"Small Data" Machine Learning

What do you do if you have a single letter Twitter handle and your reply stream is virtually useless due to people using “@a” in ways that make you lose faith in humanity (“I’m @a bar” is the best of it)? These days, you might call machine learning to the rescue. ML is a hot new topic, but may be a bit difficult to get started with in a large project. This session explains how I used ML and a couple of other tricks to build a reply stream cleaner that sanitizes my Twitter consumption and will hopefully inspire you to use ML in your own projects.

1. Small Data Machine Learning Andrei Zmievski
2. WORK We are all superheroes, because we help our customers keep their mission-critical apps running smoothly. If interested, I can show you a demo of what I’m working on. Come find me.
3. WORK We are all superheroes, because we help our customers keep their mission-critical apps running smoothly. If interested, I can show you a demo of what I’m working on. Come find me.
4. MATH
5. MATH SOME
6. MATH SOME AWE
7. @a Acquired in October 2008 Had a different account earlier, but then @k asked if I wanted it.. Know many other single-letter Twitterers.
8. FAME Advantages
9. FAME FORTUNE
10. FAME FORTUNE Wall Street Journal?!
11. FAME FORTUNE FOLLOWERS
12. lol, what?! FAME FORTUNE FOLLOWERS
13. 140-length(“@a “)=137 MAXIMUM REPLY SPACE!
14. CONS Disadvantages Visual filtering is next to impossible Could be a set of hard-coded rules derived empirically
15. CONS I hate humanity Disadvantages Visual filtering is next to impossible Could be a set of hard-coded rules derived empirically
16. CONS I hate humanity Disadvantages Visual filtering is next to impossible Could be a set of hard-coded rules derived empirically
17. Machine Learning to the Rescue! Being grumpy makes you learn stuff
18. REPLYCLEANER Even with false negatives, reduces garbage to where visual filtering is possible - uses trained model to classify tweets into good/bad - blocks the authors of the bad ones, since Twitter does not have a way to remove an individual tweet from the timeline
19. REPLYCLEANER Even with false negatives, reduces garbage to where visual filtering is possible - uses trained model to classify tweets into good/bad - blocks the authors of the bad ones, since Twitter does not have a way to remove an individual tweet from the timeline
20. REPLYCLEANER
21. REPLYCLEANER
22. REPLYCLEANER
23. REPLYCLEANER
25. I still hate humanity
26. I still hate humanity I still hate humanity
27. Machine Learning A branch of Artificial Intelligence No widely accepted definition
28. “Field of study that gives computers the ability to learn without being explicitly programmed.” — Arthur Samuel (1959)
29. SPAM FILTERING
30. RECOMMENDATIONS
31. TRANSLATION
32. CLUSTERING And many more: medical diagnoses, detecting credit card fraud, etc.
33. supervised unsupervised Labeled dataset, training maps input to desired outputs Example: regression - predicting house prices, classification - spam filtering
34. supervised unsupervised no labels in the dataset, algorithm needs to find structure Example: clustering
35. Feature individual measurable property of the phenomenon under observation usually numeric
37. Feature Vector a set of features for an observation Think of it as an array
38. features # of rooms sq. footage house age yard? feature vector and weights vector 1 added to pad the vector (account for the initial offset / bias / intercept weight, simplifies calculation) dot product produces a linear predictor
39. features 102.3 0.94 -10.1 83.0 weights # of rooms sq. footage house age yard? feature vector and weights vector 1 added to pad the vector (account for the initial offset / bias / intercept weight, simplifies calculation) dot product produces a linear predictor
40. features 102.3 0.94 -10.1 83.0 weights # of rooms sq. footage house age yard? 1 45.7 feature vector and weights vector 1 added to pad the vector (account for the initial offset / bias / intercept weight, simplifies calculation) dot product produces a linear predictor
41. features 102.3 0.94 -10.1 83.0 weights # of rooms sq. footage house age yard? 1 45.7 feature vector and weights vector 1 added to pad the vector (account for the initial offset / bias / intercept weight, simplifies calculation) dot product produces a linear predictor
42. features 102.3 0.94 -10.1 83.0 = weights prediction # of rooms sq. footage house age yard? 1 45.7 feature vector and weights vector 1 added to pad the vector (account for the initial offset / bias / intercept weight, simplifies calculation) dot product produces a linear predictor
43. X = ⇥ 1 x1 x2 . . . ⇤ ✓ = ⇥ ✓0 ✓1 ✓2 . . . ⇤ dot product
44. X = ⇥ 1 x1 x2 . . . ⇤ ✓ = ⇥ ✓0 ✓1 ✓2 . . . ⇤ ✓ · X = ✓0 + ✓1x1 + ✓2x2 + . . . dot product
45. training data learning algorithm hypothesis Hypothesis (decision function): what the system has learned so far Hypothesis is applied to new data
46. hθ (X) The task of our algorithm is to determine the parameters of the hypothesis.
