| 138 |
where [[rho]]...[[rho]]X,Y W 0 which implies using the expression for the partial correlation that [[rho]]X,Y [[rho]]X,W [[rho]]Y,W Since [[rho]]X,Y <1,[[rho]]X,W <1,[[rho]]Y,W <1 this in turn implies that under the hypothesis of conditional independence [[rho]]X,Y <[[rho]]X,W or [[rho]]Y,W Hence if W is a random variable representing relevance then thecorrelation between it and either index term is greater than the correlation between the index terms
...Qualitatively I shall try and generalise this to functions other than correlation coefficients,Linfott [27]defines a type of informational correlation measure by rij 1 exp 2 I xi,xj [1 2]0 <rij <1 or where I xi,xj is the now familiar expected mutual information measure
...I xi,xj <I xi,W or I xj,W,where I
...Discrimination Gain Hypothesis:Under the hypothesis ofconditional independence the statistical information contained in oneindex term about another is less than the information contained ineither index term about relevance
... |
