Related papers: Two-Dimensional Variable Selection and Its Applica…

An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…

We consider the problem of variable selection in regression models. In particular, we are interested in selecting explanatory covariates linked with the response variable and we want to determine which covariates are relevant, that is which…

Penalized regression has become a standard tool for model building across a wide range of application domains. Common practice is to tune the amount of penalization to tradeoff bias and variance or to optimize some other measure of…

We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…

The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held…

We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…

Nonlinear Mixed effects models are hidden variables models that are widely used in many fields such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters…

This paper introduces a novel penalty decomposition algorithm customized for addressing the non-differentiable and nonconvex problem of extended mean-variance-CVaR portfolio optimization with short-selling and cardinality constraints. The…

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…

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…

The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…

We consider approaches for improving the efficiency of algorithms for fitting nonconvex penalized regression models such as SCAD and MCP in high dimensions. In particular, we develop rules for discarding variables during cyclic coordinate…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…

Analysis of high-dimensional data is currently a popular field of research, thanks to many applications e.g. in genetics (DNA data in genomewide association studies), spectrometry or web analysis. At the same time, the type of problems that…

Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…

Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…

Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…

The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…