# evidence

## Purpose

Re-estimate hyperparameters using evidence approximation.

## Synopsis

    [net] = evidence(net, x, t)
    [net, gamma, logev] = evidence(net, x, t, num)

## Description

`[net] = evidence(net, x, t)` re-estimates the hyperparameters `alpha` and `beta` by applying Bayesian re-estimation formulae for `num` iterations. The hyperparameter `alpha` can be a simple scalar associated with an isotropic prior on the weights, or can be a vector in which each component is associated with a group of weights as defined by the `index` matrix in the `net` data structure. These more complex priors can be set up for an MLP using `mlpprior`. Initial values for the iterative re-estimation are taken from the network data structure `net` passed as an input argument, while the return argument `net` contains the re-estimated values.

`[net, gamma, logev] = evidence(net, x, t, num)` allows the re-estimation formula to be applied for `num` cycles in which the re-estimated values for the hyperparameters from each cycle are used to re-evaluate the Hessian matrix for the next cycle. The return value `gamma` is the number of well-determined parameters and `logev` is the log of the evidence.

## See Also

`mlpprior`, `netgrad`, `nethess`, `demev1`, `demard`

Pages: Index

Copyright (c) Ian T Nabney (1996-9)