Pattern Recognition and Machine Learning by Bishop
The multidimensional Gaussian can be diagonalized by diagonalizing the precision matrix = T1, then exp(xT x) ˘=exp(y Dy), where D= diag(d 1;:::;d D). One limitation is the unimodal nature of the Gaussian, i.e. it has a single peak. Partitioned Gaussians. Let x˘N(xj ; ), where = 1 and x= x a x b = a b = aa ab ba bb: : { Conditional ...
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Pattern Classi cation by Duda et al. - Home | tommyodland.com
tommyodland.comThe Bayesian framework is analytically tractable when using Gaussians. For in-stance, we can compute p( jD) if we assume p( ) ˘N( 0; 0). The distribution p( ) is called a conjugate prior and p( jD) is a reproducing density, since a normal prior transforms to a normal posterior (with di erent parameters) when new data is observed.
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