47. hθ (X) input data The task of our algorithm is to determine the parameters of the hypothesis.
48. hθ (X) parameters input data The task of our algorithm is to determine the parameters of the hypothesis.
49. hθ (X) parameters input data prediction y The task of our algorithm is to determine the parameters of the hypothesis.
50. LINEAR REGRESSION 5 10 15 20 25 30 35 40 80 120 160 200 whisky age whisky price $ Models the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. Here X = whisky age, y = whisky price. Linear regression does not work well for classification because its output is unbounded. Thresholding on some value is tricky and does not produce good results.
51. LINEAR REGRESSION 5 10 15 20 25 30 35 40 80 120 160 200 whisky age whisky price $ Models the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. Here X = whisky age, y = whisky price. Linear regression does not work well for classification because its output is unbounded. Thresholding on some value is tricky and does not produce good results.
52. LINEAR REGRESSION 5 10 15 20 25 30 35 40 80 120 160 200 whisky age whisky price $ Models the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. Here X = whisky age, y = whisky price. Linear regression does not work well for classification because its output is unbounded. Thresholding on some value is tricky and does not produce good results.
53. LOGISTIC REGRESSION g(z) = 1 1 + e z 0.5 1 0 z Logistic function (also sigmoid function). Asymptotes at 0 and 1. Crosses 0.5 at origin. z is just our old dot product, the linear predictor.
54. LOGISTIC REGRESSION g(z) = 1 1 + e z 0.5 1 0 z z = ✓ · X Logistic function (also sigmoid function). Asymptotes at 0 and 1. Crosses 0.5 at origin. z is just our old dot product, the linear predictor.
55. h✓(X) = 1 1 + e ✓·X Probability that y=1 for input X LOGISTIC REGRESSION If hypothesis describes spam, then given X=body of email, if y=0.7, means there’s 70% chance it’s spam. Thresholding on that is up to you.
56. Building the Tool
57. Corpus collection of source data used for training and testing the model
58. Twitter MongoDB phirehose hooks into streaming API
59. Twitter MongoDB phirehose 8500 tweets hooks into streaming API
60. Feature Identification
61. independent & discriminant Independent: feature A should not co-occur (correlate) with feature B highly. Discriminant: a feature should provide uniquely classifiable data (what letter a tweet starts with is not a good feature).
62. ‣ @a at the end of the tweet ‣ @a... ‣ length < N chars ‣ # of user mentions in the tweet ‣ # of hashtags ‣ language! ‣ @a followed by punctuation and a word character (except for apostrophe) possible features
63. feature = extractor(tweet) For each feature, write a small function that takes a tweet and returns a numeric value
64. corpus extractors feature vectors Run the set of these functions over the corpus and build up feature vectors Array of arrays Save to DB
65. Language Matters high correlation between the language of the tweet and its category (good/bad)
66. Indonesian or Tagalog? Garbage.
67. id Indonesian 3548 en English 1804 tl Tagalog 733 es Spanish 329 so Somalian 305 ja Japanese 300 pt Portuguese 262 ar Arabic 256 nl Dutch 150 it Italian 137 sw Swahili 118 fr French 92 Top 12 Languages I guarantee you people aren’t tweeting at me in Swahili.
68. Language Detection Can’t trust the language field in user’s profile data. Used character N-grams and character sets for detection. Has its own error rate, so needs some post-processing.
69. Language Detection Text_LanguageDetect textcat pecl / pear / Can’t trust the language field in user’s profile data. Used character N-grams and character sets for detection. Has its own error rate, so needs some post-processing.
70. ✓ Clean-up text (remove mentions, links, etc) ✓ Run language detection ✓ If unknown/low weight, pretend it’s English, else: ✓ If not a character set-determined language, try harder: ✓ Tokenize into words ✓ Difference with English vocabulary ✓ If words remain, run parts-of-speech tagger on each ✓ For NNS, VBZ, and VBD run stemming algorithm ✓ If result is in English vocabulary, remove from remaining ✓ If remaining list is not empty, calculate: unusual_word_ratio = size(remaining)/size(words) ✓ If ratio < 20%, pretend it’s English EnglishNotEnglish A lot of this is heuristic-based, after some trial-and-error. Seems to help with my corpus.
