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We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…

Information Theory · Computer Science 2022-09-05 Anelia Somekh-Baruch

This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the…

Machine Learning · Computer Science 2023-10-17 Jingwen Fu , Nanning Zheng

In deep learning, classification tasks are formalized as optimization problems often solved via the minimization of the cross-entropy. However, recent advancements in the design of objective functions allow the usage of the $f$-divergence…

Machine Learning · Computer Science 2024-05-17 Nicola Novello , Andrea M. Tonello

We show that the convergence proof of a recent algorithm called dist-EF-SGD for distributed stochastic gradient descent with communication efficiency using error-feedback of Zheng et al. (NeurIPS 2019) is problematic mathematically.…

Optimization and Control · Mathematics 2021-05-11 Tran Thi Phuong , Le Trieu Phong

The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…

Information Theory · Computer Science 2021-02-23 Lampros Gavalakis , Ioannis Kontoyiannis

This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regression code, codewords are linear combinations of subsets of columns of a design matrix. It is…

Information Theory · Computer Science 2017-07-17 Ramji Venkataramanan , Sekhar Tatikonda

We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f (x)$, this method requires first…

Probability · Mathematics 2026-01-07 Nikola Zlatanov

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…

Statistics Theory · Mathematics 2009-09-09 Jean-Yves Audibert

We propose a new convex loss for Support Vector Machines, both for the binary classification and for the regression models. Therefore, we show the mathematical derivation of the dual problems and we experiment with them on several small…

Machine Learning · Computer Science 2026-03-02 Filippo Portera

Despite the ubiquitous use of stochastic optimization algorithms in machine learning, the precise impact of these algorithms and their dynamics on generalization performance in realistic non-convex settings is still poorly understood. While…

Machine Learning · Statistics 2022-07-12 Liam Hodgkinson , Umut Şimşekli , Rajiv Khanna , Michael W. Mahoney

This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…

Information Theory · Computer Science 2016-11-15 Victoria Kostina , Sergio Verdú

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

Statistics Theory · Mathematics 2008-03-04 Jean-Yves Audibert

We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds…

Machine Learning · Computer Science 2023-11-29 Michael Gastpar , Ido Nachum , Jonathan Shafer , Thomas Weinberger

We investigate the generalization error of statistical learning models in a Federated Learning (FL) setting. Specifically, we study the evolution of the generalization error with the number of communication rounds $R$ between $K$ clients…

Machine Learning · Statistics 2024-06-11 Milad Sefidgaran , Romain Chor , Abdellatif Zaidi , Yijun Wan

We provide new insight into the convergence properties of the Douglas-Rachford algorithm for the problem $\min_x \{f(x)+g(x)\}$, where $f$ and $g$ are convex functions. Our approach relies on and highlights the natural primal-dual symmetry…

Optimization and Control · Mathematics 2021-11-12 Javier Peña , Juan C. Vera , Luis F. Zuluaga

For a class $F$ of complex-valued functions on a set $D$, we denote by $g_n(F)$ its sampling numbers, i.e., the minimal worst-case error on $F$, measured in $L_2$, that can be achieved with a recovery algorithm based on $n$ function…

Numerical Analysis · Mathematics 2023-05-15 Matthieu Dolbeault , David Krieg , Mario Ullrich

This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and…

Information Theory · Computer Science 2024-08-20 Huiyuan Yang , Yuxuan Shi , Shuo Shao , Xiaojun Yuan

We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…

Mathematical Physics · Physics 2007-05-23 C. Kuelske

Backward error analysis allows finding a modified loss function, which the parameter updates really follow under the influence of an optimization method. The additional loss terms included in this modified function is called implicit…

Machine Learning · Computer Science 2025-03-06 Jinwoo Lim , Suhyun Kim , Soo-Mook Moon

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…

Information Theory · Computer Science 2022-12-05 James Melbourne , Saurav Talukdar , Shreyas Bhaban , Mokshay Madiman , Murti V. Salapaka