Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce α-stable graphical (α-SG) models, a class of multivariate stable densities that can also be represented as Bayesian networks whose edges encode linear dependencies between random variables. One major hurdle to the extensive use of stable distributions is the lack of a closed-form analytical expression for their densities. This makes penalized maximumlikelihood based learning computationally demanding. We establish theoretically that the Bayesian information criterion (BIC) can asymptotically be reduced to the computationally more tractable minimum dispersion criterion (MDC) and develop StabLe, a structure learning algorithm based on MDC. We use simulated datasets for five benchmark network topologies to empirically demonstrate how StabLe improves upon ordinary least squares (OLS) regression. We also apply StabLe to microarray gene expression data for lymphoblastoid cells from 727 individuals belonging to eight global population groups. We establish that StabLe improves test set performance relative to OLS via tenfold cross-validation. Finally, we develop SGEX, a method for quantifying differential expression of genes between different population groups.

Brain decoding is a data analysis paradigm for neuroimaging experiments that is based on predicting the stimulus presented to the subject from the concurrent brain activity. In order to make inference at the group level, a straightforward but sometimes unsuccessful approach is to train a classifier on the trials of a group of subjects and then to test it on unseen trials from new subjects. The extreme difficulty is related to the structural and functional variability across the subjects. We call this approach "decoding across subjects". In this work, we address the problem of decoding across subjects for magnetoencephalographic (MEG) experiments and we provide the following contributions: first, we formally describe the problem and show that it belongs to a machine learning sub-field called transductive transfer learning (TTL). Second, we propose to use a simple TTL technique that accounts for the differences between train data and test data. Third, we propose the use of ensemble learning, and specifically of stacked generalization, to address the variability across subjects within train data, with the aim of producing more stable classifiers. On a face vs. scramble task MEG dataset of 16 subjects, we compare the standard approach of not modelling the differences across subjects, to the proposed one of combining TTL and ensemble learning. We show that the proposed approach is consistently more accurate than the standard one.

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration, and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

Massive Open Online Courses (MOOCs) bring together thousands of people from different geographies and demographic backgrounds -- but to date, little is known about how they learn or communicate. We introduce a new content-analysed MOOC dataset and use Bayesian Non-negative Matrix Factorization (BNMF) to extract communities of learners based on the nature of their online forum posts. We see that BNMF yields a superior probabilistic generative model for online discussions when compared to other models, and that the communities it learns are differentiated by their composite students' demographic and course performance indicators. These findings suggest that computationally efficient probabilistic generative modelling of MOOCs can reveal important insights for educational researchers and practitioners and help to develop more intelligent and responsive online learning environments.

The intent of this research is to generate a set of non-dominated policies from which one of two agents (the leader) can select a most preferred policy to control a dynamic system that is also affected by the control decisions of the other agent (the follower). The problem is described by an infinite horizon, partially observed Markov game (POMG). At each decision epoch, each agent knows: its past and present states, its past actions, and noise corrupted observations of the other agent's past and present states. The actions of each agent are determined at each decision epoch based on these data. The leader considers multiple objectives in selecting its policy. The follower considers a single objective in selecting its policy with complete knowledge of and in response to the policy selected by the leader. This leader-follower assumption allows the POMG to be transformed into a specially structured, partially observed Markov decision process (POMDP). This POMDP is used to determine the follower's best response policy. A multi-objective genetic algorithm (MOGA) is used to create the next generation of leader policies based on the fitness measures of each leader policy in the current generation. Computing a fitness measure for a leader policy requires a value determination calculation, given the leader policy and the follower's best response policy. The policies from which the leader can select a most preferred policy are the non-dominated policies of the final generation of leader policies created by the MOGA. An example is presented that illustrates how these results can be used to support a manager of a liquid egg production process (the leader) in selecting a sequence of actions to best control this process over time, given that there is an attacker (the follower) who seeks to contaminate the liquid egg production process with a chemical or biological toxin.

Making sense of the physical world has always been at the core of mapping. Up until recently, this has always dependent on using the human eye. Using airborne lasers, it has become possible to quickly "see" more of the world in many more dimensions. The resulting enormous point clouds serve as data sources for applications far beyond the original mapping purposes ranging from flooding protection and forestry to threat mitigation. In order to process these large quantities of data, novel methods are required. In this contribution, we develop models to automatically classify ground cover and soil types. Using the logic of machine learning, we critically review the advantages of supervised and unsupervised methods. Focusing on decision trees, we improve accuracy by including beam vector components and using a genetic algorithm. We find that our approach delivers consistently high quality classifications, surpassing classical methods.

Conditional gradient methods are old and well studied optimization algorithms. Their origin dates at least to the 50's and the Frank-Wolfe algorithm for quadratic programming [18] but they apply to much more general optimization problems. General formulations of conditional gradient algorithms have been studied in the past and various convergence properties of these algorithms have been proven. Moreover, such algorithms have found application in many fields, such as optimal control, statistics, signal processing, computational geometry and machine learning. Currently, interest in conditional gradient methods is undergoing a revival because of their computational advantages when applied to certain large scale optimization problems. Such examples are regularization problems involving sparsity or low rank constraints, which appear in many widely used methods in machine learning. Inspired by such algorithms, in this chapter we study a first-order method for solving certain convex optimization problems. We focus on problems of the form min {f(x) g(Ax) ω(x): x H}. 1 over a real Hilbert space H. We assume that f is a convex function with Hölder continuous gradient, g a Lipschitz continuous convex function, A a bounded linear operator and ω a convex function defined over a bounded domain.

In this paper there is proposed a generalized version of the SVM for binary classification problems in the case of using an arbitrary transformation x -> y. An approach similar to the classic SVM method is used. The problem is widely explained. Various formulations of primal and dual problems are proposed. For one of the most important cases the formulae are derived in detail. A simple computational example is demonstrated. The algorithm and its implementation is presented in Octave language.

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive formulations for global, multi-task and local metric learning. The resulting algorithms have several advantages over existing methods in the literature: a much smaller number of parameters to be estimated and a principled way to generalize learned metrics to new testing data points. To analyze the approach theoretically, we derive a generalization bound that justifies the sparse combination. Empirically, we evaluate our algorithms on several datasets against state-of-the-art metric learning methods. The results are consistent with our theoretical findings and demonstrate the superiority of our approach in terms of classification performance and scalability.

We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a polytime Apply function is known to exist for certain languages (e.g., OBDDs) and not exist for others (e.g., DNNF), its existence for certain languages remains unknown. Among the latter is the recently introduced language of Sentential Decision Diagrams (SDDs), for which a polytime Apply function exists for unreduced SDDs, but remains unknown for reduced ones (i.e. canonical SDDs). We resolve this open question in this paper and consider some of its theoretical and practical implications. Some of the findings we report question the common wisdom on the relationship between bottom-up compilation, language canonicity and the complexity of the Apply function.