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Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…

Most machine learning classifiers are designed to output posterior probabilities for the classes given the input sample. These probabilities may be used to make the categorical decision on the class of the sample; provided as input to a…

Penalized empirical risk minimization with a surrogate loss function is often used to learn a high-dimensional linear decision rule in classification problems. Although much of the literature focus on the generalization error, there is a…

This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

The gapped local alignment score of two random sequences follows a Gumbel distribution. If computers could estimate the parameters of the Gumbel distribution within one second, the use of arbitrary alignment scoring schemes could increase…

The problem tackled in this paper is the determination of sample size for a given level and power in the context of a simple linear regression model. At a technical level, the simple linear regression model is a five-parameter model. It is…

Inherent risk scoring is an important function in anti-money laundering, used for determining the riskiness of an individual during onboarding $\textit{before}$ fraudulent transactions occur. It is, however, often fraught with two…

The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models. A key implementing step is score matching, that is, the estimation of the…

This article is devoted to the problem of predicting the value taken by a random permutation $\Sigma$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an…

This article investigates the probabilistic relationship between quantum classification of Boolean functions and their Hamming distance. By integrating concepts from quantum computing, information theory, and combinatorics, we explore how…

State-of-the-art results in typical classification tasks are mostly achieved by unexplainable machine learning methods, like deep neural networks, for instance. Contrarily, in this paper, we investigate the application of rule learning…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…

We consider the problem of sequential decision making under uncertainty in which the loss caused by a decision depends on the following binary observation. In competitive on-line learning, the goal is to design decision algorithms that are…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover,…