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.

We propose a new approach for Collaborative Filtering which is based on Boolean Matrix Factorisation (BMF) and Formal Concept Analysis. In a series of experiments on real data (Movielens dataset) we compare the approach with the SVD- and NMF-based algorithms in terms of Mean Average Error (MAE). One of the experimental consequences is that it is enough to have a binary-scaled rating data to obtain almost the same quality in terms of MAE by BMF than for the SVD-based algorithm in case of non-scaled data.

Artificial Immune System (AIS-MACA) a novel computational intelligence technique is can be used for strengthening the automated protein prediction system with more adaptability and incorporating more parallelism to the system. Most of the existing approaches are sequential which will classify the input into four major classes and these are designed for similar sequences. AIS-MACA is designed to identify ten classes from the sequences that share twilight zone similarity and identity with the training sequences with mixed and hybrid variations. This method also predicts three states (helix, strand, and coil) for the secondary structure. Our comprehensive design considers 10 feature selection methods and 4 classifiers to develop MACA (Multiple Attractor Cellular Automata) based classifiers that are build for each of the ten classes. We have tested the proposed classifier with twilight-zone and 1-high-similarity benchmark datasets with over three dozens of modern competing predictors shows that AIS-MACA provides the best overall accuracy that ranges between 80% and 89.8% depending on the dataset.

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.

Given a set $V$ of $n$ objects, an online ranking system outputs at each time step a full ranking of the set, observes a feedback of some form and suffers a loss. We study the setting in which the (adversarial) feedback is an element in $V$, and the loss is the position (0th, 1st, 2nd...) of the item in the outputted ranking. More generally, we study a setting in which the feedback is a subset $U$ of at most $k$ elements in $V$, and the loss is the sum of the positions of those elements. We present an algorithm of expected regret $O(n^{3/2}\sqrt{Tk})$ over a time horizon of $T$ steps with respect to the best single ranking in hindsight. This improves previous algorithms and analyses either by a factor of either $\Omega(\sqrt{k})$, a factor of $\Omega(\sqrt{\log n})$ or by improving running time from quadratic to $O(n\log n)$ per round. We also prove a matching lower bound. Our techniques also imply an improved regret bound for online rank aggregation over the Spearman correlation measure, and to other more complex ranking loss functions.

Given a subset S of vertices of an undirected graph G, the cut-improvement problem asks us to find a subset S that is similar to A but has smaller conductance. A very elegant algorithm for this problem has been given by Andersen and Lang [AL08] and requires solving a small number of single-commodity maximum flow computations over the whole graph G. In this paper, we introduce LocalImprove, the first cut-improvement algorithm that is local, i.e. that runs in time dependent on the size of the input set A rather than on the size of the entire graph. Moreover, LocalImprove achieves this local behaviour while essentially matching the same theoretical guarantee as the global algorithm of Andersen and Lang. The main application of LocalImprove is to the design of better local-graph-partitioning algorithms. All previously known local algorithms for graph partitioning are random-walk based and can only guarantee an output conductance of O(\sqrt{OPT}) when the target set has conductance OPT \in [0,1]. Very recently, Zhu, Lattanzi and Mirrokni [ZLM13] improved this to O(OPT / \sqrt{CONN}) where the internal connectivity parameter CONN \in [0,1] is defined as the reciprocal of the mixing time of the random walk over the graph induced by the target set. In this work, we show how to use LocalImprove to obtain a constant approximation O(OPT) as long as CONN/OPT = Omega(1). This yields the first flow-based algorithm. Moreover, its performance strictly outperforms the ones based on random walks and surprisingly matches that of the best known global algorithm, which is SDP-based, in this parameter regime [MMV12]. Finally, our results show that spectral methods are not the only viable approach to the construction of local graph partitioning algorithm and open door to the study of algorithms with even better approximation and locality guarantees.

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.