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Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the…

In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…

Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…

Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are…

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet…

It is often said that a deep learning model is "invariant" to some specific type of transformation. However, what is meant by this statement strongly depends on the context in which it is made. In this paper we explore the nature of…

Inference about dependencies in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods…

Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a…

We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…

We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…

We consider minimax-optimal designs for the prediction of individual parameters in random coefficient regression models. We focus on the minimax-criterion, which minimizes the "worst case" for the basic criterion with respect to the…

Group Convolutional Neural Networks (G-CNNs) constrain learned features to respect the symmetries in the selected group, and lead to better generalization when these symmetries appear in the data. If this is not the case, however,…

Despite ongoing theoretical research on cross-validation (CV), many theoretical questions remain widely open. This motivates our investigation into how properties of algorithm-distribution pairs can affect the choice for the number of folds…

The statistical properties of estimator using covariance matrix for the account of point-to-point correlations due to systematic errors are analyzed. It is shown that the covariance matrix estimator (CME) is consistent for the realistic…

We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…

Traditionally model averaging has been viewed as an alternative to model selection with the ultimate goal to incorporate the uncertainty associated with the model selection process in standard errors and confidence intervals by using a…

Recently, a variety of new equivariant neural network model architectures have been proposed that generalize better over rotational and reflectional symmetries than standard models. These models are relevant to robotics because many…

We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint…

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain…