Related papers: Moving Beyond Sub-Gaussianity in High-Dimensional …
In this paper we study the joint distributional convergence of the largest eigenvalues of the sample covariance matrix of a $p$-dimensional time series with iid entries when $p$ converges to infinity together with the sample size $n$. We…
The upper tail problem in a random graph asks to estimate the probability that the number of copies of some fixed subgraph in an Erd\H{o}s--R\'enyi random graph exceeds its expectation by some constant factor. There has been much exciting…
This work considers stationary vector count time series models defined via deterministic functions of a latent stationary vector Gaussian series. The construction is very general and ensures a pre-specified marginal distribution for the…
Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…
Large deviation behavior of the largest eigenvalue $\lambda_1$ of Gaussian networks (Erd\H{o}s-R\'enyi random graphs $\mathcal{G}_{n,p}$ with i.i.d. Gaussian weights on the edges) has been the topic of considerable interest. Recently in…
Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
We consider linear prediction with a convex Lipschitz loss, or more generally, stochastic convex optimization problems of generalized linear form, i.e.~where each instantaneous loss is a scalar convex function of a linear function. We show…
This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…
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…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Exponential tail bounds for sums play an important role in statistics, but the example of the $t$-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns…
Consider the following three important problems in statistical inference, namely, constructing confidence intervals for (1) the error of a high-dimensional ($p>n$) regression estimator, (2) the linear regression noise level, and (3) the…