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Propensity score (PS) methods are widely used in observational studies to reduce confounding and estimate causal treatment effects. However, the validity of PS-based causal estimators depends heavily on correct model specification, and…
Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…
With the recent advent of high-throughput genotyping techniques, genetic data for genome-wide association studies (GWAS) have become increasingly available, which entails the development of efficient and effective statistical approaches.…
We propose a new approach to safe variable preselection in high-dimensional penalized regression, such as the lasso. Preselection - to start with a manageable set of covariates - has often been implemented without clear appreciation of its…
Causal effect estimation is a critical task in statistical learning that aims to find the causal effect on subjects by identifying causal links between a number of predictor (or, explanatory) variables and the outcome of a treatment. In a…
Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…
Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…
Statistical and machine learning theory has developed several conditions ensuring that popular estimators such as the Lasso or the Dantzig selector perform well in high-dimensional sparse regression, including the restricted eigenvalue,…
The estimation of the generalization error of classifiers often relies on a validation set. Such a set is hardly available in few-shot learning scenarios, a highly disregarded shortcoming in the field. In these scenarios, it is common to…
To date, efforts to produce high-quality polygenic risk scores from genome-wide studies of common disease have focused on estimating and aggregating the effects of multiple SNPs. Here we propose a novel statistical approach for genetic risk…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…
In this paper, association results from genome-wide association studies (GWAS) are combined with a deep learning framework to test the predictive capacity of statistically significant single nucleotide polymorphism (SNPs) associated with…
In Regression Discontinuity (RD) design, self-selection leads to different distributions of covariates on two sides of the policy intervention, which essentially violates the continuity of potential outcome assumption. The standard RD…
This paper addresses the asymptotic performance of popular spatial regression estimators of the linear effect of an exposure on an outcome under ``spatial confounding" -- the presence of an unmeasured spatially-structured variable…
Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with human traits or diseases in the past decade. Nevertheless, much of the heritability of many traits is still unaccounted for. Commonly used…
Generalized linear models are often assumed to fit propensity scores, which are used to compute inverse probability weighted (IPW) estimators. In order to derive the asymptotic properties of IPW estimators, the propensity score is supposed…
In the high-dimensional regression model a response variable is linearly related to $p$ covariates, but the sample size $n$ is smaller than $p$. We assume that only a small subset of covariates is `active' (i.e., the corresponding…
Primordial non-Gaussianity introduces a scale-dependent variation in the clustering of density peaks corresponding to rare objects. This variation, parametrized by the bias, is investigated on scales where a linear perturbation theory is…
High-dimensional regression models with regularized sparse estimation are widely applied. For statistical inferences, debiased methods are available about single coefficients or predictions with sparse new covariate vectors (also called…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…