Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimum estimation via gradients of partition functions and information
  measures: a statistical-mechanical perspective   In continuation to a recent work on the statistical--mechanical analysis of
minimum mean square error (MMSE) estimation in Gaussian noise via its relation
to the mutual information (the I-MMSE relation), here we propose a simple and
more direct relationship between optimum estimation and certain information
measures (e.g., the information density and the Fisher information), which can
be viewed as partition functions and hence are amenable to analysis using
statistical--mechanical techniques. The proposed approach has several
advantages, most notably, its applicability to general sources and channels, as
opposed to the I-MMSE relation and its variants which hold only for certain
classes of channels (e.g., additive white Gaussian noise channels). We then
demonstrate the derivation of the conditional mean estimator and the MMSE in a
few examples. Two of these examples turn out to be generalizable to a fairly
wide class of sources and channels. For this class, the proposed approach is
shown to yield an approximate conditional mean estimator and an MMSE formula
that has the flavor of a single-letter expression. We also show how our
approach can easily be generalized to situations of mismatched estimation.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int