readme.glm

Bayes网络工具箱

A probability density P(y) is in the exponential family if it can be
written in the form
  P(y) = c(y) * exp[ eta' * t(y) - psi(eta) ]
where eta is called the natural parameter of the distribution
and t(y) is the sufficient statistic.

A probability density P(y|x) is in the Generalized Linear Models (GLIM)
family if it is in the exponential family and
1. t(y) = y
2. eta = theta'*x

We define the link function f to be
   f(eta) = f(theta'*x) = E[y|x,theta] = d/d(eta) psi(eta)

See McCullagh and Nelder, "Generalized Linear Models", Chapman and
Hall, 1983.

Softmax is a special case of a GLIM in which 
  f(eta_i) = exp(eta_i) / sum_j exp(eta_j)
where we have a parameter vector eta_i for each discrete value i of y.
If y is binary, this reduces to the logistic function,
  f(eta) = 1 / (1 + exp(-eta)),
where eta = eta_1 - eta_2.

We use code from the netlab package for fitting a softmax function.
See http://www.ncrg.aston.ac.uk/netlab/