Related papers: Outlier-robust Estimation of a Sparse Linear Model…
In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…
Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases,…
In this paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse…
Multivariate Gaussian is often used as a first approximation to the distribution of high-dimensional data. Determining the parameters of this distribution under various constraints is a widely studied problem in statistics, and is often…
Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
Cellwise contamination remains a challenging problem for data scientists, particularly in research fields that require the selection of sparse features. Traditional robust methods may not be feasible nor efficient in dealing with such…
In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…
We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…
In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic…
We propose an inlier-based outlier detection method capable of both identifying the outliers and explaining why they are outliers, by identifying the outlier-specific features. Specifically, we employ an inlier-based outlier detection…
We consider the problem of estimating a sparse linear regression vector $\beta^*$ under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is available on the sparsity pattern,…
Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…
Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible…
This paper study sparse classification problems. We show that under single-index models, vanilla Lasso could give good estimate of unknown parameters. With this result, we see that even if the model is not linear, and even if the response…
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed…
Robust low-rank approximation under row-wise adversarial corruption can be achieved with a single pass, randomized procedure that detects and removes outlier rows by thresholding their projected norms. We propose a scalable, non-iterative…