(Note: in real life there is often a hierarchy, not present in the above problem statement; and also, you get papers on ML approaches to Garb. Coll.)
More Text Classification ExamplesMany search engine functionalities use classification
Assigning labels to documents or web-pages:
Labels are most often topics such as Yahoo-categories
"finance," "sports," "news>world>asia>business"
Labels may be genres
"editorials" "movie-reviews" "news”
Labels may be opinion on a person/product
“like”, “hate”, “neutral”
Labels may be domain-specific
"interesting-to-me" : "not-interesting-to-me”
“contains adult language” : “doesn’t”
language identification: English, French, Chinese, …
search vertical: about Linux versus not
“link spam” : “not link spam"
Classification Methods (1)
Used by the original Yahoo! Directory
Looksmart, about.com, ODP, PubMed
Very accurate when job is done by experts
Consistent when the problem size and team is small
Difficult and expensive to scale
Means we need automatic classification methods for big problems
Classification Methods (2)
Hand-coded rule-based classifiers
One technique used by CS dept’s spam filter, Reuters, CIA, etc.
It’s what Google Alerts is doing
Widely deployed in government and enterprise
Companies provide “IDE” for writing such rules
E.g., assign category if document contains a given boolean combination of words
Commercial systems have complex query languages (everything in IR query languages +score accumulators)
Accuracy is often very high if a rule has been carefully refined over time by a subject expert
Building and maintaining these rules is expensive
A Verity topic A complex classification rule
Classification Methods (3)
Supervised learning of a document-label assignment function
Many systems partly or wholly rely on machine learning (Autonomy, Microsoft, Enkata, Yahoo!, …)
k-Nearest Neighbors (simple, powerful)
Naive Bayes (simple, common method)
Support-vector machines (new, generally more powerful)
… plus many other methods
No free lunch: requires hand-classified training data
But data can be built up (and refined) by amateurs
Many commercial systems use a mixture of methods
In relevance feedback, the user marks a few documents as relevant/nonrelevant
The choices can be viewed as classes or categories
The IR system then uses these judgments to build a better model of the information need
So, relevance feedback can be viewed as a form of text classification (deciding between several classes)
Probabilistic relevance feedback
Rather than reweighting in a vector space…
If user has told us some relevant and some nonrelevant documents, then we can proceed to build a probabilistic classifier
such as the Naive Bayes model we will look at today:
P(tk|R) = |Drk| / |Dr|
P(tk|NR) = |Dnrk| / |Dnr|
tk is a term; Dr is the set of known relevant documents; Drk is the subset that contain tk; Dnr is the set of known nonrelevant documents; Dnrk is the subset that contain tk.
Recall a few probability basics
For events a and b:
- Bayes’ Rule
Learning and classification methods based on probability theory
Bayes theorem plays a critical role
Builds a generative model that approximates how data is produced
Has prior probability of each category given no information about an item.
Model produces a posterior probability
Distribution over the possible categories given an item
Naïve Bayes methods use a bag of words as the item description
The bag of words representation
The bag of words representation
Bayes’ Rule for text classification
For a document d and a class c
Naive Bayes Classifiers
Task: Classify a new instance d based on a tuple of attribute values into one of the classes cj ∈ C
- MAP is “maximum a posteriori” = most likely class
Naïve Bayes Classifier: Naïve Bayes Assumption
Can be estimated from the frequency of classes in the training examples.
Could only be estimated if a very, very large number of training examples was available.
Naïve Bayes Conditional Independence Assumption:
Assume that the probability of observing the conjunction of attributes is equal to the product of the individual probabilities P(xi|cj).
The Multivariate Bernoulli NB Classifier [Like Prob IR BIM; not language model; less used]
Conditional Independence Assumption: features detect term presence and are independent of each other given the class:
- This model is appropriate for binary variables
Multivariate Bernoulli model
Learning the Model
First attempt: maximum likelihood estimates
- Simply use the frequencies in the data
Problem with Maximum Likelihood
What if we have seen no training documents with the word muscle-ache and classified in the topic Flu?
Zero probabilities cannot be conditioned away, no matter the other evidence!
Smoothing to Avoid Overfitting
Somewhat more subtle version
Stochastic Language Models
Model probability of generating any string
Stochastic Language Models
Model probability of generating strings (each word in turn) in a language (commonly all strings over alphabet ∑). E.g., a unigram model
Unigram and higher-order models
Naïve Bayes via a class conditional language model = multinomial NB
The probability of the words is done as a class-specific unigram language model
Using Multinomial Naive Bayes Classifiers to Classify Text: Basic method
Attributes are text positions, values are words.
Still too many possibilities
Assume that classification is independent of the positions of the words
Use same parameters for each position
Result is bag of words model (over tokens not types)
Naive Bayes and Language Modeling
Naïve Bayes classifiers can use any sort of feature
URL, email address, dictionaries, network features
But if, as in the previous slides
We use only word features
we use all of the words in the text (not a subset)
Naïve Bayes is basically the same as language modeling
Multinomial Naive Bayes: Learning
- From training corpus, extract Vocabulary
- Calculate required P(cj) and P(xk | cj) terms
- For each cj in C do
- docsj ← subset of documents for which the target class is cj
- Textj ← single document containing all docsj
- for each word xk in Vocabulary
- nk ← number of occurrences of xk in Textj
Naive Bayes: Classifying
positions ← all word positions in current document
which contain tokens found in Vocabulary
Return cNB, where
Naive Bayes: Time Complexity
Training Time: O(|D|Lave + |C||V|)) where Lave is the average length of a document in D.
Assumes all counts are pre-computed in O(|D|Lave) time during one pass through all of the data. ← Why ?
Generally just O(|D|Lave) since usually |C||V| < |D|Lave
Test Time: O(|C| Lt) where Lt is the average length of a test document.
Very efficient overall, linearly proportional to the time needed to just read in all the data.
Underflow Prevention: using logs
Multiplying lots of probabilities, which are between 0 and 1 by definition, can result in floating-point underflow.
Since log(xy) = log(x) + log(y), it is better to perform all computations by summing logs of probabilities rather than multiplying probabilities.
Class with highest final un-normalized log probability score is still the most probable.
Note that model is now just max of sum of weights…
Chinese Beijing Chinese
Chinese Chinese Shanghai
Tokyo Japan Chinese
Chinese Chinese Chinese Tokyo Japan
Two Naive Bayes Models
Model 1: Multivariate Bernoulli
One feature Xw for each word in dictionary
for loop iterates over dictionary
Xw = true in document d if w appears in d
Naive Bayes assumption:
Given the document’s topic, appearance of one word in the document tells us nothing about chances that another word appears
This is the model used in the binary independence model in classic probabilistic relevance feedback on hand-classified data
Model 2: Multinomial = Class conditional unigram
One feature Xi for each word pos in document
feature’s values are all words in dictionary
Value of Xi is the word in position i
Naïve Bayes assumption:
Given the document’s topic, word in one position in the document tells us nothing about words in other positions
Word appearance does not depend on position
P(Xi = w | c) = P(Xj = w | c)
Just have one multinomial feature predicting all words
for all positions i,j, word w, and class c
Multivariate Bernoulli model:
|fraction of documents of topic cj in which word w appears|
|fraction of times in which word w appears among all words in documents of topic cj|
- Can create a mega-document for topic j by concatenating all documents in this topic
- Use frequency of w in mega-document
Which to use for classification?
Multinomial vs Multivariate Bernoulli?
Multinomial model is almost always more effective in text applications!
See results figures later
There has been exploration of multinomial naïve bayes variants which often work better in practice
Binarized multinomial Naïve Bayes, etc.
Topic of PA4
Feature Selection: Why?
Text collections have a large number of features
10,000 – 1,000,000 unique words … and more
May make using a particular classifier feasible
Some classifiers can’t deal with 1,000,000 features
Reduces training time
Training time for some methods is quadratic or worse in the number of features
Makes runtime models smaller and faster
Can improve generalization (performance)
Eliminates noise features
Feature Selection: How?
Hypothesis testing statistics:
Are we confident that the value of one categorical variable is associated with the value of another
Chi-square test (χ2)
How much information does the value of one categorical variable give you about the value of another
They’re similar, but χ2 measures confidence in association, (based on available statistics), while MI measures extent of association (assuming perfect knowledge of probabilities)
|2 statistic (CHI)
|2 is interested in (fo – fe)2/fe summed over all table entries: is the observed number what you’d expect given the marginals?
