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Recommender models aim to capture user preferences from historical feedback and then predict user-specific feedback on candidate items. However, the presence of various unmeasured confounders causes deviations between the user preferences…

In a multivariate linear regression model with $p>1$ covariates, implementation of penalization techniques often implies a preliminary univariate standardization step. Although this prevents scale effects on the covariates selection…

Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…

High-dimensional data sets are often analyzed and explored via the construction of a latent low-dimensional space which enables convenient visualization and efficient predictive modeling or clustering. For complex data structures, linear…

As statistical classifiers become integrated into real-world applications, it is important to consider not only their accuracy but also their robustness to changes in the data distribution. In this paper, we consider the case where there is…

Hidden confounding remains a central challenge in estimating treatment effects from observational data, as unobserved variables can lead to biased causal estimates. While recent work has explored the use of large language models (LLMs) for…

Performing causal inference in observational studies requires we assume confounding variables are correctly adjusted for. G-computation methods are often used in these scenarios, with several recent proposals using Bayesian versions of…

We consider the Lasso for a noiseless experiment where one has observations $X \beta^0$ and uses the penalized version of basis pursuit. We compute for some special designs the compatibility constant, a quantity closely related to the…

We consider penalized estimation in hidden Markov models (HMMs) with multivariate Normal observations. In the moderate-to-large dimensional setting, estimation for HMMs remains challenging in practice, due to several concerns arising from…

Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…

Valid estimation of treatment effects from observational data requires proper control of confounding. If the number of covariates is large relative to the number of observations, then controlling for all available covariates is infeasible.…

High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…

We propose a general adaptive LASSO method for a quantile regression model. Our method is very interesting when we know nothing about the first two moments of the model error. We first prove that the obtained estimators satisfy the oracle…

In the era of fast-paced precision medicine, observational studies play a major role in properly evaluating new treatments in clinical practice. Yet, unobserved confounding can significantly compromise causal conclusions drawn from…

Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…

When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which…

We study the problem of learning personalized decision policies from observational data while accounting for possible unobserved confounding. Previous approaches, which assume unconfoundedness, i.e., that no unobserved confounders affect…

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building…

Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…

We consider linear regression model estimation where the covariate of interest is randomly censored. Under a non-informative censoring mechanism, one may obtain valid estimates by deleting censored observations. However, this comes at a…