Related papers: Log-ratio Lasso: Scalable, Sparse Estimation for L…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
In genomic analysis, biomarker discovery, image recognition, and other systems involving machine learning, input variables can often be organized into different groups by their source or semantic category. Eliminating some groups of…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
This paper considers the design of tunable decision schemes capable of rejecting with high probability mismatched signals embedded in Gaussian interference with unknown covariance matrix. To this end, a sparse recovery technique is…
Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some…
Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled…
This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…
Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
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…
Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
Although the log-likelihood is widely used in model selection, the log-likelihood ratio has had few applications in this area. We develop a log-likelihood ratio based method for selecting regression models by focusing on the set of models…
There are a variety of settings where vague prior information may be available on the importance of predictors in high-dimensional regression settings. Examples include ordering on the variables offered by their empirical variances (which…
In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…