"Small Data" Machine Learning

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Small Data Machine Learning Andrei Zmievski

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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.

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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.

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MATH

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MATH SOME

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MATH SOME AWE

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@a Acquired in October 2008 Had a different account earlier, but then @k asked if I wanted it.. Know many other single-letter Twitterers.

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FAME Advantages

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FAME FORTUNE

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FAME FORTUNE Wall Street Journal?!

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FAME FORTUNE FOLLOWERS

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lol, what?! FAME FORTUNE FOLLOWERS

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140-length(“@a “)=137 MAXIMUM REPLY SPACE!

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CONS Disadvantages Visual ﬁltering is next to impossible Could be a set of hard-coded rules derived empirically

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CONS I hate humanity Disadvantages Visual ﬁltering is next to impossible Could be a set of hard-coded rules derived empirically

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CONS I hate humanity Disadvantages Visual ﬁltering is next to impossible Could be a set of hard-coded rules derived empirically

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Machine Learning to the Rescue! Being grumpy makes you learn stuff

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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

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REPLYCLEANER

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REPLYCLEANER

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REPLYCLEANER

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REPLYCLEANER

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I still hate humanity

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I still hate humanity I still hate humanity

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Machine Learning A branch of Artiﬁcial Intelligence No widely accepted deﬁnition

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“Field of study that gives computers the ability to learn without being explicitly programmed.” — Arthur Samuel (1959)

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SPAM FILTERING

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RECOMMENDATIONS

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TRANSLATION

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CLUSTERING And many more: medical diagnoses, detecting credit card fraud, etc.

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supervised unsupervised Labeled dataset, training maps input to desired outputs Example: regression - predicting house prices, classiﬁcation - spam ﬁltering

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supervised unsupervised no labels in the dataset, algorithm needs to ﬁnd structure Example: clustering

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Feature individual measurable property of the phenomenon under observation usually numeric

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Feature Vector a set of features for an observation Think of it as an array

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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

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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

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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

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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

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X = ⇥ 1 x1 x2 . . . ⇤ ✓ = ⇥ ✓0 ✓1 ✓2 . . . ⇤ dot product

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X = ⇥ 1 x1 x2 . . . ⇤ ✓ = ⇥ ✓0 ✓1 ✓2 . . . ⇤ ✓ · X = ✓0 + ✓1x1 + ✓2x2 + . . . dot product

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training data learning algorithm hypothesis Hypothesis (decision function): what the system has learned so far Hypothesis is applied to new data

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hθ (X) The task of our algorithm is to determine the parameters of the hypothesis.

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hθ (X) input data The task of our algorithm is to determine the parameters of the hypothesis.

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hθ (X) parameters input data The task of our algorithm is to determine the parameters of the hypothesis.

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hθ (X) parameters input data prediction y The task of our algorithm is to determine the parameters of the hypothesis.

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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.

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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.

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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.

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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.

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Building the Tool

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Corpus collection of source data used for training and testing the model

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Twitter MongoDB phirehose hooks into streaming API

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Twitter MongoDB phirehose 8500 tweets hooks into streaming API

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Feature Identiﬁcation

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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).

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‣ @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

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feature = extractor(tweet) For each feature, write a small function that takes a tweet and returns a numeric value

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corpus extractors feature vectors Run the set of these functions over the corpus and build up feature vectors Array of arrays Save to DB

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Language Matters high correlation between the language of the tweet and its category (good/bad)

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Indonesian or Tagalog? Garbage.

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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.

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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.

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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.

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✓ 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.

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BINARY CLASSIFICATION Grunt work Built a web-based tool to display tweets a page at a time and select good ones

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feature vectors labels (good/bad) I N P U T O U T P U T Had my input and output

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BIAS CORRECTION One more thing to address

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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

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BIAS CORRECTION BAD GOOD

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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

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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

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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

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OVERSAMPLING Synthetic Synthesize feature vectors by determining what constitutes a good tweet and do weighted random selection of feature values.

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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)

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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)

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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)

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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)

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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)

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Model Training We have the hypothesis (decision function) and the training set, How do we actually determine the weights/parameters?

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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.

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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.

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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.

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Cost(h✓(x), y) = ( log (h✓(x)) if y = 1 log (1 h✓(x)) if y = 0 LOGISTIC COST

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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.

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minimize cost OVER θ Finding the best values of Theta that minimize the cost

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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.

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✓i ↵ = ✓i @J(✓) @✓i GRADIENT DESCENT Each step adjusts the parameters according to the slope

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↵ = each parameter ✓i ✓i @J(✓) @✓i Have to update them simultaneously (the whole vector at a time).

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✓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

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✓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.

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✓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!

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] θ = [T0 T1] ↵= 0.05 Replace parameter (weights) vector with the temporaries.

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y1 = 1 y2 = 0 X1 = [1 12.0] X2 = [1 -3.5] θ = [0.088 0.305] ↵= 0.05 Do next iteration

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Trai ning CROSS Used to assess the results of the training.

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DATA

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DATA TRAINING

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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).

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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..

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Load the model The weights we have calculated via training Easiest is to load them from DB (can be used to test different models).

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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.

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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.

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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.

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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.

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Classifying Tweets This is the moment we’ve been waiting for.

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Classifying Tweets GOOD This is the moment we’ve been waiting for.

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Classifying Tweets GOOD BAD This is the moment we’ve been waiting for.

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h✓(X) = 1 1 + e ✓·X Remember this? First is our hypothesis.

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h✓(X) = 1 1 + e ✓·X Remember this? ✓·X = ✓0 + ✓1X1 + ✓2X2 + . . . First is our hypothesis.

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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.

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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.

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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.

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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.

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BAD? block user! Also save the tweet to DB for future analysis.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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)

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Questions?