Related papers: Universality of estimators for high-dimensional li…
Over the past decade, characterizing the exact asymptotic risk of regularized estimators in high-dimensional regression has emerged as a popular line of work. This literature considers the proportional asymptotics framework, where the…
Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…
We generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence…
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…
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…
Over the last decade, a wave of research has characterized the exact asymptotic risk of many high-dimensional models in the proportional regime. Two foundational results have driven this progress: Gaussian universality, which shows that the…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
In this paper, we aim to estimate block-diagonal covariance matrices for Gaussian data in high dimension and in fixed dimension. We first estimate the block-diagonal structure of the covariance matrix by theoretical and practical estimators…
We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, a random feature model with a nonlinear activation function is asymptotically equivalent to a…
In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…
We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…
We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors may exhibit bias and aliasing effects that are not present…
While classical in many theoretical settings - and in particular in statistical physics-inspired works - the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
This paper concerns about the limiting distributions of change point estimators, in a high-dimensional linear regression time series context, where a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed at every…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…
We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates $X$ is given with no response $Y$. We do not make any sparsity assumptions on the vector of…