Statistics

An Analysis of Weighted Least Squares Method and Layered Least Squares Method with the Basis Block Lower Triangular Matrix Form

  • Tomonari Kitahara
  • Takashi Tsuchiya
    • Categories Convex Optimization, Linear Programming, Statistics Tags , , , ,

    In this paper, we analyze the limiting behavior of the weighted least squares problem $\min_{x\in\Re^n}\sum_{i=1}^p\|D_i(A_ix-b_i)\|^2$, where each $D_i$ is a positive definite diagonal matrix. We consider the situation where the magnitude of the weights are drastically different block-wisely so that $\max(D_1)\geq\min(D_1) \gg \max(D_2) \geq \min(D_2) \gg \max(D_3) \geq \ldots \gg \max(D_{p-1}) \geq \min(D_{p-1}) \gg \max(D_p)$. … Read more

    Convex Optimization Methods for Dimension Reduction and Coefficient Estimation in Multivariate Linear Regression

  • Zhaosong Lu
  • Renato D.C. Monteiro
  • Ming Yuan
    • Categories Convex Optimization, Nonsmooth Optimization, Statistics Tags , , , , , ,

    In this paper, we study convex optimization methods for computing the trace norm regularized least squares estimate in multivariate linear regression. The so-called factor estimation and selection (FES) method, recently proposed by Yuan et al. [17], conducts parameter estimation and factor selection simultaneously and have been shown to enjoy nice properties in both large and … Read more

    LASSO-Patternsearch Algorithm with Application to Ophthalmology and Genomic Data

  • Barbara Klein
  • Stephen Wright
  • Ronald Klein
  • Kristine Lee
  • Weiliang Shi
  • Grace Wahba
    • Categories Nonsmooth Optimization, Statistics Tags , ,

    The LASSO-Patternsearch algorithm is proposed as a two-step method to identify clusters or patterns of multiple risk factors for outcomes of interest in demographic and genomic studies. The predictor variables are dichotomous or can be coded as dichotomous. Many diseases are suspected of having multiple interacting risk factors acting in concert, and it is of … Read more

    Constraint Orbital Branching

  • Jeff Linderoth
  • James Ostrowski
  • Fabrizio Rossi
  • Stefano Smriglio
    • Categories Integer Programming, Statistics

    Orbital branching is a method for branching on variables in integer programming that reduces the likelihood of evaluating redundant, isomorphic nodes in the branch-and-bound procedure. In this work, the orbital branching methodology is extended so that the branching disjunction can be based on an arbitrary constraint. Many important families of integer programs are structured such … Read more

    l_1 Trend Filtering

  • Stephen Boyd
  • Dimitry Gorinevsky
  • Seung-Jean Kim
  • Kwangmoo Koh
    • Categories Convex and Nonsmooth Optimization, Other Topics, Statistics Tags , , , , , , ,

    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

  • Anatoli Juditsky
  • Arkadi Nemirovski
    • Categories Convex Optimization, Statistics Tags , ,

    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

  • Yael Berstein
  • Jon Lee
  • Hugo Maruri-Aguilar
  • Shmuel Onn
  • Eva Riccomagno
  • Robert Weismantel
  • Henry Wynn
    • Categories Graphs and Matroids, Nonlinear Optimization, Statistics Tags , , , , ,

    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

  • Zhaosong Lu
    • Categories Convex and Nonsmooth Optimization, Statistics Tags , ,

    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

  • Maryam Fazel
  • Benjamin Recht
  • Pablo A. Parrilo
    • Categories Convex and Nonsmooth Optimization, Semi-definite Programming, Statistics Tags , , ,

    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

  • Abdallah Abd-Elfattah
  • Ziedan D. M.
  • Amal S. Hassan
    • Categories Applications - OR and Management Sciences, Statistics Tags

    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