Related papers: biniLasso: Automated cut-point detection via spars…
Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for…
The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of…
To deal with high-dimensional unlabeled datasets in many areas, principal component analysis (PCA) has become a rising technique for unsupervised feature selection (UFS). However, most existing PCA-based methods only consider the structure…
Biclustering is an essential unsupervised machine learning technique for simultaneously clustering rows and columns of a data matrix, with widespread applications in genomics, transcriptomics, and other high-dimensional omics data. Despite…
We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…
Binary segmentation, which is sequential in nature is thus far the most widely used method for identifying multiple change points in statistical models. Here we propose a top down methodology called arbitrary segmentation that proceeds in a…
We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample…
We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…
This paper introduces a multi-way tensor generalization of the Bigraphical Lasso (BiGLasso), which uses a two-way sparse Kronecker-sum multivariate-normal model for the precision matrix to parsimoniously model conditional dependence…
In genomic studies, identifying biomarkers associated with a variable of interest is a major concern in biomedical research. Regularized approaches are classically used to perform variable selection in high-dimensional linear models.…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
Time series segmentation, a.k.a. multiple change-point detection, is a well-established problem. However, few solutions are designed specifically for high-dimensional situations. In this paper, our interest is in segmenting the second-order…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
This paper extends the idea of decoupling shrinkage and sparsity for continuous priors to Bayesian Quantile Regression (BQR). The procedure follows two steps: In the first step, we shrink the quantile regression posterior through state of…