71. BINARY CLASSIFICATION Grunt work Built a web-based tool to display tweets a page at a time and select good ones
72. feature vectors labels (good/bad) I N P U T O U T P U T Had my input and output
73. BIAS CORRECTION One more thing to address
74. BIAS CORRECTION BAD GOOD 99% = bad (less < 100 tweets were good) Training a model as-is would not produce good results Need to adjust the bias
75. BIAS CORRECTION BAD GOOD
76. O V E R SAMPLING Oversampling: use multiple copies of good tweets to equalize with bad Problem: bias very high, each good tweet would have to be copied 100 times, and not contribute any variance to the good category
77. O V E R SAMPLING Oversampling: use multiple copies of good tweets to equalize with bad Problem: bias very high, each good tweet would have to be copied 100 times, and not contribute any variance to the good category
78. O V E R SAMPLING UNDER Undersampling: drop most of the bad tweets to equalize with good Problem: total corpus ends up being < 200 tweets, not enough for training
79. SAMPLING UNDER Undersampling: drop most of the bad tweets to equalize with good Problem: total corpus ends up being < 200 tweets, not enough for training
80. OVERSAMPLING Synthetic Synthesize feature vectors by determining what constitutes a good tweet and do weighted random selection of feature values.
81. chance feature 90% “good” language 70% 25% 5% no hashtags 1 hashtag 2 hashtags 2% @a at the end 85% rand length > 10 The actual synthesis is somewhat more complex and was also trial-and-error based Synthesized tweets + existing good tweets = 2/3 of # of bad tweets in the training corpus (limited to 1000)
82. chance feature 90% “good” language 70% 25% 5% no hashtags 1 hashtag 2 hashtags 2% @a at the end 85% rand length > 10 1 The actual synthesis is somewhat more complex and was also trial-and-error based Synthesized tweets + existing good tweets = 2/3 of # of bad tweets in the training corpus (limited to 1000)
83. chance feature 90% “good” language 70% 25% 5% no hashtags 1 hashtag 2 hashtags 2% @a at the end 85% rand length > 10 1 2 The actual synthesis is somewhat more complex and was also trial-and-error based Synthesized tweets + existing good tweets = 2/3 of # of bad tweets in the training corpus (limited to 1000)
84. chance feature 90% “good” language 70% 25% 5% no hashtags 1 hashtag 2 hashtags 2% @a at the end 85% rand length > 10 1 2 0 The actual synthesis is somewhat more complex and was also trial-and-error based Synthesized tweets + existing good tweets = 2/3 of # of bad tweets in the training corpus (limited to 1000)
85. chance feature 90% “good” language 70% 25% 5% no hashtags 1 hashtag 2 hashtags 2% @a at the end 85% rand length > 10 1 2 0 77 The actual synthesis is somewhat more complex and was also trial-and-error based Synthesized tweets + existing good tweets = 2/3 of # of bad tweets in the training corpus (limited to 1000)
86. Model Training We have the hypothesis (decision function) and the training set, How do we actually determine the weights/parameters?
87. COST FUNCTION Measures how far the prediction of the system is from the reality. The cost depends on the parameters. The less the cost, the closer we’re to the ideal parameters for the model.
88. REALITY PREDICTION COST FUNCTION Measures how far the prediction of the system is from the reality. The cost depends on the parameters. The less the cost, the closer we’re to the ideal parameters for the model.
89. COST FUNCTION J ( ✓ ) = 1 m m X i=1 Cost ( h✓( x ) , y ) Measures how far the prediction of the system is from the reality. The cost depends on the parameters. The less the cost, the closer we’re to the ideal parameters for the model.
90. Cost(h✓(x), y) = ( log (h✓(x)) if y = 1 log (1 h✓(x)) if y = 0 LOGISTIC COST
91. 1 0 y=1 y=0 1 0 Correct guess Incorrect guess Cost = 0 Cost = huge When y=1 and h(x) is 1 (good guess), cost is 0, but the closer h(x) gets to 0 (wrong guess), the more we penalize the algorithm. Same for y=0.
92. minimize cost OVER θ Finding the best values of Theta that minimize the cost
93. GRADIENT DESCENT Random starting point. Pretend you’re standing on a hill. Find the direction of the steepest descent and take a step. Repeat. Imagine a ball rolling down from a hill.
