Related papers: Computational-Statistical Gaps in Gaussian Single-…

In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) $d$-dimensional inputs through their projection onto a low-dimensional $r = O_d(1)$ subspace, and we study efficient agnostic…

We focus on the task of learning a single index model $\sigma(w^\star \cdot x)$ with respect to the isotropic Gaussian distribution in $d$ dimensions. Prior work has shown that the sample complexity of learning $w^\star$ is governed by the…

Sparse high-dimensional functions have arisen as a rich framework to study the behavior of gradient-descent methods using shallow neural networks, showcasing their ability to perform feature learning beyond linear models. Amongst those…

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…

We consider computationally-efficient estimation of population parameters when observations are subject to missing data. In particular, we consider estimation under the realizable contamination model of missing data in which an $\epsilon$…

The problem of learning single index and multi index models has gained significant interest as a fundamental task in high-dimensional statistics. Many recent works have analysed gradient-based methods, particularly in the setting of…

Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate…

Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose a novel Factor Augmented Single-Index…

Extracting meaningful information from high-dimensional data poses a formidable modeling challenge, particularly when the data is obscured by noise or represented through different modalities. This research proposes a novel non-parametric…

This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

We study computational-statistical gaps for improper learning in sparse linear regression. More specifically, given $n$ samples from a $k$-sparse linear model in dimension $d$, we ask what is the minimum sample complexity to efficiently (in…

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning. However, beyond linear regression, the theoretical advantage of full-batch gradient descent (GD, which always reuses…

What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly…

Significant recent work has studied the ability of gradient descent to recover a hidden planted direction $\theta^\star \in S^{d-1}$ in different high-dimensional settings, including tensor PCA and single-index models. The key quantity that…

Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…