arXiv subjects

Anuj Kumar Yadav

Publications and source records attributed to Anuj Kumar Yadav.

7 recordsLinked to original sources

arXiv2026

Geometry of R\'enyi Entropy on the Majorization Lattice

Majorization is a stochastic ordering relation that compares the relative diversity of probability distributions with numerous applications in econometrics, spectral theory, and ecology. It is well-known that the majorization partial order forms a complete lattice on the set of ordered probability distributions. In this work, we study the properties of R\'enyi entropy on the majorization lattice. We establish a fundamental relation between the comonotone coupling and the independent coupling associated with a collection of marginal distributions. Consequently, we show that, for every order $\alpha \in [0,\infty]$, the R\'enyi entropy is subadditive on the majorization lattice. We further characterize the supermodular regime, showing that R\'enyi entropy is supermodular on the majorization lattice for $\alpha \in \{0\} \,\cup \, [1,\infty]$. For the Tsallis entropy, we show that it also satisfies subadditivity on the majorization lattice, for every order $\alpha \in [0,\infty)$. Finally, we show that, unlike the R\'enyi entropy, the Tsallis entropy is supermodular on the majorization lattice for every $\alpha \in [0,\infty)$.

cs.IT↗

arXiv2026

Locally Private Parametric Methods for Change-Point Detection

We study parametric change-point detection, where the goal is to identify distributional changes in time series, under local differential privacy. In the non-private setting, we derive improved finite-sample accuracy guarantees for a change-point detection algorithm based on the generalized log-likelihood ratio test, via martingale methods. In the private setting, we propose two locally differentially private algorithms based on randomized response and binary mechanisms, and analyze their theoretical performance. We derive bounds on detection accuracy and validate our results through empirical evaluation. Our results characterize the statistical cost of local differential privacy in change-point detection and show how privacy degrades performance relative to a non-private benchmark. As part of this analysis, we establish a structural result for strong data processing inequalities (SDPI), proving that SDPI coefficients for R\'enyi divergences and their symmetric variants (Jeffreys-R\'enyi divergences) are achieved by binary input distributions. These results on SDPI coefficients are also of independent interest, with applications to statistical estimation, data compression, and Markov chain mixing.

stat.ML↗

arXiv2026

Log-Likelihood Loss for Semantic Compression

We study lossy source coding under a distortion measure defined by the negative log-likelihood induced by a prescribed conditional distribution $P_{X|U}$. This \emph{log-likelihood distortion} models compression settings in which the reconstruction is a semantic representation from which the source can be probabilistically generated, rather than a pointwise approximation. We formulate the corresponding rate-distortion problem and characterize fundamental properties of the resulting rate-distortion function, including its connections to lossy compression under log-loss, classical rate-distortion problems with arbitrary distortion measures, and rate-distortion with perfect perception.

cs.IT↗

arXiv2024

Wiretapped Commitment over Binary Channels

We propose the problem of wiretapped commitment, where two parties, say committer Alice and receiver Bob, engage in a commitment protocol using a noisy channel as a resource, in the presence of an eavesdropper, say Eve. Noisy versions of Alice's transmission over the wiretap channel are received at both Bob and Eve. We seek to determine the maximum commitment throughput in the presence of an eavesdropper, i.e., wiretapped commitment capacity, where in addition to the standard security requirements for two-party commitment, one seeks to ensure that Eve doesn't learn about the commit string. A key interest in this work is to explore the effect of collusion (or lack of it) between the eavesdropper Eve and either Alice or Bob. Toward the same, we present results on the wiretapped commitment capacity under the so-called 1-private regime (when Alice or Bob cannot collude with Eve) and the 2-private regime (when Alice or Bob may possibly collude with Eve).

cs.IT↗

arXiv2023

Commitment over Gaussian Unfair Noisy Channels

Commitment is a key primitive which resides at the heart of several cryptographic protocols. Noisy channels can help realize information-theoretically secure commitment schemes, however, their imprecise statistical characterization can severely impair such schemes, especially their security guarantees. Keeping our focus on channel unreliability in this work, we study commitment over unreliable continuous alphabet channels called the Gaussian unfair noisy channels or Gaussian UNCs. We present the first results on the optimal throughput or commitment capacity of Gaussian UNCs. It is known that classical Gaussian channels have infinite commitment capacity, even under finite transmit power constraints. For unreliable Gaussian UNCs, we prove the surprising result that their commitment capacity may be finite, and in some cases, zero. When commitment is possible, we present achievable rate lower bounds by constructing positive - throughput protocols under given input power constraint, and (two-sided) channel elasticity at committer Alice and receiver Bob. Our achievability results establish an interesting fact - Gaussian UNCs with zero elasticity have infinite commitment capacity - which brings a completely new perspective to why classic Gaussian channels, i.e., Gaussian UNCs with zero elasticity, have infinite capacity. Finally, we precisely characterize the positive commitment capacity threshold for a Gaussian UNC in terms of the channel elasticity, when the transmit power tends to infinity.

cs.IT↗

arXiv2023

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

Given two jointly distributed random variables $(X,Y)$, a functional representation of $X$ is a random variable $Z$ independent of $Y$, and a deterministic function $g(\cdot, \cdot)$ such that $X=g(Y,Z)$. The problem of finding a minimum entropy functional representation is known to be equivalent to the problem of finding a minimum entropy coupling where, given a collection of probability distributions $P_1, \dots, P_m$, the goal is to find a coupling $X_1, \dots, X_m$ ($X_i \sim P_i)$ with the smallest entropy $H_α(X_1, \dots, X_m)$. This paper presents a new information spectrum converse, and applies it to obtain direct lower bounds on minimum entropy in both problems. The new results improve on all known lower bounds, including previous lower bounds based on the concept of majorization. In particular, the presented proofs leverage both - the information spectrum and the majorization - perspectives on minimum entropy couplings and functional representations.

cs.IT↗

arXiv2021

On Reverse Elastic Channels and the Asymmetry of Commitment Capacity under Channel Elasticity

Commitment is an important cryptographic primitive. It is well known that noisy channels are a promising resource to realize commitment in an information-theoretically secure manner. However, oftentimes, channel behaviour may be poorly characterized thereby limiting the commitment throughput and/or degrading the security guarantees; particularly problematic is when a dishonest party, unbeknown to the honest one, can maliciously alter the channel characteristics. Reverse elastic channels (RECs) are an interesting class of such unreliable channels, where only a dishonest committer, say, Alice can maliciously alter the channel. RECs have attracted recent interest in the study of several cryptographic primitives. Our principal contribution is the REC commitment capacity characterization; this proves a recent related conjecture. A key result is our tight converse which analyses a specific cheating strategy by Alice. RECs are closely related to the classic unfair noisy channels (UNCs); elastic channels (ECs), where only a dishonest receiver Bob can alter the channel, are similarly related. In stark contrast to UNCs, both RECs and ECs always exhibit positive commitment throughput for all non-trivial parameters. Interestingly, our results show that channels with exclusive one-sided elasticity for dishonest parties, exhibit a fundamental asymmetry where a committer with one-sided elasticity has a more debilitating effect on the commitment throughput than a receiver.

cs.IT↗