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Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a…

Machine Learning · Statistics 2024-02-06 Noam Levi , Alon Beck , Yohai Bar-Sinai

We provide a new kriging procedure of processes on graphs. Based on the construction of Gaussian random processes indexed by graphs, we extend to this framework the usual linear prediction method for spatial random fields, known as kriging.…

Statistics Theory · Mathematics 2014-06-26 Thibault Espinasse , Jean-Michel Loubes

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…

Machine Learning · Computer Science 2024-06-11 Xuyang Zhao , Huiyuan Wang , Weiran Huang , Wei Lin

We propose a three-step divide-and-conquer strategy within the Bayesian paradigm that delivers massive scalability for any spatial process model. We partition the data into a large number of subsets, apply a readily available Bayesian…

Methodology · Statistics 2019-06-13 Rajarshi Guhaniyogi , Cheng Li , Terrance D. Savitsky , Sanvesh Srivastava

Targeted Learning is a subfield of statistics that unifies advances in causal inference, machine learning and statistical theory to help answer scientifically impactful questions with statistical confidence. Targeted Learning is driven by…

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

Machine Learning · Computer Science 2020-02-17 Mert Al , Zejiang Hou , Sun-Yuan Kung

One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of $\epsilon$-approximation of datasets, obtaining datasets which are much smaller than or are…

Machine Learning · Computer Science 2021-03-24 Timothy Nguyen , Zhourong Chen , Jaehoon Lee

In complex simulation environments, certain parameter space regions may result in non-convergent or unphysical outcomes. All parameters can therefore be labeled with a binary class describing whether or not they lead to valid results. In…

Applications · Statistics 2019-02-19 Raoul Heese , Michal Walczak , Tobias Seidel , Norbert Asprion , Michael Bortz

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

Statistics Theory · Mathematics 2022-10-04 Mamadou Lamine Diop , William Kengne

Strategic classification regards the problem of learning in settings where users can strategically modify their features to improve outcomes. This setting applies broadly and has received much recent attention. But despite its practical…

Machine Learning · Computer Science 2021-06-15 Sagi Levanon , Nir Rosenfeld

Gaussian process-based models are attractive for estimating heterogeneous treatment effects (HTE), but their computational cost limits scalability in causal inference settings. In this work, we address this challenge by extending Patchwork…

Methodology · Statistics 2026-05-07 Hajime Ogawa , Shonosuke Sugasawa

Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…

Machine Learning · Computer Science 2017-08-08 Zhengchu Guo , Lei Shi , Qiang Wu

We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability~$1$. Our approach is based on the novel notion…

Machine Learning · Computer Science 2023-07-31 Matin Ansaripour , Krishnendu Chatterjee , Thomas A. Henzinger , Mathias Lechner , Đorđe Žikelić

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to…

Machine Learning · Computer Science 2023-06-08 Aaditya Naik , Yinjun Wu , Mayur Naik , Eric Wong

Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…

Machine Learning · Statistics 2021-01-15 Danica J. Sutherland , Junier B. Oliva , Barnabás Póczos , Jeff Schneider

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

Machine Learning · Computer Science 2023-01-13 Tomer Koren , Roi Livni , Yishay Mansour , Uri Sherman

The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…

Statistics Theory · Mathematics 2023-03-17 Anna Scampicchio , Elena Arcari , Melanie N. Zeilinger

We address the problem of training conversion prediction models in advertising domains under privacy constraints, where direct links between ad clicks and conversions are unavailable. Motivated by privacy-preserving browser APIs and the…

Machine Learning · Computer Science 2026-02-09 Lorne Applebaum , Robert Busa-Fekete , August Y. Chen , Claudio Gentile , Tomer Koren , Aryan Mokhtari

We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale. These estimators interpolate the…

Machine Learning · Statistics 2021-11-11 Nicolò Pagliana , Alessandro Rudi , Ernesto De Vito , Lorenzo Rosasco

The inference performance of the pseudolikelihood method is discussed in the framework of the inverse Ising problem when the $\ell_2$-regularized (ridge) linear regression is adopted. This setup is introduced for theoretically investigating…

Disordered Systems and Neural Networks · Physics 2021-10-19 Xiangming Meng , Tomoyuki Obuchi , Yoshiyuki Kabashima