The combination of multiple classifiers using ensemble methods is increasingly important for making progress in a variety of difficult prediction problems. We present a comparative analysis of several ensemble methods through two case studies in genomics, namely the prediction of genetic interactions and protein functions, to demonstrate their efficacy on real-world datasets and draw useful conclusions about their behavior. These methods include simple aggregation, meta-learning, cluster-based meta-learning, and ensemble selection using heterogeneous classifiers trained on resampled data to improve the diversity of their predictions. We present a detailed analysis of these methods across 4 genomics datasets and find the best of these methods offer statistically significant improvements over the state of the art in their respective domains. In addition, we establish a novel connection between ensemble selection and meta-learning, demonstrating how both of these disparate methods establish a balance between ensemble diversity and performance.

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise and their solutions are discussed, and an initial account of using the system is given.

We present five methods to the problem of network anomaly detection. These methods cover most of the common techniques in the anomaly detection field, including Statistical Hypothesis Tests (SHT), Support Vector Machines (SVM) and clustering analysis. We evaluate all methods in a simulated network that consists of nominal data, three flow-level anomalies and one packet-level attack. Through analyzing the results, we point out the advantages and disadvantages of each method and conclude that combining the results of the individual methods can yield improved anomaly detection results.

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on the sample complexity, both governed by the margin-adapted dimension of the data distribution. The upper bounds are universal, and the lower bounds hold for the rich family of sub-Gaussian distributions with independent features. We conclude that this new quantity tightly characterizes the true sample complexity of large-margin classification. To prove the lower bound, we develop several new tools of independent interest. These include new connections between shattering and hardness of learning, new properties of shattering with linear classifiers, and a new lower bound on the smallest eigenvalue of a random Gram matrix generated by sub-Gaussian variables. Our results can be used to quantitatively compare large margin learning to other learning rules, and to improve the effectiveness of methods that use sample complexity bounds, such as active learning.

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully automated procedure that goes from raw data to an identified model. Both pre-processing parameters and GP hyper-parameters are tuned by maximizing the marginal likelihood of the probabilistic model. We obtain a Bayesian model of the system's dynamics which is able to report its uncertainty in regions where the data is scarce. The automated approach, the modeling of uncertainty and its relatively low computational cost make of GP-FNARX a good candidate for applications in robotics and adaptive control.

We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the simplest type of LSVMs called Local Linear Support Vector Machines (LLSVMs). For the first time we establish conditions under which LLSVMs make Bayes consistent predictions at each test point $x_0$. We also establish rates at which the local risk of LLSVMs converges to the minimum value of expected local risk at each point $x_0$. Using stability arguments we establish generalization error bounds for LLSVMs.

Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the singular value decompositions of the flattenings. We show that it is a non-trivial assumption for a tensor to have such an orthogonal decomposition, and we show that it is unique (up to natural symmetries) in case it exists, in which case we also demonstrate how it can be efficiently and reliably obtained by a sequence of singular value decompositions. We demonstrate how the factoring algorithm can be applied for parameter identification in latent variable and mixture models.

The use of alternative measures to evaluate classifier performance is gaining attention, specially for imbalanced problems. However, the use of these measures in the classifier design process is still unsolved. In this work we propose a classifier designed specifically to optimize one of these alternative measures, namely, the so-called F-measure. Nevertheless, the technique is general, and it can be used to optimize other evaluation measures. An algorithm to train the novel classifier is proposed, and the numerical scheme is tested with several databases, showing the optimality and robustness of the presented classifier.

We propose several novel methods for enhancing the multi-class SVMs by applying the generalization performance of binary classifiers as the core idea. This concept will be applied on the existing algorithms, i.e., the Decision Directed Acyclic Graph (DDAG), the Adaptive Directed Acyclic Graphs (ADAG), and Max Wins. Although in the previous approaches there have been many attempts to use some information such as the margin size and the number of support vectors as performance estimators for binary SVMs, they may not accurately reflect the actual performance of the binary SVMs. We show that the generalization ability evaluated via a cross-validation mechanism is more suitable to directly extract the actual performance of binary SVMs. Our methods are built around this performance measure, and each of them is crafted to overcome the weakness of the previous algorithm. The proposed methods include the Reordering Adaptive Directed Acyclic Graph (RADAG), Strong Elimination of the classifiers (SE), Weak Elimination of the classifiers (WE), and Voting based Candidate Filtering (VCF). Experimental results demonstrate that our methods give significantly higher accuracy than all of the traditional ones. Especially, WE provides significantly superior results compared to Max Wins which is recognized as the state of the art algorithm in terms of both accuracy and classification speed with two times faster in average.

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.