Related papers: Sparse Linear Regression With Missing Data
Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…
We study a seemingly unexpected and relatively less understood overfitting aspect of a fundamental tool in sparse linear modeling - best subset selection, which minimizes the residual sum of squares subject to a constraint on the number of…
We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…
The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
We investigate regression for variable length sequential data containing missing samples and introduce a novel tree architecture based on the Long Short-Term Memory (LSTM) networks. In our architecture, we employ a variable number of LSTM…
Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient…
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
Regression is the workhorse of statistics, and is often faced with real data that contain outliers. When these are casewise outliers, that is, cases that are entirely wrong or belong to a different population, the issue can be remedied by…
In the Sparse Linear Regression (SLR) problem, given a $d \times n$ matrix $M$ and a $d$-dimensional query $q$, the goal is to compute a $k$-sparse $n$-dimensional vector $\tau$ such that the error $||M \tau-q||$ is minimized. This problem…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
Although various distributed machine learning schemes have been proposed recently for pure linear models and fully nonparametric models, little attention has been paid on distributed optimization for semi-paramemetric models with…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…