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We give an overview of statistical models and likelihood, together with two of its variants: penalized and hierarchical likelihood. The Kullback-Leibler divergence is referred to repeatedly, for defining the misspecification risk of a…

Statistics Theory · Mathematics 2008-09-01 Daniel Commenges

We study reinforcement learning from human feedback under misspecification. Sometimes human feedback is systematically wrong on certain types of inputs, like a broken compass that points the wrong way in specific regions. We prove that when…

Artificial Intelligence · Computer Science 2025-09-16 Madhava Gaikwad

Despite extensive theoretical work on biologically plausible learning rules, clear evidence about whether and how such rules are implemented in the brain has been difficult to obtain. We consider biologically plausible supervised- and…

Neural and Evolutionary Computing · Computer Science 2022-10-18 Jacob P. Portes , Christian Schmid , James M. Murray

This paper investigates a novel nonlinear update rule based on temporal difference (TD) errors in reinforcement learning (RL). The update rule in the standard RL states that the TD error is linearly proportional to the degree of updates,…

Machine Learning · Computer Science 2026-02-25 Keiichiro Takahashi , Taisuke Kobayashi , Tomoya Yamanokuchi , Takamitsu Matsubara

Reinforcement learning (RL) is a general framework for adaptive control, which has proven to be efficient in many domains, e.g., board games, video games or autonomous vehicles. In such problems, an agent faces a sequential decision-making…

Machine Learning · Computer Science 2020-06-16 Olivier Buffet , Olivier Pietquin , Paul Weng

The main goal of statistical learning theory is to provide a fundamental framework for the problem of decision making and model construction based on sets of data. Here, we present a brief introduction to the fundamentals of statistical…

Machine Learning · Computer Science 2019-02-14 Michael Banf

We study the training dynamics of neural classifiers through the lens of binary hypothesis testing. We re-formalize classification as a collection of binary tests between class-conditional distributions induced by learned representations…

Machine Learning · Computer Science 2026-05-18 Kadircan Aksoy , Protim Bhattacharjee , Peter Jung

A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…

Data Analysis, Statistics and Probability · Physics 2011-05-26 Nikolai Gagunashvili

To date, distributional reinforcement learning (distributional RL) methods have exclusively focused on the discounted setting, where an agent aims to optimize a discounted sum of rewards over time. In this work, we extend distributional RL…

Machine Learning · Computer Science 2026-01-14 Juan Sebastian Rojas , Chi-Guhn Lee

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

Statistics Theory · Mathematics 2025-09-22 François Bachoc , Louis Béthune , Alberto González-Sanz , Jean-Michel Loubes

While deep learning has achieved remarkable success, there is no clear explanation about why it works so well. In order to discuss this question quantitatively, we need a mathematical framework that explains what learning is in the first…

Machine Learning · Computer Science 2023-11-23 Taisuke Katayose

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…

Machine Learning · Statistics 2023-12-01 Matthew J. Holland , Kazuki Tanabe

Inverse reinforcement learning (IRL) aims to infer a reward from expert demonstrations, motivated by the idea that the reward, rather than the policy, is the most succinct and transferable description of a task [Ng et al., 2000]. However,…

Machine Learning · Computer Science 2025-02-05 Andreas Schlaginhaufen , Maryam Kamgarpour

We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…

Artificial Intelligence · Computer Science 2007-11-27 Peter D. Grunwald , Joseph Y. Halpern

The problem of statistical learning is to construct a predictor of a random variable $Y$ as a function of a related random variable $X$ on the basis of an i.i.d. training sample from the joint distribution of $(X,Y)$. Allowable predictors…

Information Theory · Computer Science 2016-11-15 Maxim Raginsky

This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…

Machine Learning · Computer Science 2023-06-27 Peter Binev , Andrea Bonito , Ronald DeVore , Guergana Petrova

Machine learning models always make a prediction, even when it is likely to be inaccurate. This behavior should be avoided in many decision support applications, where mistakes can have severe consequences. Albeit already studied in 1970,…

Machine Learning · Computer Science 2024-02-22 Kilian Hendrickx , Lorenzo Perini , Dries Van der Plas , Wannes Meert , Jesse Davis

Causal representation learning (CRL) aims at recovering latent causal variables from high-dimensional observations to solve causal downstream tasks, such as predicting the effect of new interventions or more robust classification. A…

Machine Learning · Computer Science 2025-03-06 Dingling Yao , Dario Rancati , Riccardo Cadei , Marco Fumero , Francesco Locatello

In this paper, we address the issue of fairness in preference-based reinforcement learning (PbRL) in the presence of multiple objectives. The main objective is to design control policies that can optimize multiple objectives while treating…

Machine Learning · Computer Science 2023-09-04 Umer Siddique , Abhinav Sinha , Yongcan Cao

In this paper we consider the basic version of Reinforcement Learning (RL) that involves computing optimal data driven (adaptive) policies for Markovian decision process with unknown transition probabilities. We provide a brief survey of…

Machine Learning · Computer Science 2019-09-16 Wesley Cowan , Michael N. Katehakis , Daniel Pirutinsky