INFO 4300 / CS4300 Information Retrieval slides adapted from - - PowerPoint PPT Presentation

INFO 4300 / CS4300 Information Retrieval slides adapted from Hinrich Sch¨ utze’s, linked from http://informationretrieval.org/

IR 24/25: Text Classification and Naive Bayes

Paul Ginsparg

Cornell University, Ithaca, NY

29 Nov 2011

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Administrativa

Assignment 4 due Fri 2 Dec (extended to Sun 4 Dec). Final examination: Wed, 14 Dec, from 7:00-9:30 p.m., in Upson B17

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Overview

1

Recap of Text classification

2

Naive Bayes

3

Discussion

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Outline

1

Recap of Text classification

2

Naive Bayes

3

Discussion

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Relevance feedback

In relevance feedback, the user marks documents as relevant/nonrelevant. Relevant/nonrelevant can be viewed as classes or categories. For each document, the user decides which of these two classes is correct. The IR system then uses these class assignments to build a better query (“model”) of the information need . . . . . . and returns better documents. Relevance feedback is a form of text classification. The notion of text classification (TC) is very general and has many applications within and beyond information retrieval.

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Another TC task: spam filtering

From: ‘‘’’ <takworlld@hotmail.com> Subject: real estate is the only way... gem

• alvgkay

Anyone can buy real estate with no money down Stop paying rent TODAY ! There is no need to spend hundreds or even thousands for similar courses I am 22 years old and I have already purchased 6 properties using the methods outlined in this truly INCREDIBLE ebook. Change your life NOW ! ================================================= Click Below to order: http://www.wholesaledaily.com/sales/nmd.htm ================================================= How would you write a program that would automatically detect and delete this type of message?

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Formal definition of TC — summary

Training Given: A document space X

Documents are represented in some high-dimensional space.

A fixed set of classes C = {c1, c2, . . . , cJ}

human-defined for needs of application (e.g., rel vs. non-rel).

A training set D of labeled documents d, c ∈ X × C Using a learning method or learning algorithm, we then wish to learn a classifier γ that maps documents to classes: γ : X → C Application/Testing Given: a description d ∈ X of a document Determine: γ(d) ∈ C, i.e., the class most appropriate for d

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Topic classification

classes: training set: test set:

regions industries subject areas γ(d′) =China

first private Chinese airline

UK China poultry coffee elections sports

London congestion Big Ben Parliament the Queen Windsor Beijing Olympics Great Wall tourism communist Mao chicken feed ducks pate turkey bird flu beans roasting robusta arabica harvest Kenya votes recount run-off seat campaign TV ads baseball diamond soccer forward captain team

d′

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Examples of how search engines use classification

Standing queries (e.g., Google Alerts) Language identification (classes: English vs. French etc.) The automatic detection of spam pages (spam vs. nonspam) The automatic detection of sexually explicit content (sexually explicit vs. not) Sentiment detection: is a movie or product review positive or negative (positive vs. negative) Topic-specific or vertical search – restrict search to a “vertical” like “related to health” (relevant to vertical vs. not)

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Classification methods: 1. Manual

Manual classification was used by Yahoo in the beginning of the web. Also: ODP, PubMed Very accurate if job is done by experts Consistent when the problem size and team is small Scaling manual classification is difficult and expensive. → We need automatic methods for classification.

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Classification methods: 2. Rule-based

Our Google Alerts example was rule-based classification. There are “IDE” type development environments for writing very complex rules efficiently. (e.g., Verity integrated development environment) Often: Boolean combinations (as in Google Alerts) Accuracy is very high if a rule has been carefully refined over time by a subject expert. Building and maintaining rule-based classification systems is expensive.

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Classification methods: 3. Statistical/Probabilistic

As per our definition of the classification problem – text classification as a learning problem Supervised learning of a the classification function γ and its application to classifying new documents We have looked at a couple of methods for doing this: Rocchio, kNN. Now Naive Bayes No free lunch: requires hand-classified training data But this manual classification can be done by non-experts.

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Classification methods — summary

• 1. Manual (accurate if done by experts, consistent for problem size

and team is small difficult and expensive to scale)

• 2. Rule-based (accuracy very high if a rule has been carefully

refined over time by a subject expert, building and maintaining expensive)

• 3. Statistical/Probabilistic

As per our definition of the classification problem – text classification as a learning problem Supervised learning of a the classification function γ and its application to classifying new documents We have looked at a couple of methods for doing this: Rocchio, kNN. Now Naive Bayes No free lunch: requires hand-classified training data But this manual classification can be done by non-experts.

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Outline

1

Recap of Text classification

2

Naive Bayes

3

Discussion

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The Naive Bayes classifier

The Naive Bayes classifier is a probabilistic classifier. We compute the probability of a document d being in a class c as follows: P(c|d) ∝ P(c)

• 1≤k≤nd

P(tk|c) nd is the length of the document. (number of tokens) P(tk|c) is the conditional probability of term tk occurring in a document of class c P(tk|c) as a measure of how much evidence tk contributes that c is the correct class. P(c) is the prior probability of c. If a document’s terms do not provide clear evidence for one class vs. another, we choose the c with higher P(c).

