used extensively for “pretraining” (e.g. autoencoding, dimensionality reduction, language modeling*) 30

Unsupervised Learning • “Finding structure in data” (vs. predicting labels) • In data science, this is typically for “exploratory analysis”. “What the $@%! is this data even?! Enlighten me.” • Or for preprocessing/featurizing—e.g. so you can use article “topics” to predict clicks. • In ML, right now, used extensively for “pretraining” (e.g. autoencoding, dimensionality reduction, language modeling*) 31

Unsupervised Learning • “Finding structure in data” (vs. predicting labels) • In data science, this is typically for “exploratory analysis”. “What the $@%! is this data even?! Enlighten me.” • Or for preprocessing/featurizing—e.g. so you can use article “topics” to predict clicks. • In ML, right now, used extensively for “pretraining” (e.g. autoencoding, dimensionality reduction, language modeling*) 32

Unsupervised Learning • “Finding structure in data” (vs. predicting labels) • In data science, this is typically for “exploratory analysis”. “What the $@%! is this data even?! Enlighten me.” • Or for preprocessing/featurizing—e.g. so you can use article “topics” to predict clicks. • In ML, right now, used extensively for “pretraining” (e.g. autoencoding, dimensionality reduction, language modeling*) 33

Clicker Question! 34

Clustering Discussion Question! What is it good for…? (…because those free-form answers were enlightening last time…) 35

Clustering • Find groups of customers with similar tastes • Find topics within a set of news articles • Find genres within a library of music • Extrapolating—make predictions about your new business based on behavior of similar old businesses 36

harmonic complexity Clustering tempo 37

harmonic complexity Clustering tempo 38

K Means define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 39

K Means “Hyperparameters” (i.e. not model parameters) define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 40

K Means How many clusters we want to find define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 41

K Means When to quit. Things aren’ t changing, or we have gotten bored. define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 42

K Means Randomly guess what the means are (lots of ways to do this) define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 43

K Means Repeat until your hyperparameters say to stop define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 44

K Means Assign each point to its closest mean define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 45

K Means Recompute the means to be the mean of the points assigned to each cluster define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 46

harmonic complexity K Means tempo 47

K Means guess what the means are harmonic complexity X X tempo 48

K Means Assign each point to harmonic complexity closest mean X X tempo 49

K Means re-compute means to be center of harmonic complexity clusters X X tempo 50

K Means Assign each point to harmonic complexity closest mean X X tempo 51

K Means re-compute means to be center of harmonic complexity clusters X X tempo 52

K Means Assign each point to harmonic complexity closest mean X X tempo 53

K Means re-compute means to be center of harmonic complexity clusters X X tempo 54

K Means harmonic complexity Converged! X X tempo 55

Clicker Question! 56 56

Clicker Question! What is the “loss” that we are trying to minimize here? (a)Number of clusters (b)Distance of points to their respective clusters (c) Distance between clusters (d)Probability of observed data 57 57

Clicker Question! What is the “loss” that we are trying to minimize here? (a)Number of clusters (b)Distance of points to their respective clusters (c) Distance between clusters (d)Probability of observed data 58 58

Clicker Question! What is the “loss” that we are trying to minimize here? (a)Number of clusters (b)Distance of points to their respective clusters (c) Distance between clusters (d)Probability of observed data This in just a few slides! 59 59

Clicker(/Discussion) Question! Is this a good objective? (a)Yes (b)No (c) Sure, why not. 60 60

Clicker(/Discussion) Question! Is this a good objective? (a)Yes (b)No (c) Sure, why not. Potential problems? (Hint: hyperparameters, generalization…) 61 61

How many clusters? mean dist to center X X 1 2 3 4 …….. N 62

How many clusters? mean dist to center X X 1 2 3 4 …….. N 63

How many clusters? mean dist to center X 1 2 3 4 …….. N 64

How many clusters? mean dist to center X X X X X X X X X X X X X X 1 2 3 4 …….. N 65

How many clusters? mean dist to center X “Elbow Point” X 1 2 3 4 …….. N 66

Other techniques: How many clusters? • Silhouette • Intuition/Divine Intervention • LGTM mean dist to center X “Elbow Point” X 1 2 3 4 …….. N 67

Other techniques: How many clusters? • Silhouette • Intuition/Divine Intervention • LGTM mean dist to center X “Elbow Point” distance to own cluster X distance to next best cluster 1 2 3 4 …….. N 68

69

Expectation Maximization (EM) 70

Expectation Maximization (EM) define parameters: K, max_iter, min_diff iter = 0 change = inf means = [random() for _ in range(K)] while iter < max_iter and change > min_diff: update_assignments() compute_new_means() change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 71

