Concepts
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example,in Figure 6
...I x 1,x 2 I x 2,x 3 I x 2,x 4 I x 2,x 5 I x 5 x 6 is a maximum
...Once the dependence tree has been found the approximating distribution can be written down immediately in the form A 2
...ti Prob xi 1 xj i 1 ri Prob xi 1 x j i 0 and r 1 Prob x 1 1 P xi xj i [ti [xi]1 ti [1][xi]][xj i []ri [xi]1 ri [1][xi]][1][xj i]then This is a non linear weighting function which will simplify to the one derived from A 1 when the variables are assumed to be independent,that is,when ti ri
...g x log P x w 1 log P x w 2 which now involves the calculation or estimation of twice as many parameters as in the linear case
...It is easier to see how g x combines differentweights for different terms if one looks at the weights contributed to g x for a given |
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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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any given document whether it is relevant or non relevant
...PQ relevance document where the Q is meant to emphasise that it is for a specific query
...P relevance document
...Let us now assume following Robertson [7]that:1 The relevance of a document to a request is independent of other documents in the collection
...With this assumption we can now state a principle,in terms of probability of relevance,which shows that probabilistic information can be used in an optimal manner in retrieval
...The probability ranking principle
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In general we would have two tables of this kind when setting up our function g x,one for estimating the parameters associated with P x w 1 and one for P x w 2
...The estimates shown above are examples of point estimates
...Two basic assumptions made in deriving any estimation rule through Bayesian decision theory are:1 the form of the prior distribution on the parameter space,i
...probability distribution on the possible values of the binomial parameter;and 2 the form of the loss function used to measure the error made in estimating the parameter
...Once these two assumptions are made explicit by defining the form of the distribution and loss function,then,together with Bayes Principle which seeks to minimise the posterior conditional expected loss given the observations,we can derive a number of different estimation rules
...where x is the number of successes in n trials,and a and b are parameters dictated by the particularcombination of prior and loss |
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