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Happy to be a collaborator on this paper to add inference to the ReliefF method for feature selection. We have done a lot of work on this algorithm that is capable of detecting epistasis.

Le TT, Urbanowicz RJ, Moore JH, McKinney BA. Statistical Inference Relief (STIR) feature selection. Bioinformatics. 2018 Sep 18., in press

Abstract

MOTIVATION:
Relief is a family of machine learning algorithms that uses nearest-neighbors to select features whose association with an outcome may be due to epistasis or statistical interactions with other features in high-dimensional data. Relief-based estimators are non-parametric in the statistical sense that they do not have a parameterized model with an underlying probability distribution for the estimator, making it difficult to determine the statistical significance of Relief-based attribute estimates. Thus, a statistical inferential formalism is needed to avoid imposing arbitrary thresholds to select the most important features.

METHODS:
We reconceptualize the Relief-based feature selection algorithm to create a new family of STatistical Inference Relief (STIR) estimators that retains the ability to identify interactions while incorporating sample variance of the nearest neighbor distances into the attribute importance estimation. This variance permits the calculation of statistical significance of features and adjustment for multiple testing of Relief-based scores. Specifically, we develop a pseudo t-test version of Relief-based algorithms for case-control data.

RESULTS:
We demonstrate the statistical power and control of type I error of the STIR family of feature selection methods on a panel of simulated data that exhibits properties reflected in real gene expression data, including main effects and network interaction effects. We compare the performance of STIR when the adaptive radius method is used as the nearest neighbor constructor with STIR when the fixed-k nearest neighbor constructor is used. We apply STIR to real RNA-Seq data from a study of major depressive disorder and discuss STIR's straightforward extension to genome-wide association studies.

AVAILABILITY:
Code and data available at http://insilico.utulsa.edu/software/STIR.

I love seeing new extensions and modifications to our MDR method. Here is a new from Dr. Lou.

Hou TT, Lin F, Bai S, Cleves MA, Xu HM, Lou XY. Generalized multifactor dimensionality reduction approaches to identification of genetic interactions underlying ordinal traits. Genet Epidemiol, in press (2018)

Abstract

The manifestation of complex traits is influenced by gene–gene and gene–environment interactions, and the identification of multifactor interactions is an important but challenging undertaking for genetic studies. Many complex phenotypes such as disease severity are measured on an ordinal scale with more than two categories. A proportional odds model can improve statistical power for these outcomes, when compared to a logit model either collapsing the categories into two mutually exclusive groups or limiting the analysis to pairs of categories. In this study, we propose a proportional odds model‐based generalized multifactor dimensionality reduction (GMDR) method for detection of interactions underlying polytomous ordinal phenotypes. Computer simulations demonstrated that this new GMDR method has a higher power and more accurate predictive ability than the GMDR methods based on a logit model and a multinomial logit model. We applied this new method to the genetic analysis of low‐density lipoprotein (LDL) cholesterol, a causal risk factor for coronary artery disease, in the Multi‐Ethnic Study of Atherosclerosis, and identified a significant joint action of the CELSR2, SERPINA12, HPGD, and APOB genes. This finding provides new information to advance the limited knowledge about genetic regulation and gene interactions in metabolic pathways of LDL cholesterol. In conclusion, the proportional odds model‐based GMDR is a useful tool that can boost statistical power and prediction accuracy in studying multifactor interactions underlying ordinal traits.