Related papers: Adaptive l1-regularization for short-selling contr…

In model predictive control (MPC), the choice of cost-weighting matrices and designing the Hessian matrix directly affects the trade-off between rapid state regulation and minimizing the control effort. However, traditional MPC in quadratic…

We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the…

We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…

In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many…

In a Markovian framework, we consider the problem of finding the minimal initial value of a controlled process allowing to reach a stochastic target with a given level of expected loss. This question arises typically in approximate hedging…

Reweighted l1-algorithms have attracted a lot of attention in the field of applied mathematics. A unified framework of such algorithms has been recently proposed by Zhao and Li. In this paper we construct a few new examples of reweighted…

Markowitz mean-variance portfolios with sample mean and covariance as input parameters feature numerous issues in practice. They perform poorly out of sample due to estimation error, they experience extreme weights together with high…

Here we propose a novel searching scheme for a tuning parameter in high-dimensional penalized regression methods to address variable selection and modeling when sample sizes are limited compared to the data dimensions. Our method is…

We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is $L_1$ regularization, which is often used in compressed sensing, a technique for reconstructing…

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…

This paper presents a controller design framework aiming to balance control performance and actuation rate. Control performance is evaluated by an infinite-horizon average cost, and the number of control actions is penalized via…

Covariance selection seeks to estimate a covariance matrix by maximum likelihood while restricting the number of nonzero inverse covariance matrix coefficients. A single penalty parameter usually controls the tradeoff between log likelihood…

We theoretically and empirically study portfolio optimization under transaction costs and establish a link between turnover penalization and covariance shrinkage with the penalization governed by transaction costs. We show how the ex ante…

Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…

We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…

We propose a method that simultaneously identifies a linear time-invariant model of a building's temperature dynamics and a transformed version of the unmeasured disturbance affecting the building. Our method uses l1-regularization to…

Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…

Ultra high-throughput sequencing of transcriptomes (RNA-Seq) has enabled the accurate estimation of gene expression at individual isoform level. However, systematic biases introduced during the sequencing and mapping processes as well as…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…