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Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…

Recent works in self-supervised learning have advanced the state-of-the-art by relying on the contrastive learning paradigm, which learns representations by pushing positive pairs, or similar examples from the same class, closer together…

We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…

In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…

Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…

The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…

Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null…

The divergence of perturbative expansions for the vast majority of macroscopic systems, which follows from Dyson's collapse argument, prevents Feynman's diagrammatic technique from being directly used for controllable studies of strongly…

For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features.…

Causal analyses for observational studies are often complicated by covariate imbalances among treatment groups, and matching methodologies alleviate this complication by finding subsets of treatment groups that exhibit covariate balance. It…

In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based…

This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with…

In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…

Datasets typically contain inaccuracies due to human error and societal biases, and these inaccuracies can affect the outcomes of models trained on such datasets. We present a technique for certifying whether linear regression models are…

In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency. While…

An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…

We propose a differentiable nonlinear least squares framework to account for uncertainty in relative pose estimation from feature correspondences. Specifically, we introduce a symmetric version of the probabilistic normal epipolar…

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…