Related papers: High-dimensional covariance regression with applic…

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data…

Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…

Generalization theory has been established for sparse deep neural networks under high-dimensional regime. Beyond generalization, parameter estimation is also important since it is crucial for variable selection and interpretability of deep…

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…

Genetic studies often involve quantitative traits. Identifying genetic features that influence quantitative traits can help to uncover the etiology of diseases. Quantile regression method considers the conditional quantiles of the response…

We study sample covariance matrices arising from multi-level components of variance. Thus, let $ B_n=\frac{1}{N}\sum_{j=1}^NT_{j}^{1/2}x_jx_j^TT_{j}^{1/2}$, where $x_j\in R^n$ are i.i.d. standard Gaussian, and…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the…

We consider the inference problem for high-dimensional linear models, when covariates have an underlying spatial organization reflected in their correlation. A typical example of such a setting is high-resolution imaging, in which…

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints…

We consider Heterogeneous Transfer Learning (HTL) from a source to a new target domain for high-dimensional regression with differing feature sets. Most homogeneous TL methods assume that target and source domains share the same feature…

Heavy-tailed distributions have been studied in statistics, random matrix theory, physics, and econometrics as models of correlated systems, among other domains. Further, heavy-tail distributed eigenvalues of the covariance matrix of the…

Recent technological advancements have led to the rapid generation of high-throughput biological data, which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with…

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…

Local polynomial regression of order one or higher often performs poorly in areas with sparse data. In contrast, local constant regression tends to be more robust in these regions, although it is generally the least accurate approach,…

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…

Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…