Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal Inertia Components and Applications   We explore properties and applications of the Principal Inertia Components
(PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the
intersection of information and estimation theory, and provide a fine-grained
decomposition of the dependence between $X$ and $Y$. Moreover, the PICs
describe which functions of $X$ can or cannot be reliably inferred (in terms of
MMSE) given an observation of $Y$. We demonstrate that the PICs play an
important role in information theory, and they can be used to characterize
information-theoretic limits of certain estimation problems. In privacy
settings, we prove that the PICs are related to fundamental limits of perfect
privacy.

3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph