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### Naïve Bayes Classifier

CS 652 Information Extraction and Integration

- A ranking is an ordering of the documents retrieved that (hopefully) reflects the relevance of the documents to the user query
- A ranking is based on fundamental premises regarding the notion of relevance, such as:
- common sets of index terms
- sharing of weighted terms
- likelihood of relevance

- Eachset of premises leads to a distinct IR model

Set Theoretic

Generalized Vector (Space)

Latent Semantic Index

Neural Networks

Structured Models

Fuzzy

Extended Boolean

Non-Overlapping Lists

Proximal Nodes

Classic Models

Probabilistic

Boolean

Vector (Space)

Probabilistic

Inference Network

Belief Network

Browsing

Flat

Structure Guided

Hypertext

IR Models

U

s

e

r

T

a

s

k

Retrieval

Browsing

Each document is described by a set of representative keywords or index terms

Index terms are document words (i.e. nouns), which have meaning by themselves for remembering the main themes of a document

However, search engines assume that all words are index terms (full text representation)

- Not all terms are equally useful for representing the document contents
- The importance of the index terms is represented by weights associated to them
- Let
- kibe an index term
- djbe a document
- wij is a weight associated with (ki,dj ),which quantifies the importance of ki for describing the contents of dj

- Define:
- wij > 0 whenever ki dj
- wiq>= 0 associated with the pair (ki,q)
- vec(dj ) = (w1j, w2j, ..., wtj),document vectorof dj
- vec(q) = (w1q, w2q, ..., wtq),query vectorof q
- The unitary vectors vec(di) and vec(qj) are assumed to be orthonormal (i.e., index terms are assumed to occur independently within the documents)

- Queries and documents are represented as weighted vectors

j

dj

q

i

Sim(q,dj ) = cos() = [vec(dj) vec(q)] / |dj | |q|

= [ti=1wij wiq ] / ti=1wij2 ti=1wiq2

where is the inner product operator & |q| is the length of q

Since wij0and wiq 0, 1 sim(q, dj ) 0

A document is retrieved even if it matches the query terms only partially

- Sim(q, dj ) = [ti=1 wij wiq ] / |dj | |q|
- How to compute the weights wijand wiq?
- A good weight must take into account two effects:
quantification of intra-document contents (similarity)

- tf factor, the term frequency within a document
quantification of inter-documents separation (dissi- milarity)

- idf factor, the inverse document frequency

- tf factor, the term frequency within a document
- wij = tf(i, j) idf(i)

- Let,
- N be the total number of documents in the collection
- nibe the number of documents which containki
- freq(i, j), theraw frequency of kiwithin dj

- A normalizedtf factor is given by
- f(i, j) = freq(i, j) / max(freq(l, j)),
- where the maximum is computed over all terms which occur within the document dj

- The inverse document frequency (idf)factor is
- idf(i) = log (N / ni )
- the log is used to make the values of tf and idf comparable. It can also be interpreted as the amount of information associated with term ki.

- The best term-weighting schemes use weights which are give by
- wij = f(i, j) log(N / ni)
- the strategy is called a tf-idf weighting scheme

- For the query term weights, a suggestion is
- Wiq = (0.5 + [0.5 freq(i, q) / max(freq(l, q))]) log(N/ni)

- The vector model with tf-idf weights is a good ranking strategy with general collections
- The VSM is usually as good as the known ranking alternatives. It is also simple and fast to compute

- Advantages:
- term-weighting improves quality of the answer set
- partial matching allows retrieval of documents that approximate the query conditions
- cosine ranking formula sorts documents according to degree of similarity to the query
- A popular IR model because of its simplicity & speed

- Disadvantages:
- assumes mutuallyindependence of index terms (??);
- not clear that this is bad though

CS 652 Information Extraction and Integration

Bayes Theorem

The basic starting point for inference problems using probability theory as logic

Bayes Theorem

.008

.992

.98

.02

.03

.97

P(+|cancer)P(cancer)=(.98).008=.0078

P(+|~cancer)P(~cancer)=(.03).992=.0298

Naïve Bayes Subtleties

m-estimate of probability

Learning to Classify Text

- Classify text into manually defined groups
- Estimate probability of class membership
- Rank by relevance
- Discover grouping, relationships
- Between texts
- Between real-world entities mentioned in text

How to Improve

- More training data
- Better training data
- Better text representation
- Usual IR tricks (term weighting, etc.)
- Manually construct good predictor features

- Hand off hard cases to human being

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