Expectation Maximization (EM) define parameters: K, max_iter, min_diff iter = 0 change = inf randomly initialize params while not converged: data = estimate_likelihood(params) params = maximize_likelihood(data) change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 72

Expectation Maximization (EM) define parameters: K, max_iter, min_diff E Step: estimate the likelihood of data iter = 0 under current parameter setting change = inf randomly initialize params while not converged: data = estimate_likelihood(params) params = maximize_likelihood(data) change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 73

Expectation Maximization (EM) define parameters: K, max_iter, min_diff M Step: adjust the the parameters so as to iter = 0 maximize the expectation of the data change = inf randomly initialize params while not converged: data = estimate_likelihood(params) params = maximize_likelihood(data) change = max_i(dist(new_mean_i, old_mean_i)) iter += 1 74

Expectation Maximization (EM) E step: Assign each point to harmonic complexity closest mean X X tempo http://www.dirkhovy.com/portfolio/papers/download/an_evening_with_EM.pdf 75

Expectation Maximization (EM) M step: Compute harmonic complexity means to be X center of clusters X tempo http://www.dirkhovy.com/portfolio/papers/download/an_evening_with_EM.pdf 76

Expectation Maximization (EM) harmonic complexity 0.4 X 0.6 X EM -> “soft” K-Means, where points belong to a probability distribution over clusters… tempo http://www.dirkhovy.com/portfolio/papers/download/an_evening_with_EM.pdf 77


 #tbt Slide from crowdsourcing lecture Quality Control Was arrested actress Heather • Why was Heather Heather Locklear Arrested for Locklear because of the driving under driving under the influence of drugs Locklear arrested? 
 the effect of an unknown medicine The actress Heather Locklear, The actress Heather Locklear that Driving while medicated is known to the Amanda through Amanda of the popular series Melrose Place, was arrested this the role from the series "Melrose • Why did the bystander weekend in Santa Barbara Place" was arrested at this Incentive Pay (California) after driving under the weekend in Santa Barbara (Californium) because of the influence of drugs. A witness call emergency driving under the effect of an viewed her performing inappropriate maneuvers while unknown medicine. A female services? trying to take her car out from a witness observed she attempted parking in Montecito, as revealed in quite strange way how to go from their parking space in to People magazine by a There was a lot of noise Montecito, speaker of the traffic spokesman for the Californian police of californium told the Highway Police. The witness • Where did the witness stated that around 4.30pm Ms. warehouse `People'. The female witness told in detail, that Locklear Locklear "hit the accelerator very 'pressed `after 16:30 clock violently, making excessive noise see her acting while trying to take her car out accelerator and a lot of noise did from the parking with abrupt back when she attempted to move their abnormally? 
 and forth maneuvers. While car towards behind or forward from the parking space, and when reversing, she passed several 
 it went backwards, she pulled times in front of his sunglasses." itself together unites Male at their Shortly after, the witness, who, in In a parking lot a first time, apparently had not sunglasses'. A little later the recognized the actress, saw Ms. female witness that did probably Second-Pass HIT Statistical Models 78


 #tbt Slide from crowdsourcing lecture Quality Control Was arrested actress Heather • Why was Heather Heather Locklear Arrested for Locklear because of the driving under driving under the influence of drugs Locklear arrested? 
 the effect of an unknown medicine The actress Heather Locklear, The actress Heather Locklear that Driving while medicated is known to the Amanda through Amanda of the popular series the role from the series "Melrose Melrose Place, was arrested this • Why did the bystander Place" was arrested at this weekend in Santa Barbara Incentive Pay weekend in Santa Barbara (California) after driving under the (Californium) because of the influence of drugs. A witness call emergency driving under the effect of an viewed her performing inappropriate maneuvers while unknown medicine. A female services? witness observed she attempted trying to take her car out from a in quite strange way how to go parking in Montecito, as revealed from their parking space in to People magazine by a There was a lot of noise spokesman for the Californian Montecito, speaker of the traffic police of californium told the Highway Police. The witness • Where did the witness warehouse `People'. The female stated that around 4.30pm Ms. Locklear "hit the accelerator very witness told in detail, that Locklear 'pressed `after 16:30 clock violently, making excessive noise see her acting while trying to take her car out accelerator and a lot of noise did when she attempted to move their from the parking with abrupt back abnormally? 
 car towards behind or forward and forth maneuvers. While from the parking space, and when reversing, she passed several 
 it went backwards, she pulled times in front of his sunglasses." Shortly after, the witness, who, in itself together unites Male at their In a parking lot sunglasses'. A little later the a first time, apparently had not female witness that did probably recognized the actress, saw Ms. Second-Pass HIT Statistical Models (That I don’ t think we actually covered, but its cool its fine…) 79

