A data augmentation approach for a class of statistical inference problems

Rodrigo Carvajal; Rafael Orellana; Dimitrios Katselis; Pedro Escárate; Juan Carlos Agüero

doi:10.1371/journal.pone.0208499

A data augmentation approach for a class of statistical inference problems

PLoS One. 2018 Dec 10;13(12):e0208499. doi: 10.1371/journal.pone.0208499. eCollection 2018.

Authors

Rodrigo Carvajal¹, Rafael Orellana^{1

2}, Dimitrios Katselis³, Pedro Escárate^{4

5}, Juan Carlos Agüero¹

Affiliations

¹ Electronics Engineering Department, Universidad Técnica Federico Santa María, Valparaíso, Chile.
² Universidad de Los Andes, Mérida, Venezuela.
³ Coordinated Science Laboratory and Information Trust Institute, University of Illinois, Urbana-Champaign, Illinois, United States of America.
⁴ Large Binocular Telescope Observatory, Steward Observatory, University of Arizona, Tucson, AZ, United States of America.
⁵ Instituto de Electricidad y Electrónica, Facultad de Ciencias de la Ingeniería, Universidad Austral, Valdivia, Chile.

Abstract

We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms*
Computer Simulation
Forecasting / methods
Image Processing, Computer-Assisted
Likelihood Functions
Models, Statistical*

Grants and funding

This work was partially supported by the Fondo Nacional de Desarrollo Científico y Tecnológico-Chile through grants No. 3140054 and 1181158. This work was also partially supported by the Comisión Nacional de Investigación Científica y Tecnológica, Advanced Center for Electrical and Electronic Engineering (AC3E, Proyecto Basal FB0008), Chile. The work of R. Orellana was partially supported by the PIIC program of the Universidad Técnica Federico Santa María, scholarship 015/2018. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.