Information Storage and Retrieval(信息存储与检索)_probability_model

Probability of a relevant document
P(relevto 1.
0<= P <=1
The probability that a document is not relevant to the query is defined as:
Probability of a relevant document
[1] there are N documents in a DB [2] n of them (N) are relevant to a query( n<=N) in a DB [3] a document is randomly retrieved from the DB, therefore: The probability that a randomly retrieved document is relevant to the query is defined as:
P(rel | retrieved) > 0.5
Discrimination function
[5]. Discrimination function is defined as:
P(rel | retrieved) Dis(retrieved)=-------------------------P(not rel | retrieved)
Probability theory
P( Event ) is always smaller than or equal to 1.
0<= P <=1
The probability that an event does not happen is:
P(not event)=1-P(event)
Probability theory
Discrimination function
If event A is statistically independent from event B, it means that occurrence of event A(B) has no impact on event
B(A). In other words, Event A and event B
Example
P(H0|H1) = 0.6 P(H0|H2) = 0.07 P(H0|H3) = 0.001 What should be our guess about Joe's profession? Most likely, it is H1.
Statistical independence
P(not relevance)=1-P(relevance) P(not relevance)= 1-(n/N) P(not relevance)= (N-n)/N
Discrimination function
[1] A query can divide the database into two basic sets: the retrieved and the not retrieved. [2]. Since not all of documents retrieved are truly relevant, therefore, the probability of a retrieved document that is relevant or not relevant should be considered as:
Example
Let H0 = “Joe earns more than $70,000/year” H1 = “Joe is a doctor” H2 = “Joe is a college professor” H3 = “Joe works in food services” Suppose we do a survey and we find out (from observed/questionnaires, etc.--sampled doctors, college profs, food services folks for their salary $70,000/year) Hi is a hypothesis.
Probability retrieval model
The basic idea of probability retrieval model is that given a document and a query it should be possible to calculate the possibility that the document is relevance to a query. Probability retrieval model attempts to address the IR problem within a probabilistic framework.
P( rel | retrieved) and P(not rel | retrieved)
Discrimination function
[3] Ideally, a retrieval criteria should be set up to examine that the possibility that a retrieved document is relevant is larger than it is not relevant, that is:
Conditional probability The conditional probability of event A occurring given that event B has occurred is denoted by:
P(A|B)
It means that knowledge of B can affect the perception of the probability of A.
P(relevance)=n/N
Representation of Document
“Binary” Boolean presentation: documents are represented as binary vectors of terms :
D(x1, x2,… xj,…, xn) xj=1 if it is relevant, or 0 otherwise. Which is similar to the vector IR model. And finally all documents form a binary document-term matrix.
are statistically independent if an occurrence of either of them does not depend on the other.
Probability theory
The following equation is correct if event A is statistically independent from the event B
P(A*B)=P(A)*P(B)
Bayes theorem
P(B|A)*P(A) P(A|B)= ------------------P(B)
The theory allows us to invert conditional probability. Suppose event A and event B are statistically independent.
Documents are retrieved if and only if Dis(retrieved)>1
Discrimination function
[6]. Adjustment of the discrimination function If users want a more precision for the result, they can modify the two discrimination function. For example: P(rel|retrieved) > 3*P(not rel |retrieved) P(rel|retrieved) > 3*(1-P(rel |retrieved)) P(rel|retrieved) + 3*P(rel |retrieved)>3 P(rel|retrieved) > 0.75
Information Storage and Retrieval
540-671 Probability Model
What is the probability?
The occurrence likelihood of a specific event, which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty. An event with a probability of 0 can be considered an impossibility.
What is the probability?
Summary: All possible events must be clearly defined. All events are mutually exclusive. Special event must be identified when you compute a probability. Probability ranges from 0 to 1. No negative! Possibility for all possible events is equal to 1. Theoretically speaking, all events considered should have even chances.