Goal: Find “true” labels despite noisy annotations from workers… worker1 worker2 worker3 worker4 worker5 email1 spam not not not spam email2 spam spam spam spam spam email3 not spam not not spam email4 spam spam spam spam not email5 spam not not not spam 80

Goal: Find “true” labels despite noisy annotations from workers… worker1 worker2 worker3 worker4 worker5 email1 spam not not not spam Easy! If you tell me how much to trust each worker, I can trivially email2 spam spam spam spam spam compute labels email3 not spam not not spam email4 spam spam spam spam not email5 spam not not not spam 81

Goal: Find “true” labels despite noisy annotations from workers… worker1 worker2 worker3 worker4 worker5 email1 spam not not not spam Easy! If you tell me how much to trust each worker, I can trivially email2 spam spam spam spam spam compute labels Sure, just tell me email3 not spam not not spam the labels and I can easily figure out which email4 spam spam spam spam not workers to trust. email5 spam not not not spam 82

Goal: Find “true” labels despite EM EVERYTHING!!!! noisy annotations from workers… worker1 worker2 worker3 worker4 worker5 email1 spam not not not spam Easy! If you tell me how much to trust each worker, I can trivially email2 spam spam spam spam spam compute labels Sure, just tell me email3 not spam not not spam the labels and I can easily figure out which email4 spam spam spam spam not workers to trust. email5 spam not not not spam 83

spam not w1 w2 w3 w4 w5 w1 spam ? ? email1 spam not not not spam not ? ? email2 spam spam spam spam spam spam not w2 email3 not spam not not spam spam ? ? email4 spam spam spam spam not not ? ? email5 spam not not not spam spam not w3 spam not spam ? ? email1 ? ? not ? ? spam not w4 email2 ? ? spam ? ? email3 ? ? not ? ? email4 ? ? spam not w5 spam ? ? email5 ? ? not ? ? 84

spam not w1 w2 w3 w4 w5 w1 spam ? ? email1 spam not not not spam not ? ? email2 spam spam spam spam spam spam not w2 email3 not spam not not spam spam ? ? email4 spam spam spam spam not not ? ? email5 spam not not not spam P(email1 is spam) spam not w3 spam not spam ? ? email1 ? ? not ? ? spam not w4 email2 ? ? spam ? ? email3 ? ? not ? ? email4 ? ? spam not w5 spam ? ? email5 ? ? not ? ? 85

spam not w1 w2 w3 w4 w5 w1 spam ? ? email1 spam not not not spam not ? ? email2 spam spam spam spam spam spam not w2 email3 not spam not not spam P(w1 says spam | not spam) spam ? ? email4 spam spam spam spam not not ? ? email5 spam not not not spam spam not w3 spam not spam ? ? email1 ? ? not ? ? spam not w4 email2 ? ? spam ? ? email3 ? ? not ? ? email4 ? ? spam not w5 spam ? ? email5 ? ? not ? ? 86

spam not w1 w2 w3 w4 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Assume spam not w2 email3 not spam not not spam spam 1 0 email4 spam spam spam spam not all workers not 0 1 email5 spam not not not spam are spam not w3 perfect spam not spam 1 0 email1 ? ? not 0 1 spam not w4 email2 ? ? spam 1 0 email3 ? ? not 0 1 email4 ? ? spam not w5 spam 1 0 email5 ? ? not 0 1 87

spam not w1 w2 w3 w4 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Compute spam not w2 email3 not spam not not spam labels spam 1 0 email4 spam spam spam spam not using not 0 1 email5 spam not not not spam majority spam not w3 vote spam not spam 1 0 email1 ? ? not 0 1 spam not w4 email2 ? ? spam 1 0 email3 ? ? not 0 1 email4 ? ? spam not w5 spam 1 0 email5 ? ? not 0 1 88

Clicker Question! 89 89

spam not w1 w2 w3 w4 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Compute spam not w2 email3 not spam not not spam labels spam 1 0 email4 spam spam spam spam not using not 0 1 email5 spam not not not spam majority spam not w3 vote spam not spam 1 0 email1 ? ? not 0 1 Clicker Question! spam not w4 email2 ? ? spam 1 0 (a)0.4, 0.6 email3 ? ? not 0 1 (b)0.6, 0.4 email4 ? ? spam not w5 (c) 0.8, 0.2 spam 1 0 (d)1.0, 0.0 email5 ? ? not 0 1 90

