Statistics

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

This work develops a block aggregation approach to spatial estimation and prediction when the response is observed at a coarse spatial scale, for example as counts of events in administrative areas, or blocks, while covariates are available…

To defend against Byzantine attacks in decentralized learning, most existing methods rely on robust aggregation rules to mitigate the influence of malicious machines. However, these strategies inherently introduce bias, leading to inexact…

We study targeted maximum likelihood estimation (TMLE) of the average treatment effect in a semiparametric regression model whose mean function is indexed by a finite-dimensional parameter, while the additive error distribution is left…

We introduce a novel framework for uncertainty quantification in clustering that combines martingale posterior distributions with density-based clustering. Unlike classical model-based approaches, which define clusters at the latent level…

We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance to the algebraic decision boundary. We use the Euclidean…

We consider finite-sample inference for a single regression coefficient in the fixed-design linear model $Y = Z\beta + bX + \varepsilon$, where $\varepsilon\in\mathbb{R}^n$ may exhibit complex dependence or heterogeneity. We develop a group…

This paper presents a framework for causal inference in the presence of censored data,where the failure time is marked by a continuous variable referred to as a mark.The mark is observed after treatment and is not meaningful when the…

Existing approaches to modelling antibody concentration data are mostly based on finite mixture models that rely on the assumption that individuals can be divided into two distinct groups: seronegative and seropositive. Here, we challenge…

Evaluation of the safety perceptions of roundabout users is crucial for improving road safety in mixed-traffic environments. The crash- and conflict-based analyses do not incorporate the socio-demographic characteristics of the roundabout…

This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle…

As a form of "small A", quantile machine learning is used to forecast diurnal and nocturnal $Q(.90)$ air temperatures for Paris, France from late spring through the summer months of 2021. The data are provided by the Paris-Montsouris…

Detecting outliers in Functional Data Analysis is challenging because curves can stray from the majority in many different ways. The Modified Epigraph Index (MEI) and Modified Hypograph Index (MHI) rank functions by the fraction of the…

For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…

This paper presents ``randomized SINDy", a sequential machine learning algorithm designed for dynamic data that has a time-dependent structure. It employs a probabilistic approach, with its PAC learning property rigorously proven through…

This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs), with Korobov functions serving as a benchmark. We focus on 2D CNNs, comprising multi-channel convolutional layers with…

In this paper we show how to exploit interventional data to acquire the joint conditional distribution of all the variables using the Maximum Entropy principle. To this end, we extend the Causal Maximum Entropy method to make use of…

Given a family of pretrained models and a hold-out set, how can we construct a valid conformal prediction set while selecting a model that minimizes the width of the set? If we use the same hold-out data set both to select a model (the…

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product…

Non-parametric approaches to test for trends in time series make use of the Mann-Kendall statistic. Based on asymptotic arguments, these tests assume that its distribution follows a Gaussian distribution, even for autocorrelated time…