Related papers: Rejoinder to "Multivariate quantiles and multiple-…
$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave…
We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…
Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance.…
In this paper we present a survey of the joint program with Fabrice Baudoin originated with the paper \cite{BG1}, and continued with the works \cite{BG2}, \cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont and…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
We propose the general way of study the universal estimator for the regression problem in learning theory considered in "Universal algorithms for learning theory Part I: piecewise constant functions" and "Universal algorithms for learning…
This article discusses several matters related to Sobolev, Poincare, and isoperimetric inequalities in various settings.
Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the…
We present recent results on optimal algorithms for numerical integration and several open problems. The paper has six parts: 1. Introduction 2. Lower Bounds 3. Universality 4. General Domains 5. iid Information 6. Concluding Remarks
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.
Preliminary version of a contribution to the "Quantum Field Theory. Non-Perturbative QFT" topical area of "Modern Encyclopedia of Mathematical Physics" (SELECTA), eds. Aref'eva I, and Sternheimer D, Springer (2007). Consists of two parts -…
$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
We consider quantile estimation in a semi-supervised setting, characterized by two available data sets: (i) a small or moderate sized labeled data set containing observations for a response and a set of possibly high dimensional covariates,…
We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$ type penalty is imposed to achieve…
Discussion of "Multivariate Bayesian Logistic Regression for Analysis of Clinical Trial Safety Issues" by W. DuMouchel [arXiv:1210.0385].
Discussion of "Multivariate Bayesian Logistic Regression for Analysis of Clinical Trial Safety Issues" by W. DuMouchel [arXiv:1210.0385].
Functional data analysis is a growing research field as more and more practical applications involve functional data. In this paper, we focus on the problem of regression and classification with functional predictors: the model suggested…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…