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Maximum a posteriori class

Our goal is to find the “best” class. The best class in Naive Bayes classification is the most likely

• r maximum a posteriori (MAP) class cmap:

cmap = arg max

c∈C

ˆ P(c|d) = arg max

c∈C

ˆ P(c)

• 1≤k≤nd

ˆ P(tk|c) We write ˆ P for P since these values are estimates from the training set.

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Taking the log

Multiplying lots of small probabilities can result in floating point underflow. Since log(xy) = log(x) + log(y), we can sum log probabilities instead of multiplying probabilities. Since log is a monotonic function, the class with the highest score does not change. So what we usually compute in practice is: cmap = arg max

c∈C

• log ˆ

P(c) +

• 1≤k≤nd

log ˆ P(tk|c)

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Naive Bayes classifier

Classification rule: cmap = arg max

c∈C

• log ˆ

P(c) +

• 1≤k≤nd

log ˆ P(tk|c)

• Simple interpretation:

Each conditional parameter log ˆ P(tk|c) is a weight that indicates how good an indicator tk is for c. The prior log ˆ P(c) is a weight that indicates the relative frequency of c. The sum of log prior and term weights is then a measure of how much evidence there is for the document being in the class. We select the class with the most evidence.

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Parameter estimation

How to estimate parameters ˆ P(c) and ˆ P(tk|c) from training data? Prior: ˆ P(c) = Nc N Nc: number of docs in class c; N: total number of docs Conditional probabilities: ˆ P(t|c) = Tct

• t′∈V Tct′

Tct is the number of tokens of t in training documents from class c (includes multiple occurrences) We’ve made a Naive Bayes independence assumption here: ˆ P(tk1|c) = ˆ P(tk2|c) (i.e., position independence of terms)

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The problem with maximum likelihood estimates: Zeros

C=China X1=Beijing X2=and X3=Taipei X4=join X5=WTO

P(China|d) ∝ P(China) · P(Beijing|China) · P(and|China) · P(Taipei|China) · P(join|China) · P(WTO|China) If WTO never occurs in class China: ˆ P(WTO|China) = TChina,WTO

• t′∈V TChina,t′

= 0

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The problem with maximum likelihood estimates: Zeros (cont’d)

If there were no occurrences of WTO in documents in class China, we’d get a zero estimate: ˆ P(WTO|China) = TChina,WTO

• t′∈V TChina,t′

= 0 → We will get P(China|d) = 0 for any document that contains WTO! Zero probabilities cannot be conditioned away.

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To avoid zeros: Add-one smoothing

Add one to each count to avoid zeros: ˆ P(t|c) = Tct + 1

• t′∈V (Tct′ + 1) =

Tct + 1 (

t′∈V Tct′) + B

B is the number of different words (in this case the size of the vocabulary: |V | = M)

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Naive Bayes: Summary

Estimate parameters from the training corpus using add-one smoothing For a new document, for each class, compute sum of (i) log of prior, and (ii) logs of conditional probabilities of the terms Assign the document to the class with the largest score

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Naive Bayes: Training

TrainMultinomialNB(C, D) 1 V ← ExtractVocabulary(D) 2 N ← CountDocs(D) 3 for each c ∈ C 4 do Nc ← CountDocsInClass(D, c) 5 prior[c] ← Nc/N 6 textc ← ConcatenateTextOfAllDocsInClass(D, c) 7 for each t ∈ V 8 do Tct ← CountTokensOfTerm(textc, t) 9 for each t ∈ V 10 do condprob[t][c] ←

Tct+1 P

t′(Tct′+1)

11 return V , prior, condprob

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Naive Bayes: Testing

ApplyMultinomialNB(C, V , prior, condprob, d) 1 W ← ExtractTokensFromDoc(V , d) 2 for each c ∈ C 3 do score[c] ← log prior[c] 4 for each t ∈ W 5 do score[c]+ = log condprob[t][c] 6 return arg maxc∈C score[c]

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Exercise

docID words in document in c = China? training set 1 Chinese Beijing Chinese yes 2 Chinese Chinese Shanghai yes 3 Chinese Macao yes 4 Tokyo Japan Chinese no test set 5 Chinese Chinese Chinese Tokyo Japan ? Estimate parameters of Naive Bayes classifier Classify test document

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Example: Parameter estimates

Priors: ˆ P(c) = 3/4 and ˆ P(c) = 1/4 Conditional probabilities: ˆ P(Chinese|c) = (5 + 1)/(8 + 6) = 6/14 = 3/7 ˆ P(Tokyo|c) = ˆ P(Japan|c) = (0 + 1)/(8 + 6) = 1/14 ˆ P(Chinese|c) = ˆ P(Tokyo|c) = ˆ P(Japan|c) = (1 + 1)/(3 + 6) = 2/9 The denominators are (8 + 6) and (3 + 6) because the lengths of textc and textc are 8 and 3, respectively, and because the constant B is 6 since the vocabulary consists of six terms.

