Classification, Linear Models, Naïve Bayes

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1 Classification, Linear Models, Naïve Bayes CMSC 470 Marine Carpuat Slides credit: Dan Jurafsky & James Martin, Jacob Eisenstein

2 Today Text classification problems and their evaluation Linear classifiers Features & Weights Bag of words Naïve Bayes

3 Classification problems

4 Multiclass Classification Training Testing training data? unlabeled document label 1 label 2 label 3 label 4 supervised machine learning algorithm Feature Functions Classifier label 1? label 2? label 3? label 4?

5 Is this spam? From: "Fabian Starr Subject: Hey! Sofware for the funny prices! Get the great discounts on popular software today for PC and Macintosh % Discounts from retail price!!! All sofware is instantly available to download - No Need Wait!

6 What is the subject of this article? MEDLINE Article? MeSH Subject Category Hierarchy Antogonists and Inhibitors Blood Supply Chemistry Drug Therapy Embryology Epidemiology

7 Text Classification Assigning subject categories, topics, or genres Spam detection Authorship identification Age/gender identification Language Identification Sentiment analysis

8 Text Classification: definition Input: a document d a fixed set of classes Y = {y 1, y 2,, y J } Output: a predicted class y Y

9 Classification Methods: Supervised Machine Learning Input a document d a fixed set of classes Y = {y 1, y 2,, y J } a training set of m hand-labeled documents (d 1,y 1 ),...,(d m,y m ) Output a learned classifier d y

10 Aside: getting examples for supervised learning Human annotation By experts or non-experts (crowdsourcing) Found data How do we know how good a classifier is? Compare classifier predictions with human annotation On held out test examples Evaluation metrics: accuracy, precision, recall

11 The 2-by-2 contingency table correct not correct selected tp fp not selected fn tn

12 Precision and recall Precision: % of selected items that are correct Recall: % of correct items that are selected correct not correct selected tp fp not selected fn tn

13 A combined measure: F A combined measure that assesses the P/R tradeoff is F measure (weighted harmonic mean): F 2 1 ( b + 1) PR = = a + (1 -a) b P + R P R People usually use balanced F1 measure i.e., with = 1 (that is, = ½): F = 2PR/(P+R)

14 Linear Models for Multiclass Classification

15 Linear Models for Classification Feature function representation Weights

16 Defining features: Bag of words

17 Defining features

18 Linear Classification

19 Linear Models for Classification Feature function representation Weights

20 How can we learn weights? By hand Probability e.g.,naïve Bayes Discriminative training e.g., perceptron, support vector machines

21 Naïve Bayes Models for Text Classification

22 Generative Story for Multinomial Naïve Bayes A hypothetical stochastic process describing how training examples are generated

23 Prediction with Naïve Bayes Score(x,y) Definition of conditional probability Generative story assumptions This is a linear model!

24 Prediction with Naïve Bayes Score(x,y) Definition of conditional probability Generative story assumptions This is a linear model!

25 Prediction with Naïve Bayes Score(x,y) Definition of conditional probability Generative story assumptions This is a linear model!

26 Parameter Estimation count and normalize Parameters of a multinomial distribution Relative frequency estimator Formally: this is the maximum likelihood estimate See CIML for derivation

27 Smoothing (add alpha)

28 Naïve Bayes recap

29 Why is this model called Naïve Bayes? Another view of the same model y = argmax y P Y = y X = x) = argmax y P(Y = y)p X = x Y = y) = argmax y P(Y = y) d i=1 P X i = x i Y = y) Bayes rule + Conditional independence assumption

30 Today Text classification problems and their evaluation Linear classifiers Features & Weights Bag of words Naïve Bayes

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