Related papers: High-Dimensional Gaussian Mean Estimation under Re…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
Model averaging has demonstrated superior performance for ensemble forecasting in high-dimensional framework, its extension to incomplete datasets remains a critical but underexplored challenge. Moreover, identifying the parsimonious model…
We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In…
We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been…
We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
Missing data imputation, where a model is trained on observed data to estimate unobserved values, is a fundamental problem in machine learning. In this paper, we rigorously formulate imputation model learning as a mean-squared error risk…
We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max…
We introduce a new method for estimating the mean of an outcome variable within groups when researchers only observe the average of the outcome and group indicators across a set of aggregation units, such as geographical areas. Existing…
The US Census Bureau will deliberately corrupt data sets derived from the 2020 US Census, enhancing the privacy of respondents while potentially reducing the precision of economic analysis. To investigate whether this trade-off is…
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…
The estimation of linear causal models (also known as structural equation models) from data is a well-known problem which has received much attention in the past. Most previous work has, however, made an explicit or implicit assumption of…
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…
In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and…