We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than $\approx 1%$, of the variance of the target variables. To facilitate the prediction of the weak effects, we constrain our model structure by introducing a novel Bayesian approach of sharing information between the regression model and the noise model. Further reduction of the effective number of parameters is achieved by introducing an infinite shrinkage prior and group sparsity in the context of the Bayesian reduced rank regression, and using the Bayesian infinite factor model as a flexible low-rank noise model. In our experiments the model incorporating the novelties outperformed alternatives in genomic prediction of rich phenotype data. In particular, the information sharing between the noise and regression models led to significant improvement in prediction accuracy.

The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several extensions that improve both the quality of the vectors and the training speed. By subsampling of the frequent words we obtain significant speedup and also learn more regular word representations. We also describe a simple alternative to the hierarchical softmax called negative sampling. An inherent limitation of word representations is their indifference to word order and their inability to represent idiomatic phrases. For example, the meanings of "Canada" and "Air" cannot be easily combined to obtain "Air Canada". Motivated by this example, we present a simple method for finding phrases in text, and show that learning good vector representations for millions of phrases is possible.

The cumulative distribution network (CDN) is a recently developed class of probabilistic graphical models (PGMs) permitting a copula factorization, in which the CDF, rather than the density, is factored. Despite there being much recent interest within the machine learning community about copula representations, there has been scarce research into the CDN, its amalgamation with copula theory, and no evaluation of its performance. Algorithms for inference, sampling, and learning in these models are underdeveloped compared those of other PGMs, hindering widerspread use. One advantage of the CDN is that it allows the factors to be parameterized as copulae, combining the benefits of graphical models with those of copula theory. In brief, the use of a copula parameterization enables greater modelling flexibility by separating representation of the marginals from the dependence structure, permitting more efficient and robust learning. Another advantage is that the CDN permits the representation of implicit latent variables, whose parameterization and connectivity are not required to be specified. Unfortunately, that the model can encode only latent relationships between variables severely limits its utility. In this thesis, we present inference, learning, and sampling for CDNs, and further the state-of-the-art. First, we explain the basics of copula theory and the representation of copula CDNs. Then, we discuss inference in the models, and develop the first sampling algorithm. We explain standard learning methods, propose an algorithm for learning from data missing completely at random (MCAR), and develop a novel algorithm for learning models of arbitrary treewidth and size. Properties of the models and algorithms are investigated through Monte Carlo simulations. We conclude with further discussion of the advantages and limitations of CDNs, and suggest future work.

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we develop a new derivation that transforms the problem into that of evaluating the ratio of multivariate Gaussian orthant integrals. Moreover, we develop a new Monte Carlo procedure that evaluates these integrals. It is based on some aspects of bootstrap sampling and acceptancerejection. The proposed approach has beneficial properties compared to the existing Markov Chain Monte Carlo approach, such as simplicity, reliability, and speed.

Suppose that the Kullback-Leibler divergence between two probability measures is bounded from above by 2. What then is the maximum possible value of the Hellinger distance between them? Such questions naturally arise in many fields including mathematical statistics and machine learning, information theory, probability, statistical physics etc. and the goal of this paper is to provide a way of answering them. From the variational viewpoint, this problem can be posed as: maximize the Hellinger distance subject to a constraint on the Kullback-Leibler divergence over the space of all pairs of probability measures over all possible sample spaces. We shall prove in this paper that the value of this maximization problem remains unchanged if one restricts the sample space to be the three-element set{ 1, 2, 3} . In other words, in order to find the maximum Hellinger distance subject to an upper bound on the Kullback-Leibler divergence, one can just restrict attention to pairs of probability measures on {1, 2, 3}. Thus, the large infinite-dimensional optimization problem is reduced to an optimization problem over a small finite-dimensional space (of dimension 4) which makes it tractable.

Recently, there has been a renewed interest in the machine learning community for variants of a sparse greedy approximation procedure for concave optimization known as {the Frank-Wolfe (FW) method}. In particular, this procedure has been successfully applied to train large-scale instances of non-linear Support Vector Machines (SVMs). Specializing FW to SVM training has allowed to obtain efficient algorithms but also important theoretical results, including convergence analysis of training algorithms and new characterizations of model sparsity. In this paper, we present and analyze a novel variant of the FW method based on a new way to perform away steps, a classic strategy used to accelerate the convergence of the basic FW procedure. Our formulation and analysis is focused on a general concave maximization problem on the simplex. However, the specialization of our algorithm to quadratic forms is strongly related to some classic methods in computational geometry, namely the Gilbert and MDM algorithms. On the theoretical side, we demonstrate that the method matches the guarantees in terms of convergence rate and number of iterations obtained by using classic away steps. In particular, the method enjoys a linear rate of convergence, a result that has been recently proved for MDM on quadratic forms. On the practical side, we provide experiments on several classification datasets, and evaluate the results using statistical tests. Experiments show that our method is faster than the FW method with classic away steps, and works well even in the cases in which classic away steps slow down the algorithm. Furthermore, these improvements are obtained without sacrificing the predictive accuracy of the obtained SVM model.

We propose and analyze a new parallel coordinate descent method---`NSync---in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates under a strong convexity assumption, and comment on how to assign probabilities to the sets to optimize the bound. The complexity and practical performance of the method can outperform its uniform variant by an order of magnitude. Surprisingly, the strategy of updating a single randomly selected coordinate per iteration---with optimal probabilities---may require less iterations, both in theory and practice, than the strategy of updating all coordinates at every iteration.

Many natural language processing (NLP) applications require the computation of similarities between pairs of syntactic or semantic trees. Many researchers have used tree edit distance for this task, but this technique suffers from the drawback that it deals with single node operations only. We have extended the standard tree edit distance algorithm to deal with subtree transformation operations as well as single nodes. The extended algorithm with subtree operations, TED+ST, is more effective and flexible than the standard algorithm, especially for applications that pay attention to relations among nodes (e.g. in linguistic trees, deleting a modifier subtree should be cheaper than the sum of deleting its components individually). We describe the use of TED+ST for checking entailment between two Arabic text snippets. The preliminary results of using TED+ST were encouraging when compared with two string-based approaches and with the standard algorithm.

These are the written discussions of the paper "Bayesian measures of model complexity and fit" by D. Spiegelhalter et al. (2002), following the discussions given at the Annual Meeting of the Royal Statistical Society in Newcastle-upon-Tyne on September 3rd, 2013.

Increasing widespread use of educational technologies is producing vast amounts of data. Such data can be used to help advance our understanding of student learning and enable more intelligent, interactive, engaging, and effective education. In this article, we discuss the status and prospects of this new and powerful opportunity for data-driven development and optimization of educational technologies, focusing on intelligent tutoring systems We provide examples of use of a variety of techniques to develop or optimize the select, evaluate, suggest, and update functions of intelligent tutors, including probabilistic grammar learning, rule induction, Markov decision process, classification, and integrations of symbolic search and statistical inference.