The null hypothesis is rejected with confidence .999,
since 12.9 > 10.83 (the value for .999 confidence).
|2 statistic (CHI)
There is a simpler formula for 2x2 χ2:
N = A + B + C + D
Value for complete independence of term and category?
Feature selection via Mutual Information
In training set, choose k words which best discriminate (give most info on) the categories.
The Mutual Information between a word, class is:
For each word w and each category c
Feature selection via MI (contd.)
For each category we build a list of k most discriminating terms.
For example (on 20 Newsgroups):
sci.electronics: circuit, voltage, amp, ground, copy, battery, electronics, cooling, …
rec.autos: car, cars, engine, ford, dealer, mustang, oil, collision, autos, tires, toyota, …
Greedy: does not account for correlations between terms
Clear information-theoretic interpretation
May select rare uninformative terms
May select very slightly informative frequent terms that are not very useful for classification
Feature Selection: Frequency
The simplest feature selection method:
Just use the commonest terms
No particular foundation
But it make sense why this works
They’re the words that can be well-estimated and are most often available as evidence
In practice, this is often 90% as good as better methods
Feature selection for NB
In general feature selection is necessary for multivariate Bernoulli NB.
Otherwise you suffer from noise, multi-counting
“Feature selection” really means something different for multinomial NB. It means dictionary truncation
The multinomial NB model only has 1 feature
This “feature selection” normally isn’t needed for multinomial NB, but may help a fraction with quantities that are badly estimated
Evaluation must be done on test data that are independent of the training data (usually a disjoint set of instances).
Sometimes use cross-validation (averaging results over multiple training and test splits of the overall data)
It’s easy to get good performance on a test set that was available to the learner during training (e.g., just memorize the test set).
Measures: precision, recall, F1, classification accuracy
Classification accuracy: c/n where n is the total number of test instances and c is the number of test instances correctly classified by the system.
Adequate if one class per document
Otherwise F measure for each class
Naive Bayes vs. other methods
WebKB Experiment (1998)
Classify webpages from CS departments into:
student, faculty, course,project
Train on ~5,000 hand-labeled web pages
NB Model Comparison: WebKB
Naïve Bayes has found a home in spam filtering
Paul Graham’s A Plan for Spam
A Naive Bayes-like classifier with weird parameter estimation
Widely used in spam filters
But many features beyond words:
black hole lists, etc.
particular hand-crafted text patterns
Naïve Bayes in Spam Filtering
Basic (Naïve) Bayes spam probability
Mentions: Generic Viagra
Mentions millions of (dollar) ((dollar) NN,NNN,NNN.NN)
Phrase: impress ... girl
Phrase: 'Prestigious Non-Accredited Universities’
From: starts with many numbers
Subject is all capitals
HTML has a low ratio of text to image area
Relay in RBL, http://www.mail-abuse.com/enduserinfo_rbl.html
RCVD line looks faked
Naïve Bayes on spam email
Violation of NB Assumptions
The independence assumptions do not really hold of documents written in natural language.
Naïve Bayes Posterior Probabilities
Classification results of naïve Bayes (the class with maximum posterior probability) are usually fairly accurate.
However, due to the inadequacy of the conditional independence assumption, the actual posterior-probability numerical estimates are not.
Output probabilities are commonly very close to 0 or 1.
Correct estimation ⇒ accurate prediction, but correct probability estimation is NOT necessary for accurate prediction (just need right ordering of probabilities)
Naive Bayes is Not So Naiventitled
Very Fast Learning and Testing (basically just count the data)
Low Storage requirements
Very good in domains with many equally important features
More robust to irrelevant features than many learning methods
Irrelevant Features cancel each other without affecting results
More robust to concept drift (changing class definition over time)
Naive Bayes won 1st and 2nd place in KDD-CUP 97 competition out of 16 systems
Goal: Financial services industry direct mail response prediction: Predict if the recipient of mail will actually respond to the advertisement – 750,000 records.
A good dependable baseline for text classification (but not the best)!