l_1 Trend Filtering

The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed l_1 trend filtering method substitutes a sum of absolute values (i.e., l_1-norm) for the sum of squares used in … Read more

Nonparametric Estimation via Convex Programming

In the paper, we focus primarily on the problem of recovering a linear form g’*x of unknown “signal” x known to belong to a given convex compact set X in R^n from N independent realizations of a random variable taking values in a finite set, the distribution p of the variable being affinely parameterized by … Read more

Nonlinear Matroid Optimization and Experimental Design

We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids. Our work is … Read more

Smooth Optimization Approach for Covariance Selection

In this paper we study a smooth optimization approach for solving a class of non-smooth {\it strongly} concave maximization problems. In particular, we apply Nesterov’s smooth optimization technique \cite{Nest83-1,Nest05-1} to their dual counterparts that are smooth convex problems. It is shown that the resulting approach has $\cO(1/{\sqrt{\epsilon}})$ iteration complexity for finding an $\epsilon$-optimal solution to … Read more

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, … Read more

Efficiency of Maximum Likelihood Estimators under Different Censored Sampling Schemes for Rayleigh Distribution

The objective of this article is to study the effect of different types of censored sampling schemes on the estimation of the unknown parameter for Rayleigh distribution. The censored sampling schemes namely; type-I, type-II and progressive type-II censored sampling are to be considered. The comparisons made between the samples are based on the Fisher information, … Read more

Measures with zeros in the inverse of their moment matrix

We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this … Read more

Consistency of robust portfolio estimators

It is a matter of common knowledge that traditional Markowitz optimization based on sample means and covariances performs poorly in practice. For this reason, diverse attempts were made to improve performance of portfolio optimization. In this paper, we investigate three popular portfolio selection models built upon classical mean-variance theory. The first model is an extension … Read more

A Penalized Trimmed Squares Method for Deleting Outliers in Robust Regression

We consider the problem of identifying multiple outliers in linear regression models. In robust regression the unusual observations should be removed from the sample in order to obtain better fitting for the rest of the observations. Based on the LTS estimate, we propose a penalized trimmed square estimator PTS, where penalty costs for discarding outliers … Read more

Coordinate and Subspace Optimization Methods for Linear Least Squares with Non-Quadratic Regularization

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [10], a new iterative method called Parallel Coordinate Descent (PCD) was devised. We provide herein a convergence … Read more