The Generalized Anderson's Task (GAT) belongs among the non-Bayesian
method of the statistical decision making with non-random interventions.
The task definition is the following. The classified object is described by the
observation vector
and a binary hidden state
. The class conditional distributions , are
known to be multi-variate Gaussian distributions. The parameters
and
of these class distributions are
unknown. However, it is known that the parameters
belong to a
certain finite set of parameters
. Similarly
belong to a finite set
. Let
be a binary linear classifier with discriminant
function
defined as follows
A key assumption is the knowledge of the Gaussians
which describe the class conditional distributions.
Usually, the Gaussians are not explicitly given but a set of training
examples
is presented instead.
The labels denote the examples generated from the Gaussian component
with parameters
. The component labels can be divided into two
classes: if
and if
.
If the training set was randomly sampled from the underlying
distribution then the class conditional distributions
To make the estimation easier we assume that the input examples are projected to
a lower dimension. To this end, a linear projection
anders_exp1 | Example on estimation of density model for Anderson's task. |
anders_exp2 | Example on solving Generalized Anderson's task. |
mlcgmm | Maximal Likelihood estimation of Gaussian mixture model. |
pdfgmm | Evaluates Gaussian Mixture Model. |
pca | Principal Component Analysis. |
fld | Fisher Linear Discriminant. |
linproj | Linear data projection. |
bayescls | Bayesian classifier with reject option. |