Related papers: Robust Inference for High-Dimensional Linear Model…
We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
Estimating the 3DoF rotation from a single RGB image is an important yet challenging problem. As a popular approach, probabilistic rotation modeling additionally carries prediction uncertainty information, compared to single-prediction…
Most of the regularization methods such as the LASSO have one (or more) regularization parameter(s), and to select the value of the regularization parameter is essentially equal to select a model. Thus, to obtain a model suitable for the…
Most of previous works and applications of Bayesian factor model have assumed the normal likelihood regardless of its validity. We propose a Bayesian factor model for heavy-tailed high-dimensional data based on multivariate Student-$t$…
Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…
We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…
Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion…
This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the…
We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…
We propose a distributed method for simultaneous inference for datasets with sample size much larger than the number of covariates, i.e., N >> p, in the generalized linear models framework. When such datasets are too big to be analyzed…
We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the…
Transfer learning is an emerging paradigm for leveraging multiple sources to improve the statistical inference on a single target. In this paper, we propose a novel approach named residual importance weighted transfer learning (RIW-TL) for…
The generalized linear model (GLM) plays a key role in regression analyses. In high-dimensional data, the sparse GLM has been used but it is not robust against outliers. Recently, the robust methods have been proposed for the specific…
To improve the off-sample generalization of classical procedures minimizing the empirical risk under potentially heavy-tailed data, new robust learning algorithms have been proposed in recent years, with generalized median-of-means…
Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light…