Statistical Optimization in High Dimensions - A Research Paper

Huan Xu, Constantine Caramanis, and Shie Mannor

Received: January 2014
Accepted: March 2016
Published Online: July 5, 2016

The paper deals with optimization problems whose parameters are known only approximately, based on noisy samples. In large-scale applications, the number of samples one can collect is typically of the same order of (or even less than) the dimensionality of the problem.

Three algorithms are proposed to address this setting, combining ideas from statistics, machine learning, and robust optimization.

The key ingredients of to the algorithms are dimensionality reduction techniques from machine learning, robust optimization, and concentration of measure tools from statistics.

http://pubsonline.informs.org/doi/abs/10.1287/opre.2016.1504

Rough Set Theory and Applications

Revise Basics of Set Theory

Ch. 1. Sets - Concept Review

Ch.2. Cartesian Product of Sets and Relations - Part 2



Rough Sets Using R
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lalasriza upload

Published on 25 Jun 2014
Presented by Lala Septem Riza for the Orange County R User Group. Organized and recorded by Ray DiGiacomo, Jr. (President, OC-RUG, rayd@liondatasystems.com). RoughSets is an R package that implements algorithms based on Rough Set Theory and Fuzzy Rough Set Theory. It contains some features: missing value completion, discretization, feature selection, instance selection, rule induction, and fuzzy rough nearest neighbor classifiers.

For further information on the package, visit the following URLs:
https://cran.r-project.org/web/packages/RoughSets/index.html