94. ✓i ↵ = ✓i @J(✓) @✓i GRADIENT DESCENT Each step adjusts the parameters according to the slope
95. ↵ = each parameter ✓i ✓i @J(✓) @✓i Have to update them simultaneously (the whole vector at a time).
96. ✓i = ✓i learning rate ↵ @J(✓) @✓i Controls how big a step you take If α is big have an aggressive gradient descent If α is small take tiny steps If too small, tiny steps, takes too long If too big, can overshoot the minimum and fail to converge
97. ✓i ↵ = ✓i derivative aka “the slope” @J(✓) @✓i The slope indicates the steepness of the descent step for each weight, i.e. direction. Keep going for a number of iterations or until cost is below a threshold (convergence). Graph the cost function versus # of iterations and see where it starts to approach 0, past that are diminishing returns.
98. ✓i = ✓i ↵ m X j=1 ( h✓( x j) y j) x j i FINAL UPDATE ALGORITHM Derivative for logistic regression simplifies to this term. Have to update the weights simultaneously!
99. X1 = [1 12.0] X2 = [1 -3.5] Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
100. y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
101. y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
102. y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
103. y1 = 1 y2 = 0 h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
104. y1 = 1 y2 = 0 h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 h(X2) = 1 / (1 + e-(0.1 • 1 + 0.1 • -3.5)) = 0.438 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
105. y1 = 1 y2 = 0 h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 h(X2) = 1 / (1 + e-(0.1 • 1 + 0.1 • -3.5)) = 0.438 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] T0 ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
106. y1 = 1 y2 = 0 = 0.1 - 0.05 • ((h(X1) - y1) • X10 + (h(X2) - y2) • X20) h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 h(X2) = 1 / (1 + e-(0.1 • 1 + 0.1 • -3.5)) = 0.438 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] T0 ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
107. y1 = 1 y2 = 0 = 0.1 - 0.05 • ((h(X1) - y1) • X10 + (h(X2) - y2) • X20) = 0.1 - 0.05 • ((0.786 - 1) • 1 + (0.438 - 0) • 1) h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 h(X2) = 1 / (1 + e-(0.1 • 1 + 0.1 • -3.5)) = 0.438 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] T0 ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
108. y1 = 1 y2 = 0 = 0.1 - 0.05 • ((h(X1) - y1) • X10 + (h(X2) - y2) • X20) = 0.1 - 0.05 • ((0.786 - 1) • 1 + (0.438 - 0) • 1) = 0.088 h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 h(X2) = 1 / (1 + e-(0.1 • 1 + 0.1 • -3.5)) = 0.438 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] T0 ↵= 0.05 Hypothesis for each data point based on current parameters. Each parameter is updated in order and result is saved to a temporary.
109. y1 = 1 y2 = 0 = 0.1 - 0.05 • ((h(X1) - y1) • X10 + (h(X2) - y2) • X20) = 0.1 - 0.05 • ((0.786 - 1) • 12.0 + (0.438 - 0) • -3.5) = 0.305 h(X1) = 1 / (1 + e-(0.1 • 1 + 0.1 • 12.0)) = 0.786 h(X2) = 1 / (1 + e-(0.1 • 1 + 0.1 • -3.5)) = 0.438 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.1 0.1] T1 ↵= 0.05 Note that the hypotheses don’t change within the iteration.
110. y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] θ = [T0 T1] ↵= 0.05 Replace parameter (weights) vector with the temporaries.
111. y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.088 0.305] ↵= 0.05 Do next iteration
112. Trai ning CROSS Used to assess the results of the training.
113. DATA
114. DATA TRAINING
115. DATA TRAINING TEST Train model on training set, then test results on test set. Rinse, lather, repeat feature selection/synthesis/training until results are "good enough". Pick the best parameters and save them (DB, other).
116. Putting It All Together Let’s put our model to use, finally. The tool hooks into Twitter Streaming API, and naturally that comes with need to do certain error handling, etc. Once we get the actual tweet though..
117. Load the model The weights we have calculated via training Easiest is to load them from DB (can be used to test different models).
118. HARD CODED RULES We apply some hardcoded rules to filter out the tweets we are certain are good or bad. The truncate RT ones don’t show up on the Web or other tools anyway, so fine to skip those.
