相关论文: Ratio-consistent estimation for long range depende…

In this work, we study the positive definiteness (PDness) problem in covariance matrix estimation. For high dimensional data, many regularized estimators are proposed under structural assumptions on the true covariance matrix including…

Randomized Smoothing (RS) is a prominent technique for certifying the robustness of neural networks against adversarial perturbations. With RS, achieving high accuracy at small radii requires a small noise variance, while achieving high…

We consider the model selection consistency or sparsistency of a broad set of $\ell_1$-regularized $M$-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We observe a sample of $n$ independent $p$-dimensional Gaussian vectors with Toeplitz covariance matrix $ \Sigma = [\sigma_{|i-j|}]_{1 \leq i,j \leq p}$ and $\sigma_0=1$. We consider the problem of testing the hypothesis that $\Sigma$ is…

This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…

The color - stellar mass-to-light ratio relation (CMLR) is a widely accepted tool to estimate the stellar mass (M*) of a galaxy. However, an individual CMLR tends to give distinct M* for a same galaxy when it is applied in different bands.…

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…

This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a…

In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…

We study large deviations from the invariant measure for nonlinear Schr\"odinger equations with colored noises on determining modes. The proof is based on a new abstract criterion, inspired by [V. Jak\v{s}i\'{c} et al., Comm. Pure Appl.…

In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently,…

We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non-stationary time…

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…

Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the…

Single-cell RNA-seq provides detailed molecular snapshots of individual cells but is notoriously noisy. Variability stems from biological differences and technical factors, such as amplification bias and limited RNA capture efficiency,…

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with…

Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to…

Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented…