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In this paper, we establish generalization bounds for transductive learning algorithms in the context of information theory and PAC-Bayes, covering both the random sampling and the random splitting setting. First, we show that the…

Machine Learning · Computer Science 2025-01-22 Huayi Tang , Yong Liu

This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…

Machine Learning · Computer Science 2026-05-29 Mikael Møller Høgsgaard , Kasper Green Larsen , Liang-Yu Zou

The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided…

Machine Learning · Computer Science 2025-03-12 Mathieu Bazinet , Valentina Zantedeschi , Pascal Germain

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical…

Machine Learning · Statistics 2022-03-15 Tielang Gong , Yuxin Dong , Hong Chen , Bo Dong , Wei Feng , Chen Li

A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way.…

Machine Learning · Computer Science 2023-06-02 Andreas Maurer

We provide matching upper and lower bounds of order $\sigma^2/\log(d/n)$ for the prediction error of the minimum $\ell_1$-norm interpolator, a.k.a. basis pursuit. Our result is tight up to negligible terms when $d \gg n$, and is the first…

Statistics Theory · Mathematics 2022-03-09 Guillaume Wang , Konstantin Donhauser , Fanny Yang

We study which machine learning algorithms have tight generalization bounds. First, we present conditions that preclude the existence of tight generalization bounds. Specifically, we show that algorithms that have certain inductive biases…

Machine Learning · Computer Science 2024-10-04 Michael Gastpar , Ido Nachum , Jonathan Shafer , Thomas Weinberger

Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they…

Machine Learning · Statistics 2022-06-10 Andrea Montanari , Yiqiao Zhong

Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge…

Machine Learning · Statistics 2021-12-20 Konstantin Donhauser , Alexandru Ţifrea , Michael Aerni , Reinhard Heckel , Fanny Yang

This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the…

Econometrics · Economics 2025-04-23 Christian Brownlees , Guðmundur Stefán Guðmundsson

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…

Machine Learning · Statistics 2009-07-23 Andreas Maurer , Massimiliano Pontil

This paper deals with probabilistic upper bounds for the error in functional estimation defined on some interpolation and extrapolation designs, when the function to estimate is supposed to be analytic. The error pertaining to the estimate…

Statistics Theory · Mathematics 2011-01-26 Michel Broniatowski , Giorgio Celant , Marco Di Battista , Samuela Leoni-Aubin

We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…

Statistics Theory · Mathematics 2021-02-25 Gil Kur , Alexander Rakhlin

In several real world applications, machine learning models are deployed to make predictions on data whose distribution changes gradually along time, leading to a drift between the train and test distributions. Such models are often…

Machine Learning · Computer Science 2021-11-23 Anshul Nasery , Soumyadeep Thakur , Vihari Piratla , Abir De , Sunita Sarawagi

Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of…

Machine Learning · Computer Science 2020-06-19 Seyed Mohammadreza Mousavi Kalan , Zalan Fabian , A. Salman Avestimehr , Mahdi Soltanolkotabi

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted…

Statistics Theory · Mathematics 2007-06-13 Yoav Freund , Yishay Mansour , Robert E. Schapire

Classically, data interpolation with a parametrized model class is possible as long as the number of parameters is larger than the number of equations to be satisfied. A puzzling phenomenon in deep learning is that models are trained with…

Machine Learning · Computer Science 2022-12-27 Sébastien Bubeck , Mark Sellke

Meta-learning has arisen as a successful method for improving training performance by training over many similar tasks, especially with deep neural networks (DNNs). However, the theoretical understanding of when and why overparameterized…

Machine Learning · Computer Science 2023-04-11 Peizhong Ju , Yingbin Liang , Ness B. Shroff

Many modern neural network architectures are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Sufficiently overparameterized neural network architectures in principle have the…

Machine Learning · Computer Science 2019-02-14 Samet Oymak , Mahdi Soltanolkotabi

Designing learning algorithms that are resistant to perturbations of the underlying data distribution is a problem of wide practical and theoretical importance. We present a general approach to this problem focusing on unsupervised…

Machine Learning · Computer Science 2021-02-22 Andreas Maurer , Daniela A. Parletta , Andrea Paudice , Massimiliano Pontil