Robustness of Random Forest-based gene selection methods

Gene selection is an important part of microarray data analysis because it provides information that can lead to a better mechanistic understanding of an investigated phenomenon. At the same time, gene selection is very difficult because of the noisy nature of microarray data. As a consequence, gene selection is often performed with machine learning methods. The Random Forest method is particularly well suited for this purpose. In this work, four state-of-the-art Random Forest-based feature selection methods were compared in a gene selection context. The analysis focused on the stability of selection because, although it is necessary for determining the significance of results, it is often ignored in similar studies. The comparison of post-selection accuracy in the validation of Random Forest classifiers revealed that all investigated methods were equivalent in this context. However, the methods substantially differed with respect to the number of selected genes and the stability of selection. Of the analysed methods, the Boruta algorithm predicted the most genes as potentially important. The post-selection classifier error rate, which is a frequently used measure, was found to be a potentially deceptive measure of gene selection quality. When the number of consistently selected genes was considered, the Boruta algorithm was clearly the best. Although it was also the most computationally intensive method, the Boruta algorithm's computational demands could be reduced to levels comparable to those of other algorithms by replacing the Random Forest importance with a comparable measure from Random Ferns (a similar but simplified classifier). Despite their design assumptions, the minimal optimal selection methods, were found to select a high fraction of false positives

rFerns: An Implementation of the Random Ferns Method for General-Purpose Machine Learning

In this paper I present an extended implementation of the Random ferns algorithm contained in the R package rFerns. It differs from the original by the ability of consuming categorical and numerical attributes instead of only binary ones. Also, instead of using simple attribute subspace ensemble it employs bagging and thus produce error approximation and variable importance measure modelled after Random forest algorithm. I also present benchmarks' results which show that although Random ferns' accuracy is mostly smaller than achieved by Random forest, its speed and good quality of importance measure it provides make rFerns a reasonable choice for a specific applications

Feature Selection with the Boruta Package

This article describes a R package Boruta, implementing a novel feature selection algorithm for finding \emph{all relevant variables}. The algorithm is designed as a wrapper around a Random Forest classification algorithm. It iteratively removes the features which are proved by a statistical test to be less relevant than random probes. The Boruta package provides a convenient interface to the algorithm. The short description of the algorithm and examples of its application are presented.

Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio

Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces

Finsler and Lagrange spaces can be equivalently represented as almost Kahler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23 page

Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles

We provide a method of converting Lagrange and Finsler spaces and their Legendre transforms to Hamilton and Cartan spaces into almost Kaehler structures on tangent and cotangent bundles. In particular cases, the Hamilton spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on effective phase spaces. This allows us to define the corresponding Fedosov operators and develop deformation quantization schemes for nonlinear mechanical and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009

The Worldwide Change in the Behavior of Interest Rates and Prices in 1914

This paper evaluates the role of the destruction of the gold standard and the founding of the Federal Reserve, both of which occurred in 1914, in contributing to observed changes in the behavior of interest rates and prices after 1914. The paper presents a model of policy coordination in which the introduction of the Fed stabilizes interest rates, even if the gold standard remains intact, and it offers empirical evidence that the dismantling of the gold standard did not play a crucial role in precipitating the changes in interest rate behavior.