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Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models the overall number of regressors $p$ is very large, possibly larger than the sample…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
We give a row sampling algorithm for the quantile loss function with sample complexity nearly linear in the dimensionality of the data, improving upon the previous best algorithm whose sampling complexity has at least cubic dependence on…
High-dimensional data can often display heterogeneity due to heteroscedastic variance or inhomogeneous covariate effects. Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
In this paper, we aim to give a theoretical approximation for the penalty level of $\ell_{1}$-regularization problems. This can save much time in practice compared with the traditional methods, such as cross-validation. To achieve this…
In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
We consider the problem of automatic variable selection in a linear model with asymmetric or heavy-tailed errors when the number of explanatory variables diverges with the sample size. For this high-dimensional model, the penalized least…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
Coordinate descent (CD) algorithms have become the method of choice for solving a number of optimization problems in machine learning. They are particularly popular for training linear models, including linear support vector machine…
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…
We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
We propose a new selection rule for the coordinate selection in coordinate descent methods for huge-scale optimization. The efficiency of this novel scheme is provably better than the efficiency of uniformly random selection, and can reach…