The problem we address is extremely broad, and encompasses
many related fields in statistics.
We consider data to be a raw (unprocessed) data sample of high dimension.
By raw and unprocessed, we mean that there has not yet been an intentional dimension reduction
or filtering in which useful information could have been lost.
For example, could be a time-series (sampled recording of
acoustic or other sensor data), an image, or other
type of high-dimensional measurement.
Assume there are one or more competing statistical
hypotheses concerning , denoted by the hypothesis index ,
which can take discrete values (fixed hypotheses) such as
can take on continuous values (parameters).
Our goal is to create improved generative models, written
These generative models can be used for numerous purposes including
inference (creating generative classifiers), combination with
discriminative to form hybrid discriminative/generative classifiers,
and for sampling methods. By ``sampling methods", we mean applications
where random samples of
are required. This could
be for simulations, or for Monte Carlo methods, which are
stochastic methods to approximate integrals.