Related papers: Properties of the Strong Data Processing Constant …
In this paper we provide a new inequality useful for the proofs of strong converse theorems in the multiterminal information theory. We apply this inequality to the recent work by Tyagi and Watanabe on the strong converse theorem for the…
Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…
Stochastic gradient descent (SGD) is a promising numerical method for solving large-scale inverse problems. However, its theoretical properties remain largely underexplored in the lens of classical regularization theory. In this note, we…
The Pearcey process is a universal point process in random matrix theory and depends on a parameter $\rho \in \mathbb{R}$. Let $N(x)$ be the random variable that counts the number of points in this process that fall in the interval…
Characterizing the differential privacy (DP) of learning algorithms has become a major challenge in recent years. In parallel, many studies suggested investigating the behavior of stochastic gradient descent (SGD) with heavy-tailed noise,…
We study the universal scaling limit of random partitions obeying the Schur measure. Extending our previous analysis [arXiv:2012.06424], we obtain the higher-order Pearcey kernel describing the multi-critical behavior in the cusp scaling…
In this paper, we study the approximation and estimation of $s$-concave densities via R\'enyi divergence. We first show that the approximation of a probability measure $Q$ by an $s$-concave densities exists and is unique via the procedure…
Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…
Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…
Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…
Data processing lower bounds on the expected distortion are derived in the finite-alphabet semi-deterministic setting, where the source produces a deterministic, individual sequence, but the channel model is probabilistic, and the decoder…
The time-dependent diffusion spreadability $\mathcal{S}(t)$ is a powerful dynamical probe of the microstructure of two-phase heterogeneous media across length scales [Torquato, S., \emph{Phys. Rev. E.}, 104 054102 (2021)]. It has been shown…
Denote by $A$ the adjacency matrix of an Erdos-Renyi graph with bounded average degree. We consider the problem of maximizing $\langle A-E\{A\},X\rangle$ over the set of positive semidefinite matrices $X$ with diagonal entries $X_{ii}=1$.…
In this paper, we consider the problem of computing the barycenter of a set of probability distributions under the Sinkhorn divergence. This problem has recently found applications across various domains, including graphics, learning, and…
This paper gives improved R\'{e}nyi entropy power inequalities (R-EPIs). Consider a sum $S_n = \sum_{k=1}^n X_k$ of $n$ independent continuous random vectors taking values on $\mathbb{R}^d$, and let $\alpha \in [1, \infty]$. An R-EPI…
The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…
We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex SUSY central charges (as in N=2 in d=4 and N=(2,2) in d=2) the known results can be reinterpreted as the statement that the…
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an…