Concepts
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the system to its user will be the best that is obtainable on the basis of those data
...Of course this principle raises many questions as to the acceptability of the assumptions
...The probability ranking principle assumes that we can calculate P relevance document,not only that,it assumes that we can do it accurately
...So returning now to the immediate problem which is to calculate,or estimate,P relevance document
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we work with the ratio In the latter case we do not see the retrieval problem as one of discriminating between relevant and non relevant documents,instead we merely wish to compute the P relevance x for each document x and present the user with documents in decreasing order of this probability
...The decision rules derived above are couched in terms of P x wi
...I will now proceed to discuss ways of using this probabilistic model of retrieval and at the same time discuss some of the practical problems that arise
...The curse of dimensionality In deriving the decision rules I assumed that a document is represented by an n dimensional vector where n is the size of the index term vocabulary
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Basic probabilistic model Since we are assuming that each document is described by the presence absence of index terms any document can be represented by a binary vector,x x 1,x 2,...where xi 0 or 1 indicates absence or presence of the ith index term
...w 1 document is relevant w 2 document is non relevant
...The theory that follows is at first rather abstract,the reader is asked to bear with it,since we soon return to the nuts and bolts of retrieval
...So,in terms of these symbols,what we wish to calculate for each document is P w 1 x and perhaps P w 2 x so that we may decide which is relevant and which is non relevant
...Here P wi is the prior probability of relevance i 1 or non relevance i 2,P x wi is proportional to what is commonly known as the likelihood of relevance or non relevance given x;in the continuous case this would be a density function and we would write p x wi
...which is the probability of observing x on a random basis given that it may be either relevant or non relevant
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...It must be emphasised that in the non linear case the estimation of the parameters for g x will ideally involve a different MST for each of P x w 1 and P x w 2
...There is a choice of how one would implement the model for g x depending on whether one is interested in setting the cut off a prior or a posteriori
...If one assumes that the cut off is set a posteriori then we can rank the documents according to P w 1 x and leave the user to decide when he has seen enough
...to calculate estimate the probability of relevance for each document x
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