Accuracy, Recall, Precision, F-measure, Kappa, ACU [García et al. (2012)] and some other new proposed measures like Informedness and Markedness [Powers (2011)] are examples of different evaluation measures. Depending on the problem and the field of application one measure could be more suitable than another. While in the Behavioral Sciences, Specificity and Sensitivity are commonly used, in the Medical Sciences, ROC analysis is a standard for evaluation. On the other hand, in the Information Retrieval community and fraud detection, Recall, Precision and F-measure are considered appropriate measures for testing effectiveness. In a learning design strategy, the best rule for the specific application will be the one that get the optimal performance for the chosen measure. Looking for the best decision rule, in a Bayesian framework, implies to minimize the overall risk taking into account the different misclassification cost [Duda et al. (2001)]; in an equal misclassification cost problem we can find this optimal solution, with maximum accuracy, selecting the class that has the maximum a posteriori probability. However, finding a decision rule that looks for minimum error rate or maximum accuracy in an imbalanced domain gives solutions strongly biased to favor the majority class, getting poor performance. This problem is particularly important in those applications where the instances of a class (the majority one) heavily outnumber the instances of the other (the minority) class and it is costly to misclassify samples from the minority class.

Regularized principal components analysis, especially Sparse PCA and Functional PCA, has become widely used for dimension reduction in high-dimensional settings. Many examples of massive data, however, may benefit from estimating both sparse AND functional factors. These include neuroimaging data where there are discrete brain regions of activation (sparsity) but these regions tend to be smooth spatially (functional). Here, we introduce an optimization framework that can encourage both sparsity and smoothness of the row and/or column PCA factors. This framework generalizes many of the existing approaches to Sparse PCA, Functional PCA and two-way Sparse PCA and Functional PCA, as these are all special cases of our method. In particular, our method permits flexible combinations of sparsity and smoothness that lead to improvements in feature selection and signal recovery as well as more interpretable PCA factors. We demonstrate our method on simulated data and a neuroimaging example on EEG data. This work provides a unified framework for regularized PCA that can form the foundation for a cohesive approach to regularization in high-dimensional multivariate analysis.

Learning probabilistic logic programming languages is receiving an increasing attention and systems are available for learning the parameters (PRISM, LeProbLog, LFI-ProbLog and EMBLEM) or both the structure and the parameters (SEM-CP-logic and SLIPCASE) of these languages. In this paper we present the algorithm SLIPCOVER for "Structure LearnIng of Probabilistic logic programs by searChing OVER the clause space". It performs a beam search in the space of probabilistic clauses and a greedy search in the space of theories, using the log likelihood of the data as the guiding heuristics. To estimate the log likelihood SLIPCOVER performs Expectation Maximization with EMBLEM. The algorithm has been tested on five real world datasets and compared with SLIPCASE, SEM-CP-logic, Aleph and two algorithms for learning Markov Logic Networks (Learning using Structural Motifs (LSM) and ALEPH++ExactL1). SLIPCOVER achieves higher areas under the precision-recall and ROC curves in most cases.

Statistical estimates can often be improved by fusion of data from several different sources. One example is so-called ensemble methods which have been successfully applied in areas such as machine learning for classification and clustering. In this paper, we present an ensemble method to improve community detection by aggregating the information found in an ensemble of community structures. This ensemble can found by re-sampling methods, multiple runs of a stochastic community detection method, or by several different community detection algorithms applied to the same network. The proposed method is evaluated using random networks with community structures and compared with two commonly used community detection methods. The proposed method when applied on a stochastic community detection algorithm performs well with low computational complexity, thus offering both a new approach to community detection and an additional community detection method.

Reshef & Reshef recently published a paper in which they present a method called the Maximal Information Coefficient (MIC) that can detect all forms of statistical dependence between pairs of variables as sample size goes to infinity. While this method has been praised by some, it has also been criticized for its lack of power in finite samples. We seek to modify MIC so that it has higher power in detecting associations for limited sample sizes. Here we present the Generalized Mean Information Coefficient (GMIC), a generalization of MIC which incorporates a tuning parameter that can be used to modify the complexity of the association favored by the measure. We define GMIC and prove it maintains several key asymptotic properties of MIC. Its increased power over MIC is demonstrated using a simulation of eight different functional relationships at sixty different noise levels. The results are compared to the Pearson correlation, distance correlation, and MIC. Simulation results suggest that while generally GMIC has slightly lower power than the distance correlation measure, it achieves higher power than MIC for many forms of underlying association. For some functional relationships, GMIC surpasses all other statistics calculated. Preliminary results suggest choosing a moderate value of the tuning parameter for GMIC will yield a test that is robust across underlying relationships. GMIC is a promising new method that mitigates the power issues suffered by MIC, at the possible expense of equitability. Nonetheless, distance correlation was in our simulations more powerful for many forms of underlying relationships. At a minimum, this work motivates further consideration of maximal information-based nonparametric exploration (MINE) methods as statistical tests of independence.

