Related papers: On relative universality, regression operator, and…

Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…

A crucial aspect in reliable machine learning is to design a deployable system in generalizing new related but unobserved environments. Domain generalization aims to alleviate such a prediction gap between the observed and unseen…

We introduce the Prediction Advantage (PA), a novel performance measure for prediction functions under any loss function (e.g., classification or regression). The PA is defined as the performance advantage relative to the Bayesian risk…

We prove a universal projection theorem, giving conditions on a parametrized family of maps $\Pi_\lambda : X \to \mathbb{R}^d$ and a collection M of measures on X under which for almost every $\lambda$ equality $\dim_H \Pi_\lambda \mu =…

We prove that Riemannian contraction in a supervised learning setting implies generalization. Specifically, we show that if an optimizer is contracting in some Riemannian metric with rate $\lambda > 0$, it is uniformly algorithmically…

In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in…

Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…

We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…

We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…

Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…

It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to…

The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard…

Fisher's linear discriminant analysis (FLDA) is an important dimension reduction method in statistical pattern recognition. It has been shown that FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian assumption. However,…

We establish a profound connection between coherent risk measures, a prominent object in quantitative finance, and uniform integrability, a fundamental concept in probability theory. Instead of working with absolute values of random…

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…

We propose to learn invariant representations, in the data domain, to achieve interpretability in algorithmic fairness. Invariance implies a selectivity for high level, relevant correlations w.r.t. class label annotations, and a robustness…

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and…

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…

Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performed by a given procedure. But, despite this fundamental role in statistics, its behavior not…