Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Inference with Nonlinear Generative Models: Comments on Secure
  Learning   Unlike the classical linear model, nonlinear generative models have been
addressed sparsely in the literature. This work aims to bring attention to
these models and their secrecy potential. To this end, we invoke the replica
method to derive the asymptotic normalized cross entropy in an inverse
probability problem whose generative model is described by a Gaussian random
field with a generic covariance function. Our derivations further demonstrate
the asymptotic statistical decoupling of Bayesian inference algorithms and
specify the decoupled setting for a given nonlinear model.
  The replica solution depicts that strictly nonlinear models establish an
all-or-nothing phase transition: There exists a critical load at which the
optimal Bayesian inference changes from being perfect to an uncorrelated
learning. This finding leads to design of a new secure coding scheme which
achieves the secrecy capacity of the wiretap channel. The proposed coding has a
significantly smaller codebook size compared to the random coding scheme of
Wyner. This interesting result implies that strictly nonlinear generative
models are perfectly secured without any secure coding. We justify this latter
statement through the analysis of an illustrative model for perfectly secure
and reliable inference.

35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas