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Partial linear models have been widely used as flexible method for modelling linear components in conjunction with non-parametric ones. Despite the presence of the non-parametric part, the linear, parametric part can under certain…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
Functional linear regression has recently attracted considerable interest. Many works focus on asymptotic inference. In this paper we consider in a non asymptotic framework a simple estimation procedure based on functional Principal…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
Offline reinforcement learning seeks to utilize offline (observational) data to guide the learning of (causal) sequential decision making strategies. The hope is that offline reinforcement learning coupled with function approximation…
We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential…
In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between…
Efficient estimation under bias sampling, censoring or truncation is a difficult question which has been partially answered and the usual estimators are not always consistent. Several biased designs are considered for models with variables…
This article deals with asimple issue: if we have grouped data with a binary dependent variable and want to include fixed effects (group specific intercepts) in the specification, is Ordinary Least Squares (OLS) in any way superior to a…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Inference for the parameters indexing generalised linear models is routinely based on the assumption that the model is correct and a priori specified. This is unsatisfactory because the chosen model is usually the result of a data-adaptive…
Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested…
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…