119. HARD CODED RULES SKIP truncated retweets: "RT @A ..." We apply some hardcoded rules to filter out the tweets we are certain are good or bad. The truncate RT ones don’t show up on the Web or other tools anyway, so fine to skip those.
120. HARD CODED RULES SKIP truncated retweets: "RT @A ..." @ mentions of friends We apply some hardcoded rules to filter out the tweets we are certain are good or bad. The truncate RT ones don’t show up on the Web or other tools anyway, so fine to skip those.
121. HARD CODED RULES SKIP truncated retweets: "RT @A ..." tweets from friends @ mentions of friends We apply some hardcoded rules to filter out the tweets we are certain are good or bad. The truncate RT ones don’t show up on the Web or other tools anyway, so fine to skip those.
122. Classifying Tweets This is the moment we’ve been waiting for.
123. Classifying Tweets GOOD This is the moment we’ve been waiting for.
124. Classifying Tweets GOOD BAD This is the moment we’ve been waiting for.
125. h✓(X) = 1 1 + e ✓·X Remember this? First is our hypothesis.
126. h✓(X) = 1 1 + e ✓·X Remember this? ✓·X = ✓0 + ✓1X1 + ✓2X2 + . . . First is our hypothesis.
127. Finally h✓(X) = 1 1 + e (✓0+✓1X1+✓2X2+... ) If h > 0.5 , tweet is bad, otherwise good Remember that the output of h() is 0..1 (probability). 0.5 is your threshold, adjust it for your degree of tolerance. I used 0.9 to reduce false positives.
128. extract features 3 simple steps Invoke the feature extractor to construct the feature vector for this tweet. Evaluate the decision function over the feature vector (input the calculated feature parameters into the equation). Use the output of the classifier.
129. extract features run the model 3 simple steps Invoke the feature extractor to construct the feature vector for this tweet. Evaluate the decision function over the feature vector (input the calculated feature parameters into the equation). Use the output of the classifier.
130. extract features run the model act on the result 3 simple steps Invoke the feature extractor to construct the feature vector for this tweet. Evaluate the decision function over the feature vector (input the calculated feature parameters into the equation). Use the output of the classifier.
131. BAD? block user! Also save the tweet to DB for future analysis.
132. Lessons Learned Blocking is the only option (and is final) Streaming API delivery is incomplete ReplyCleaner judged to be ~80% effective Twitter API is a pain in the rear
133. Lessons Learned Blocking is the only option (and is final) Streaming API delivery is incomplete ReplyCleaner judged to be ~80% effective Twitter API is a pain in the rear -Connection handling, backoff in case of problems, undocumented API errors, etc.
134. Lessons Learned Blocking is the only option (and is final) Streaming API delivery is incomplete ReplyCleaner judged to be ~80% effective Twitter API is a pain in the rear -No way for blocked person to get ahold of you via Twitter anymore, so when training the model, err on the side of caution.
135. Lessons Learned Blocking is the only option (and is final) Streaming API delivery is incomplete ReplyCleaner judged to be ~80% effective Twitter API is a pain in the rear -Some tweets are shown on the website, but never seen through the API.
136. Lessons Learned Blocking is the only option (and is final) Streaming API delivery is incomplete ReplyCleaner judged to be ~80% effective Twitter API is a pain in the rear -Lots of room for improvement.
137. Lessons Learned Blocking is the only option (and is final) Streaming API delivery is incomplete ReplyCleaner judged to be ~80% effective Twitter API is a pain in the rear PHP sucks at math-y stuff -Lots of room for improvement.
138. NEXT STEPS ★ Realtime feedback ★ More features ★ Grammar analysis ★ Support Vector Machines or decision trees ★ Clockwork Raven for manual classification ★ Other minimization algos: BFGS, conjugate gradient ★ Need pecl/scikit-learn Click on the tweets that are bad and it immediately incorporates them into the model. Grammar analysis to eliminate the common "@a bar" or "two @a time" occurrences. SVMs more appropriate for biased data sets. Farm out manual classification to Mechanical Turk. May help avoid local minima, no need to pick alpha, often faster than GD.
139. TOOLS ★ MongoDB ★ pear/Text_LanguageDetect ★ English vocabulary corpus ★ Parts-Of-Speech tagging ★ SplFixedArray ★ phirehose ★ Python’s scikit-learn (for validation) ★ Code sample MongoDB (great fit for JSON data) English vocabulary corpus: http://corpus.byu.edu/ or http://www.keithv.com/software/wlist/ SplFixedArray in PHP (memory savings and slightly faster)
140. Questions?