We use partial class memberships in soft classification to model uncertain labelling and mixtures of classes. Partial class memberships are not restricted to predictions, but may also occur in reference labels (ground truth, gold standard diagnosis) for training and validation data. Classifier performance is usually expressed as fractions of the confusion matrix, such as sensitivity, specificity, negative and positive predictive values. We extend this concept to soft classification and discuss the bias and variance properties of the extended performance measures. Ambiguity in reference labels translates to differences between best-case, expected and worst-case performance. We show a second set of measures comparing expected and ideal performance which is closely related to regression performance, namely the root mean squared error RMSE and the mean absolute error MAE. All calculations apply to classical crisp classification as well as to soft classification (partial class memberships and/or one-class classifiers). The proposed performance measures allow to test classifiers with actual borderline cases. In addition, hardening of e.g. posterior probabilities into class labels is not necessary, avoiding the corresponding information loss and increase in variance. We implement the proposed performance measures in the R package "softclassval", which is available from CRAN and at http://softclassval.r-forge.r-project.org. Our reasoning as well as the importance of partial memberships for chemometric classification is illustrated by a real-word application: astrocytoma brain tumor tissue grading (80 patients, 37000 spectra) for finding surgical excision borders. As borderline cases are the actual target of the analytical technique, samples which are diagnosed to be borderline cases must be included in the validation.

A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationships of different types. Equitability is important in data exploration when the goal is to identify a relatively small set of strongest associations within a dataset as opposed to finding as many non-zero associations as possible, which often are too many to sift through. Thus an equitable statistic, such as the maximal information coefficient (MIC), can be useful for analyzing high-dimensional data sets. Here, we explore both equitability and the properties of MIC, and discuss several aspects of the theory and practice of MIC. We begin by presenting an intuition behind the equitability of MIC through the exploration of the maximization and normalization steps in its definition. We then examine the speed and optimality of the approximation algorithm used to compute MIC, and suggest some directions for improving both. Finally, we demonstrate in a range of noise models and sample sizes that MIC is more equitable than natural alternatives, such as mutual information estimation and distance correlation.

In virtually all machine learning applications, hyper-parameter tuning is required to maximize predictive accuracy. Such tuning is computationally expensive, and the cost is further exacerbated by the need for multiple evaluations (via cross-validation or bootstrap) at each configuration setting to guarantee statistically significant results. This paper presents a simple, general technique for improving the efficiency of hyper-parameter tuning by minimizing the number of resampled evaluations at each configuration. We exploit the fact that train-test samples can easily be \emph{matched} across candidate hyper-parameter configurations. This permits the use of paired hypothesis tests and power analysis that allow for statistically sound early elimination of suboptimal candidates to minimize the number of evaluations. Results on synthetic and real-world datasets demonstrate that our method improves over competitors for discrete parameter settings, and enhances state-of-the-art techniques for continuous parameter settings.

Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ Abstract The area under the ROC curve is widely used as a measure of performance of classification rules. However, it has recently been shown that the measure is fundamentally incoherent, in the sense that it treats the relative severities of misclassifications differently when different classifiers are used. To overcome this, [5, 6] proposed the H measure, which allows a given researcher to fix the distribution of relative severities to a classifier-independent setting on a given problem. Keywords: supervised classification, classifier performance, AUC, ROC curve, H measure 1. Introduction The aim of supervised classification is to construct a rule which will allow one to assign objects to one of M classes, on the basis of vectors of descriptive features of those objects. The rule will be constructed using a'training' set (machine learning and pattern recognition terminology) or'design' set (statistics terminology) of data which includes both descriptive vectors and true classes for a sample of objects.

We present an efficient algorithm for simultaneously training sparse generalized linear models across many related problems, which may arise from bootstrapping, cross-validation and nonparametric permutation testing. Our approach leverages the redundancies across problems to obtain significant computational improvements relative to solving the problems sequentially by a conventional algorithm. We demonstrate our fast simultaneous training of generalized linear models (FaSTGLZ) algorithm on a number of real-world datasets, and we run otherwise computationally intensive bootstrapping and permutation test analyses that are typically necessary for obtaining statistically rigorous classification results and meaningful interpretation. Code is freely available at http://liinc.bme.columbia.edu/fastglz.