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Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…

Machine Learning · Computer Science 2025-10-21 Cassidy Ashworth , Pietro Liò , Francesco Caso

Symmetry-aware methods for machine learning, such as data augmentation and equivariant architectures, encourage correct model behavior on all transformations (e.g. rotations or permutations) of the original dataset. These methods can…

Machine Learning · Computer Science 2026-03-31 Hannah Lawrence , Elyssa Hofgard , Vasco Portilheiro , Yuxuan Chen , Tess Smidt , Robin Walters

We present a unifying picture of PAC-Bayesian and mutual information-based upper bounds on the generalization error of randomized learning algorithms. As we show, Tong Zhang's information exponential inequality (IEI) gives a general recipe…

Machine Learning · Computer Science 2021-10-26 Pradeep Kr. Banerjee , Guido Montúfar

This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances,…

Numerical Analysis · Mathematics 2024-11-14 Yuto Miyatake , Kaoru Irie , Takeru Matsuda

Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…

Machine Learning · Computer Science 2022-08-30 Peter Súkeník , Christoph H. Lampert

Bayesian neural networks have successfully designed and optimized a robust neural network model in many application problems, including uncertainty quantification. However, with its recent success, information-theoretic understanding about…

Information Theory · Computer Science 2022-06-22 Jae Oh Woo

We provide an information-theoretic analysis of the generalization ability of Gibbs-based transfer learning algorithms by focusing on two popular transfer learning approaches, $\alpha$-weighted-ERM and two-stage-ERM. Our key result is an…

Machine Learning · Computer Science 2021-11-03 Yuheng Bu , Gholamali Aminian , Laura Toni , Miguel Rodrigues , Gregory Wornell

Let $(x_{i}, y_{i})_{i=1,\dots,n}$ denote independent samples from a general mixture distribution $\sum_{c\in\mathcal{C}}\rho_{c}P_{c}^{x}$, and consider the hypothesis class of generalized linear models $\hat{y} = F(\Theta^{\top}x)$. In…

Statistics Theory · Mathematics 2024-07-22 Yatin Dandi , Ludovic Stephan , Florent Krzakala , Bruno Loureiro , Lenka Zdeborová

We adopt an information-theoretic framework to analyze the generalization behavior of the class of iterative, noisy learning algorithms. This class is particularly suitable for study under information-theoretic metrics as the algorithms are…

Machine Learning · Computer Science 2023-07-20 Ibrahim Issa , Amedeo Roberto Esposito , Michael Gastpar

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a…

Quantum Physics · Physics 2015-06-15 Jan Naudts , Ben Anthonis

Ensembles are widely used in machine learning and, usually, provide state-of-the-art performance in many prediction tasks. From the very beginning, the diversity of an ensemble has been identified as a key factor for the superior…

Machine Learning · Computer Science 2022-02-17 Luis A. Ortega , Rafael Cabañas , Andrés R. Masegosa

Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised…

Genomics · Quantitative Biology 2026-04-27 Shanshan Ren , Thomas E. Bartlett , Lina Gerontogianni , Swati Chandna

Machine learning for molecular property prediction has focused largely on pure compounds, even though many practical applications depend on mixtures with intermolecular interactions. Recent work has expanded the availability of mixture…

Machine Learning · Computer Science 2026-05-29 Roel J. Leenhouts , Nathan K. Morgan , William Green , Jan G. Rittig , Florence H. Vermeire

This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…

Computation · Statistics 2019-12-03 Putu Ayu Sudyanti , Vinayak Rao

Ensembles of machine learning models have been well established as a powerful method of improving performance over a single model. Traditionally, ensembling algorithms train their base learners independently or sequentially with the goal of…

Machine Learning · Computer Science 2023-11-01 Alan Jeffares , Tennison Liu , Jonathan Crabbé , Mihaela van der Schaar

An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log…

Statistics Theory · Mathematics 2014-11-05 Shaowei Lin , Caroline Uhler , Bernd Sturmfels , Peter Bühlmann

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the…

Classical Analysis and ODEs · Mathematics 2012-07-03 A. Aptekarev , J. Arvesú

Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…

Statistics Theory · Mathematics 2026-05-15 Yu Zheng , Leo L. Duan , Arkaprava Roy

Nonlinear mixed effects models have become a standard platform for analysis when data is in the form of continuous and repeated measurements of subjects from a population of interest, while temporal profiles of subjects commonly follow a…

Methodology · Statistics 2022-03-04 Se Yoon Lee

Two main concepts studied in machine learning theory are generalization gap (difference between train and test error) and excess risk (difference between test error and the minimum possible error). While information-theoretic tools have…

Machine Learning · Computer Science 2023-03-01 Hassan Hafez-Kolahi , Behrad Moniri , Shohreh Kasaei