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Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…

Statistics Theory · Mathematics 2017-04-25 Zhiqiang Tan , Cun-Hui Zhang

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 James P. Crutchfield , David P. Feldman

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…

Statistics Theory · Mathematics 2025-01-30 Yihong Gu , Cong Fang , Yang Xu , Zijian Guo , Jianqing Fan

We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…

Quantum Physics · Physics 2018-03-28 Rene Schwonnek

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…

Machine Learning · Computer Science 2025-11-26 Gonzalo E. Constante-Flores , Hao Chen , Can Li

Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…

Probability · Mathematics 2026-05-29 Joseph Samuel Miller

Using established principles from Statistics and Information Theory, we show that invariance to nuisance factors in a deep neural network is equivalent to information minimality of the learned representation, and that stacking layers and…

Machine Learning · Computer Science 2018-06-29 Alessandro Achille , Stefano Soatto

Tactical selection of experiments to estimate an underlying model is an innate task across various fields. Since each experiment has costs associated with it, selecting statistically significant experiments becomes necessary. Classic linear…

Optimization and Control · Mathematics 2021-03-30 Raj K. Velicheti , Amber Srivastava , Srinivasa M. Salapaka

We analyze a contrasting dynamical behavior of Gibbs-Shannon and conditional Kullback-Leibler entropies, induced by time-evolution of continuous probability distributions. The question of predominantly purpose-dependent entropy definition…

Statistical Mechanics · Physics 2007-05-23 Piotr Garbaczewski

Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods…

Machine Learning · Statistics 2025-11-21 Akira Tanimoto

Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…

Artificial Intelligence · Computer Science 2020-05-12 Hykel Hosni , Angelo Vulpiani

Any system that models the world under finite representational capacity must compress; any compression entails a prior; and the prior is the system's bias. What has not been established is whether uncertainty participates in the dynamics…

Machine Learning · Computer Science 2026-05-20 Ahmed Gamal Eldin

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects…

Machine Learning · Computer Science 2026-05-28 Wenhao Yu , Shaohang Wei , Jiahong Liu , Yifan Li , Minda Hu , Aiwei Liu , Hao Zhang , Irwin King

The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…

Statistics Theory · Mathematics 2018-04-25 Alexander Bulinski , Alexey Kozhevin

This paper applies the recently axiomatized Optimum Information Principle (minimize the Kullback-Leibler information subject to all relevant information) to nonparametric density estimation, which provides a theoretical foundation as well…

Statistics Theory · Mathematics 2011-03-28 Alexis Akira Toda

The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a $\sigma$-finite measure, and not necessarily a probability measure. Under this…

Statistics Theory · Mathematics 2024-04-09 Samir M. Perlaza , Gaetan Bisson , Iñaki Esnaola , Alain Jean-Marie , Stefano Rini

E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is…

Information Theory · Computer Science 2014-04-24 Kenric P. Nelson , Brian J. Scannell , Herbert Landau

We introduce the first differentiable approximation of range-partition entropy, a complexity measure from computational geometry that directly bounds algorithmic runtime. Unlike architectural modifications, our method is a complementary…

Machine Learning · Computer Science 2025-11-20 Ibne Farabi Shihab , Sanjeda Akter , Anuj Sharma

We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate…

Machine Learning · Statistics 2023-01-18 Songkai Xue , Yuekai Sun , Mikhail Yurochkin

In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained…

Machine Learning · Statistics 2022-08-12 François Bachoc , Fabrice Gamboa , Max Halford , Jean-Michel Loubes , Laurent Risser