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A recent asymptotic expansion for the positive zeros $x=j_{\nu,m}$ ($m=1,2,3,\ldots$) of the Bessel function of the first kind $J_{\nu}(x)$ is studied, where the order $\nu$ is positive. Unlike previous well-known expansions in the…

Classical Analysis and ODEs · Mathematics 2025-02-17 T. M. Dunster

We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing…

Probability · Mathematics 2012-05-31 Nikolaus Schweizer

We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss $\ell$ can control the test error under all Moreau…

Machine Learning · Statistics 2022-10-24 Lijia Zhou , Frederic Koehler , Pragya Sur , Danica J. Sutherland , Nathan Srebro

We consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…

Quantum Physics · Physics 2012-05-14 Michael Nussbaum , Arleta Szkoła

This paper determines the range of feasible values of standard error exponents for binary-input memoryless symmetric channels of fixed capacity $C$ and shows that extremes are attained by the binary symmetric and the binary erasure channel.…

Information Theory · Computer Science 2012-12-06 Albert Guillen i Fabregas , Ingmar Land , Alfonso Martinez

In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and…

Probability · Mathematics 2009-08-10 Guangyue Han , Brian Marcus

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…

Quantum Physics · Physics 2023-11-23 Jason L. Pereira , Leonardo Banchi , Stefano Pirandola

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…

Statistics Theory · Mathematics 2025-03-20 Kenta Takatsu

We study error bounds for linear programming decoding of regular LDPC codes. For memoryless binary-input output-symmetric channels, we prove bounds on the word error probability that are inverse doubly-exponential in the girth of the factor…

Information Theory · Computer Science 2011-04-12 Nissim Halabi , Guy Even

Feedback holds a pivotal role in practical communication schemes, even though it does not enhance channel capacity. Its main attribute includes adaptability in transmission that allows for a higher rate of convergence of the error…

Information Theory · Computer Science 2024-03-22 Ioannis Papoutsidakis , Robert J. Piechocki , Angela Doufexi

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the…

Information Theory · Computer Science 2016-04-07 Gonzalo Vazquez-Vilar , Adrià Tauste Campo , Albert Guillén i Fàbregas , Alfonso Martinez

We study variable-length feedback (VLF) codes with noiseless feedback for discrete memoryless channels. We present a novel non-asymptotic bound, which analyzes the average error probability and average decoding time of our modified…

Information Theory · Computer Science 2025-02-12 Recep Can Yavas , Vincent Y. F. Tan

This paper shows that the probability that the error exponent of a given code randomly generated from a pairwise independent ensemble being smaller than a lower bound on the typical random-coding exponent tends to zero as the codeword…

Information Theory · Computer Science 2022-04-04 Giuseppe Cocco , Albert Guillén i Fàbregas , Josep Font-Segura

In this paper we establish new integral representations for the remainder term of the known asymptotic expansion of the logarithm of the Barnes $G$-function. Using these representations, we obtain explicit and numerically computable error…

Classical Analysis and ODEs · Mathematics 2014-10-27 Gergő Nemes

We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…

Information Theory · Computer Science 2018-05-28 Gonzalo Vazquez-Vilar , Albert Guillén i Fàbregas , Sergio Verdú

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

Machine Learning · Statistics 2016-11-17 Mohammad Hossein Rohban , Prakash Ishwar , Birant Orten , William C. Karl , Venkatesh Saligrama

For a sequence of independent identically distributed random variables having a distribution function with an unknown parameter from a set $\Theta \subset \mathbf{R}^d$, we prove an analogue of the lower bound of Bahadur asymptotic…

Statistics Theory · Mathematics 2026-04-06 Mikhail Ermakov

We investigate the maximum coding rate for a given average blocklength and error probability over a K-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback…

Information Theory · Computer Science 2018-09-03 Kasper Fløe Trillingsgaard , Wei Yang , Giuseppe Durisi , Petar Popovski

We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…

Quantum Physics · Physics 2011-05-13 K. M. R. Audenaert , M. Nussbaum , A. Szkola , F. Verstraete