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

In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…

Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving…

The notion of metric plays a key role in machine learning problems such as classification, clustering or ranking. However, it is worth noting that there is a severe lack of theoretical guarantees that can be expected on the generalization…

Normalization is ubiquitous in economics, and a growing literature shows that ``normalizations'' can matter for interpretation, counterfactual analysis, misspecification, and inference. This paper provides a general framework for these…

We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define…

Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about the…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

Understanding how much each variable contributes to an outcome is a central question across disciplines. A causal view of explainability is favorable for its ability in uncovering underlying mechanisms and generalizing to new contexts.…

In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…

The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…

This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…

Self-supervised learning models extract general-purpose representations from data. Quantifying the reliability of these representations is crucial, as many downstream models rely on them as input for their own tasks. To this end, we…

As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional…

Defining and measuring the error of a measurement is one of the most fundamental activities in experimental science. However, quantum theory shows a peculiar difficulty in extending the classical notion of root-mean-square (rms) error to…

We extend the Watanabe--Sagawa--Ueda (WSU) uncertainty relations for measurement errors to infinite-dimensional systems. The original WSU formulation provided a definition of measurement errors with a clear physical interpretation based on…

In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…

Many of the ordinal regression models that have been proposed in the literature can be seen as methods that minimize a convex surrogate of the zero-one, absolute, or squared loss functions. A key property that allows to study the…

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…

Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…