spam not w1 w2 w3 w4 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Compute spam not w2 email3 not spam not not spam labels spam 1 0 email4 spam spam spam spam not using not 0 1 email5 spam not not not spam majority spam not w3 vote spam not spam 1 0 email1 ? ? not 0 1 Clicker Question! spam not w4 email2 ? ? spam 1 0 (a)0.4, 0.6 email3 ? ? not 0 1 (b)0.6, 0.4 email4 ? ? spam not w5 (c) 0.8, 0.2 spam 1 0 (d)1.0, 0.0 email5 ? ? not 0 1 91

w1 w5 spam not w2 w3 w4 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Compute spam not w2 email3 not spam not not spam labels spam 1 0 email4 spam spam spam spam not using not 0 1 email5 spam not not not spam majority spam not w3 vote spam not spam 1 0 email1 0.4 ? not 0 1 spam not w4 email2 ? ? spam 1 0 email3 ? ? not 0 1 email4 ? ? spam not w5 spam 1 0 email5 ? ? not 0 1 92

w2 w3 w4 spam not w1 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Compute spam not w2 email3 not spam not not spam labels spam 1 0 email4 spam spam spam spam not using not 0 1 email5 spam not not not spam majority spam not w3 vote spam not spam 1 0 email1 0.4 0.6 not 0 1 spam not w4 email2 ? ? spam 1 0 email3 ? ? not 0 1 email4 ? ? spam not w5 spam 1 0 email5 ? ? not 0 1 93

spam not w1 w2 w3 w4 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Compute spam not w2 email3 not spam not not spam labels spam 1 0 email4 spam spam spam spam not using not 0 1 email5 spam not not not spam majority spam not w3 vote spam not spam 1 0 email1 0.4 0.6 not 0 1 spam not w4 email2 1 0 spam 1 0 email3 0.4 0.6 not 0 1 email4 0.8 0.2 spam not w5 spam 1 0 email5 0.4 0.6 not 0 1 94

spam not w1 w2 w3 w4 w5 w1 spam 1 0 email1 spam not not not spam not 0 1 email2 spam spam spam spam spam Assume spam not w2 email3 not spam not not spam these labels, and spam 1 0 email4 spam spam spam spam not recompute not 0 1 email5 spam not not not spam confusion spam not w3 matrices spam not spam 1 0 email1 0.4 0.6 not 0 1 spam not w4 email2 1 0 spam 1 0 email3 0.4 0.6 not 0 1 email4 0.8 0.2 spam not w5 spam 1 0 email5 0.4 0.6 not 0 1 95

spam not w1 w2 w3 w4 w5 w1 spam email1 spam not not not spam not email2 spam spam spam spam spam Assume spam not w2 email3 not spam not not spam these labels, and spam email4 spam spam spam spam not recompute not email5 spam not not not spam confusion spam not w3 matrices spam not spam email1 0.4 0.6 not spam not w4 email2 1 0 spam email3 0.4 0.6 not email4 0.8 0.2 spam not w5 spam email5 0.4 0.6 not 96

Clicker Question! 97 97

spam not w1 w2 w3 w4 w5 w1 spam ? ? email1 spam not not not spam not email2 spam spam spam spam spam Assume spam not w2 email3 not spam not not spam these labels, and spam email4 spam spam spam spam not Clicker Question! recompute not email5 spam not not not spam confusion (a)0.4, 0.6 spam not w3 matrices spam not (b)0.6, 0.4 spam (c) 0.8, 0.2 email1 0.4 0.6 not (d)1.0, 0.0 spam not w4 email2 1 0 spam email3 0.4 0.6 not email4 0.8 0.2 spam not w5 spam email5 0.4 0.6 not 98

spam not w1 w2 w3 w4 w5 w1 spam ? ? email1 spam not not not spam not email2 spam spam spam spam spam Assume spam not w2 email3 not spam not not spam these labels, and spam email4 spam spam spam spam not Clicker Question! recompute not email5 spam not not not spam confusion (a)0.4, 0.6 spam not w3 matrices spam not (b)0.6, 0.4 spam (c) 0.8, 0.2 email1 0.4 0.6 not (d)1.0, 0.0 spam not w4 email2 1 0 spam email3 0.4 0.6 not email4 0.8 0.2 spam not w5 spam email5 0.4 0.6 not 99

spam not w1 w2 w3 w4 w5 w1 spam 1 email1 spam not not not spam not email2 spam spam spam spam spam Assume spam not w2 email3 not spam not not spam these labels, and spam 1 0 email4 spam spam spam spam not recompute not 0 1 email5 spam not not not spam confusion spam not w3 matrices spam not spam 1 0 email1 0.4 0.6 not 0 1 spam not w4 email2 1 0 spam 1 0 email3 0.4 0.6 not 0 1 email4 0.8 0.2 spam not w5 spam 1 0 email5 0.4 0.6 not 0 1 100