In what follows, the symbol is always used for
the (high-dimensional) input data,
and the symbol is always used for
(lower-dimensional) features, the output of
.
We view both and as random variables (RV)
^{2.1}.
We will use a simplified notation
for a RV and the associated
probability density function (PDF).
We use the same symbol to represent the RV and a sample of that
RV. Distributions are identified by their
argument, so
and
are understood
to be the distributions of RVs and , respectively.
When there is the possibility of confusion,
we use a subscript, for example,
is understood
to be the evaluation of the density
at sample
.
If there are more than one possible distributions
of a given RV, we index them by the statistical hypothesis,
such as
,
, etc.
For a generic fixed feature PDF, we use
.

Baggenstoss
2017-05-19