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Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…

Machine Learning · Statistics 2020-12-10 Guillermo Valle-Pérez , Ard A. Louis

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

Probability · Mathematics 2017-08-31 Jiantao Jiao , Yanjun Han , Tsachy Weissman

Meta-learning optimizes an inductive bias---typically in the form of the hyperparameters of a base-learning algorithm---by observing data from a finite number of related tasks. This paper presents an information-theoretic bound on the…

Machine Learning · Computer Science 2021-02-09 Arezou Rezazadeh , Sharu Theresa Jose , Giuseppe Durisi , Osvaldo Simeone

Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…

Machine Learning · Computer Science 2019-05-17 Ben Poole , Sherjil Ozair , Aaron van den Oord , Alexander A. Alemi , George Tucker

We introduce a framework for online changepoint detection and simultaneous model learning which is applicable to highly parametrized models, such as deep neural networks. It is based on detecting changepoints across time by sequentially…

Machine Learning · Computer Science 2020-10-08 Michalis K. Titsias , Jakub Sygnowski , Yutian Chen

In this paper we address the problem of systems under an external feedback. This is performed using a large deviation approach and rate distortion from information theory. In particular we define a lower boundary for the maximum entropy…

Statistical Mechanics · Physics 2016-04-18 Alessio Gagliardi , Alessandro Pecchia , Aldo Di Carlo

Ensuring a neural network is not relying on protected attributes (e.g., race, sex, age) for predictions is crucial in advancing fair and trustworthy AI. While several promising methods for removing attribute bias in neural networks have…

Machine Learning · Computer Science 2023-11-17 Jiazhi Li , Mahyar Khayatkhoei , Jiageng Zhu , Hanchen Xie , Mohamed E. Hussein , Wael AbdAlmageed

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…

Statistics Theory · Mathematics 2013-05-06 Victor Chernozhukov , Sokbae Lee , Adam M. Rosen

Continual learning (CL) has emerged as a dominant paradigm for acquiring knowledge from sequential tasks while avoiding catastrophic forgetting. Although many CL methods have been proposed to show impressive empirical performance, the…

Machine Learning · Computer Science 2026-01-07 Wen Wen , Tieliang Gong , Zeyu Gao , Yunjiao Zhang , Weizhan Zhang , Yong-Jin Liu

In this work we consider the task of constructing prediction intervals in an inductive batch setting. We present a discriminative learning framework which optimizes the expected error rate under a budget constraint on the interval sizes.…

Machine Learning · Computer Science 2018-02-28 Nir Rosenfeld , Yishay Mansour , Elad Yom-Tov

Meta-learning, or "learning to learn", refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key…

Machine Learning · Computer Science 2021-02-24 Sharu Theresa Jose , Osvaldo Simeone

A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…

Information Theory · Computer Science 2007-11-15 Gil I. Shamir

The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…

Information Theory · Computer Science 2012-05-31 Bao-Gang Hu , Hong-Jie Xing

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting…

Statistics Theory · Mathematics 2007-07-16 Jan Poland , Marcus Hutter

We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$…

Information Theory · Computer Science 2026-05-21 Yang Lu , Matthias Frey , Margreta Kuijper , Jingge Zhu

This paper addresses the statistical problem of estimating the infinite-norm deviation from the empirical mean to the distribution mean for high-dimensional distributions on $\{0,1\}^d$, potentially with $d=\infty$. Unlike traditional…

Statistics Theory · Mathematics 2024-02-21 Moïse Blanchard , Václav Voráček

We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…

Statistics Theory · Mathematics 2026-05-26 Vladimir Vovk , Ruodu Wang

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

Statistics Theory · Mathematics 2016-10-18 Xinran Li , Peng Ding

We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…

Numerical Analysis · Mathematics 2017-01-24 Simon Becher

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

Information Theory · Computer Science 2021-11-29 Georg Pichler , Pablo Piantanida , Günther Koliander