Exercise: verify that ˆ P(Chinese|c) + ˆ P(Beijing|c) + ˆ P(Shanghai|c) + ˆ P(Macao|c) + ˆ P(Tokyo|c) + ˆ P(Japan|c) = 1 and ˆ P(Chinese|c) + ˆ P(Beijing|c) + ˆ P(Shanghai|c) + ˆ P(Macao|c) + ˆ P(Tokyo|c) + ˆ P(Japan|c) = 1

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Example: Classification

d5 = (Chinese Chinese Chinese Tokyo Japan) ˆ P(c|d5) ∝ 3/4 · (3/7)3 · 1/14 · 1/14 ≈ 0.0003 ˆ P(c|d5) ∝ 1/4 · (2/9)3 · 2/9 · 2/9 ≈ 0.0001 Thus, the classifier assigns the test document to c = China: the three occurrences of the positive indicator Chinese in d5

• utweigh the occurrences of the two negative indicators Japan

and Tokyo. Exercise: evaluate ˆ P(c|d) and ˆ P(c|d) for d6 = (Chinese Chinese Tokyo Japan) and d7 = (Chinese Tokyo Japan)

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Time complexity of Naive Bayes

mode time complexity training Θ(|D|Lave + |C||V |) testing Θ(La + |C|Ma) = Θ(|C|Ma) Lave: the average length of a doc, La: length of the test doc, Ma: number of distinct terms in the test doc Θ(|D|Lave) is the time it takes to compute all counts. Θ(|C||V |) is the time it takes to compute the parameters from the counts. Generally: |C||V | < |D|Lave Why? Test time is also linear (in the length of the test document). Thus: Naive Bayes is linear in the size of the training set (training) and the test document (testing). This is optimal.

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Outline

1

Recap of Text classification

2

Naive Bayes

3

Discussion

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Discussion 5

More Statistical Methods: Peter Norvig, “How to Write a Spelling Corrector” http://norvig.com/spell-correct.html (Recall also the above video assignment for 25 Oct: http://www.youtube.com/watch?v=yvDCzhbjYWs “The Unreasonable Effectiveness of Data”, given 23 Sep 2010.) Additional related reference: http://doi.ieeecomputersociety.org/10.1109/MIS.2009.36

• A. Halevy, P. Norvig, F. Pereira,

The Unreasonable Effectiveness of Data, Intelligent Systems Mar/Apr 2009 (copy at readings/unrealdata.pdf)

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A little theory

Find the correction c that maximizes the probability of c given the

• riginal word w:

argmaxc P(c|w) By Bayes’ Theorem, equivalent to argmaxc P(w|c)P(c)/P(w). P(w) the same for every possible c, so ignore, and consider: argmaxc P(w|c)P(c) . Three parts : P(c), the probability that a proposed correction c stands on its own. The language model: “how likely is c to appear in an English text?” (P(“the”) high, P(“zxzxzxzyyy”) near zero) P(w|c), the probability that w would be typed when author meant c. The error model: “how likely is author to type w by mistake instead of c?” argmaxc, the control mechanism: choose c that gives the best combined probability score.

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Example

w=“thew” two candidate corrections c=“the” and c=“thaw”. which has higher P(c|w)? “thaw” has only small change “a” to “e” “the” is a very common word, and perhaps the typist’s finger slipped off the “e” onto the “w”. To estimate P(c|w), have to consider both the probability of c and the probability of the change from c to w

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Complete Spelling Corrector

import re, collections def words(text): return re.findall(’[a-z]+’, text.lower()) def train(features): model = collections.defaultdict(lambda: 1) for f in features: model[f] += 1 return model NWORDS = train(words(file(’big.txt’).read())) alphabet = ’abcdefghijklmnopqrstuvwxyz’ = ⇒

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def edits1(word): s = [(word[:i], word[i:]) for i in range(len(word) + 1)] deletes = [a + b[1:] for a, b in s if b] transposes = [a + b[1] + b[0] + b[2:] for a, b in s if len(b)>1] replaces = [a + c + b[1:] for a, b in s for c in alphabet if b] inserts = [a + c + b for a, b in s for c in alphabet] return set(deletes + transposes + replaces + inserts)

def known edits2(word): return set(e2 for e1 in edits1(word) for e2 in edits1(e1) if e2 in NWORDS)

def known(words): return set(w for w in words if w in NWORDS) def correct(word): candidates = known([word]) or known(edits1(word))

• r known edits2(word) or [word]

return max(candidates, key=NWORDS.get)

(For word of length n: n deletions, n-1 transpositions, 26n alterations, and 26(n+1) insertions, for a total of 54n+25 at edit distance 1)

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