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We study the information-theoretic limits of learning a one-hidden-layer teacher network with hierarchical features from noisy queries, in the context of knowledge transfer to a smaller student model. We work in the high-dimensional regime…

Machine Learning · Statistics 2026-05-13 Minh-Toan Nguyen , Jean Barbier

Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…

Machine Learning · Statistics 2025-06-26 Johan Pensar , Henrik Nyman , Juha Niiranen , Jukka Corander

Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussian i.i.d. input data underlying the canonical teacher-student…

In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are…

Machine Learning · Statistics 2018-03-23 Giulia Denevi , Carlo Ciliberto , Dimitris Stamos , Massimiliano Pontil

Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed…

Machine Learning · Computer Science 2026-04-29 Matthew Marsh , Benoît Chachuat , Antonio del Rio Chanona

The parameters of a machine learning model are typically learned by minimizing a loss function on a set of training data. However, this can come with the risk of overtraining; in order for the model to generalize well, it is of great…

Machine Learning · Statistics 2024-05-13 Neil Dey , Jonathan P. Williams

For a set of binary response variables, conditional mean models characterize the expected value of a response variable given the others and are popularly applied in longitudinal and network data analyses. The quadratic exponential binary…

Methodology · Statistics 2025-10-02 Ong Wei Yong , Lee Shao-Man , Hsueh Chia-Ming , Chang Sheng-Mao

For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…

Machine Learning · Statistics 2025-12-15 Jean Barbier , Francesco Camilli , Minh-Toan Nguyen , Mauro Pastore , Rudy Skerk

We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the…

Machine Learning · Computer Science 2018-11-16 Jean Honorio

Though learning has become a core component of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced systems. The need to impose requirements on learning is therefore paramount,…

Machine Learning · Computer Science 2022-10-20 Luiz F. O. Chamon , Santiago Paternain , Miguel Calvo-Fullana , Alejandro Ribeiro

Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction…

Machine Learning · Statistics 2023-06-29 Hongzhe Zhang , Hongzhe Li

This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…

Econometrics · Economics 2023-03-01 Zhan Gao , M. Hashem Pesaran

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…

Statistics Theory · Mathematics 2024-01-18 Nabarun Deb , Debarghya Mukherjee

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Machine Learning · Computer Science 2020-03-03 Jian Li , Xuanyuan Luo , Mingda Qiao

In-context learning (ICL) has emerged as a particularly remarkable characteristic of Large Language Models (LLM): given a pretrained LLM and an observed dataset, LLMs can make predictions for new data points from the same distribution…

Machine Learning · Statistics 2024-06-04 Fabian Falck , Ziyu Wang , Chris Holmes

Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Machine Learning · Statistics 2024-11-05 Luc Brogat-Motte , Riccardo Bonalli , Alessandro Rudi

In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation…

Quantum Physics · Physics 2025-11-25 Akshay Bansal , Ian George , Soumik Ghosh , Jamie Sikora , Alice Zheng

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

Quantum Physics · Physics 2025-07-10 Alexandra Ramôa , Raffaele Santagati , Nathan Wiebe

We study logistic regression with total variation penalty on the canonical parameter and show that the resulting estimator satisfies a sharp oracle inequality: the excess risk of the estimator is adaptive to the number of jumps of the…

Statistics Theory · Mathematics 2020-03-06 Sara van de Geer