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Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP)…

Information Theory · Computer Science 2024-04-23 Sudarshan Adiga , Xin Xiao , Ravi Tandon , Bane Vasic , Tamal Bose

One of the principal scientific challenges in deep learning is explaining generalization, i.e., why the particular way the community now trains networks to achieve small training error also leads to small error on held-out data from the…

In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…

Statistics Theory · Mathematics 2011-11-10 Xiaotong Shen , Lifeng Wang

The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the GA is obtained in closed form. In this case, sensitivity is…

Machine Learning · Computer Science 2023-06-22 Samir M. Perlaza , Iñaki Esnaola , Gaetan Bisson , H. Vincent Poor

In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the…

Machine Learning · Computer Science 2021-05-12 Song Fang , Quanyan Zhu

Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…

Computation · Statistics 2019-08-16 Mark Huber

We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…

Machine Learning · Computer Science 2014-01-24 N. Denizcan Vanli , Suleyman S. Kozat

Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We…

Machine Learning · Computer Science 2025-04-22 Syomantak Chaudhuri , Thomas A. Courtade

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

Combinatorics · Mathematics 2017-03-06 Carlos Hoppen , Nicholas Wormald

We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and…

Machine Learning · Statistics 2023-07-04 Xubo Yue , Raed Kontar

We define On-Average KL-Privacy and present its properties and connections to differential privacy, generalization and information-theoretic quantities including max-information and mutual information. The new definition significantly…

Machine Learning · Statistics 2016-05-10 Yu-Xiang Wang , Jing Lei , Stephen E. Fienberg

We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{argument stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which…

Machine Learning · Statistics 2017-08-04 Tongliang Liu , Gábor Lugosi , Gergely Neu , Dacheng Tao

The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his…

Machine Learning · Statistics 2016-02-22 Emile Contal , Nicolas Vayatis

Differential privacy (DP) provides rigorous privacy guarantees on individual's data while also allowing for accurate statistics to be conducted on the overall, sensitive dataset. To design a private system, first private algorithms must be…

Cryptography and Security · Computer Science 2020-11-19 Mark Cesar , Ryan Rogers

Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is an important task that often relies on availability of held-out data. The ability to better predict GE based on a single training set may yield overarching DNN…

Machine Learning · Computer Science 2022-07-20 Angus Galloway , Anna Golubeva , Mahmoud Salem , Mihai Nica , Yani Ioannou , Graham W. Taylor

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems…

Machine Learning · Computer Science 2019-10-31 Lukas Gonon , Lyudmila Grigoryeva , Juan-Pablo Ortega

We provide an information-theoretic framework for studying the generalization properties of machine learning algorithms. Our framework ties together existing approaches, including uniform convergence bounds and recent methods for adaptive…

Machine Learning · Computer Science 2020-06-22 Thomas Steinke , Lydia Zakynthinou

Generalization error bounds from learning theory provide statistical guarantees on how well an algorithm will perform on previously unseen data. In this paper, we characterize the impacts of data non-IIDness due to censored feedback (a.k.a.…

Machine Learning · Computer Science 2025-04-14 Yifan Yang , Ali Payani , Parinaz Naghizadeh

Our main focus is on the generalization bound, which serves as an upper limit for the generalization error. Our analysis delves into regression and classification tasks separately to ensure a thorough examination. We assume the target…

Machine Learning · Statistics 2024-07-30 Wen-Liang Hwang

We present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates which depend optimally on…

Data Structures and Algorithms · Computer Science 2017-11-15 Mark Bun , Jelani Nelson , Uri Stemmer