Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instead, we estimate statistical significance of the observed classification accuracy, or the likelihood of observing such accuracy by chance due to spurious correlations of the high-dimensional data patterns with the class labels in the given training set. We adopt permutation testing, a non-parametric technique previously developed in classical statistics for hypothesis testing in the generative setting (i.e., comparing two probability distributions). We demonstrate the method on real examples from neuroimaging studies and DNA microarray analysis and suggest a theoretical analysis of the procedure that relates the asymptotic behavior of the test to the existing convergence bounds

Global permutation tests for multivariate ordinal data: alternatives, test statistics, and the null dilemma

We discuss two-sample global permutation tests for sets of multivariate ordinal data in possibly high-dimensional setups, motivated by the analysis of data collected by means of the World Health Organisation's International Classification of Functioning, Disability and Health. The tests do not require any modelling of the multivariate dependence structure. Specifically, we consider testing for marginal inhomogeneity and direction-independent marginal order. Max-T test statistics are known to lead to good power against alternatives with few strong individual effects. We propose test statistics that can be seen as their counterparts for alternatives with many weak individual effects. Permutation tests are valid only if the two multivariate distributions are identical under the null hypothesis. By means of simulations, we examine the practical impact of violations of this exchangeability condition. Our simulations suggest that theoretically invalid permutation tests can still be 'practically valid'. In particular, they suggest that the degree of the permutation procedure's failure may be considered as a function of the difference in group-specific covariance matrices, the proportion between group sizes, the number of variables in the set, the test statistic used, and the number of levels per variable

Classifier selection with permutation tests

This work presents a content-based recommender system for machine learning classifier algorithms. Given a new data set, a recommendation of what classifier is likely to perform best is made based on classifier performance over similar known data sets. This similarity is measured according to a data set characterization that includes several state-of-the-art metrics taking into account physical structure, statistics, and information theory. A novelty with respect to prior work is the use of a robust approach based on permutation tests to directly assess whether a given learning algorithm is able to exploit the attributes in a data set to predict class labels, and compare it to the more commonly used F-score metric for evaluating classifier performance. To evaluate our approach, we have conducted an extensive experimentation including 8 of the main machine learning classification methods with varying configurations and 65 binary data sets, leading to over 2331 experiments. Our results show that using the information from the permutation test clearly improves the quality of the recommendations.Peer ReviewedPostprint (author's final draft

Improved Error Bounds Based on Worst Likely Assignments

Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error bounds, especially for accurate classifiers, which are typically the classifiers of interest.Comment: IJCNN 201

Global and Local Two-Sample Tests via Regression

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature, there have been recent methodological developments such as classification accuracy tests. The goal of this work is to present a regression approach to comparing multivariate distributions of complex data. Depending on the chosen regression model, our framework can efficiently handle different types of variables and various structures in the data, with competitive power under many practical scenarios. Whereas previous work has been largely limited to global tests which conceal much of the local information, our approach naturally leads to a local two-sample testing framework in which we identify local differences between multivariate distributions with statistical confidence. We demonstrate the efficacy of our approach both theoretically and empirically, under some well-known parametric and nonparametric regression methods. Our proposed methods are applied to simulated data as well as a challenging astronomy data set to assess their practical usefulness

Overview of Random Forest Methodology and Practical Guidance with Emphasis on Computational Biology and Bioinformatics

The Random Forest (RF) algorithm by Leo Breiman has become a standard data analysis tool in bioinformatics. It has shown excellent performance in settings where the number of variables is much larger than the number of observations, can cope with complex interaction structures as well as highly correlated variables and returns measures of variable importance. This paper synthesizes ten years of RF development with emphasis on applications to bioinformatics and computational biology. Special attention is given to practical aspects such as the selection of parameters, available RF implementations, and important pitfalls and biases of RF and its variable importance measures (VIMs). The paper surveys recent developments of the methodology relevant to bioinformatics as well as some representative examples of RF applications in this context and possible directions for future research