Related papers: Statistical Problems with Planted Structures: Info…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
We study a random graph model named the "block model" in statistics and the "planted partition model" in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge…
In today's data-driven world, the proliferation of publicly available information raises security concerns due to the information leakage (IL) problem. IL involves unintentionally exposing sensitive information to unauthorized parties via…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
While information theory has been introduced to characterize the fundamental limitations of control and filtering for a few decades, the existing information-theoretic methods are indirect and cumbersome for analyzing the limitations of…
Information theory, rooted in computer science, and many-body physics, have traditionally been studied as (almost) independent fields. Only recently has this paradigm started to shift, with many-body physics being studied and characterized…
Avoiding overfitting is a central challenge in machine learning, yet many large neural networks readily achieve zero training loss. This puzzling contradiction necessitates new approaches to the study of overfitting. Here we quantify…
Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
We consider the problem of detecting a planted clique of size $k$ in a random graph on $n$ vertices. When the size of the clique exceeds $\Theta(\sqrt{n})$, polynomial-time algorithms for detection proliferate. We study faster -- namely,…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
We study constraint satisfaction problems on the so-called 'planted' random ensemble. We show that for a certain class of problems, e.g. graph coloring, many of the properties of the usual random ensemble are quantitatively identical in the…
A fundamental tool to prove inner bounds in classical network information theory is the so-called conditional joint typicality lemma. In addition to the lemma, one often uses unions and intersections of typical sets in the inner bound…
Information inequalities appear in many database applications such as query output size bounds, query containment, and implication between data dependencies. Recently Khamis et al. proposed to study the algorithmic aspects of information…
We give a simple, greedy $O(n^{\omega+0.5})=O(n^{2.872})$-time algorithm to list-decode planted cliques in a semirandom model introduced in [CSV17] (following [FK01]) that succeeds whenever the size of the planted clique is $k\geq…
Physical systems are often simulated using a stochastic computation where different final states result from identical initial states. Here, we derive the minimum energy cost of simulating a complex data set of a general physical system…
In a distinguishing problem, the input is a sample drawn from one of two distributions and the algorithm is tasked with identifying the source distribution. The performance of a distinguishing algorithm is measured by its advantage, i.e.,…
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…