We compare three approaches to learning numerical parameters of Bayesian networks from continuous data streams: (1) the EM algorithm applied to all data, (2) the EM algorithm applied to data increments, and (3) the online EM algorithm. Our results show that learning from all data at each step, whenever feasible, leads to the highest parameter accuracy and model classification accuracy. When facing computational limitations, incremental learning approaches are a reasonable alternative. Of these, online EM is reasonably fast, and similar to the incremental EM algorithm in terms of accuracy. For small data sets, incremental EM seems to lead to better accuracy. When the data size gets large, online EM tends to be more accurate.

We study online learning under logarithmic loss with regular parametric models. Hedayati and Bartlett (2012b) showed that a Bayesian prediction strategy with Jeffreys prior and sequential normalized maximum likelihood (SNML) coincide and are optimal if and only if the latter is exchangeable, and if and only if the optimal strategy can be calculated without knowing the time horizon in advance. They put forward the question what families have exchangeable SNML strategies. This paper fully answers this open problem for one-dimensional exponential families. The exchangeability can happen only for three classes of natural exponential family distributions, namely the Gaussian, Gamma, and the Tweedie exponential family of order 3/2. Keywords: SNML Exchangeability, Exponential Family, Online Learning, Logarithmic Loss, Bayesian Strategy, Jeffreys Prior, Fisher Information1

A mean field variational Bayes approach to support vector machines (SVMs) using the latent variable representation on Polson & Scott (2012) is presented. This representation allows circumvention of many of the shortcomings associated with classical SVMs including automatic penalty parameter selection, the ability to handle dependent samples, missing data and variable selection. We demonstrate on simulated and real datasets that our approach is easily extendable to non-standard situations and outperforms the classical SVM approach whilst remaining computationally efficient.

Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the solution space. While this naturally leads to a standard MAP estimation framework, performance is compromised by unknown trade-off parameter settings, optimization heuristics, and convergence issues stemming from non-convexity and/or poor prior selections. To mitigate some of these problems, a number of authors have recently proposed substituting a variational Bayesian (VB) strategy that marginalizes over the high-dimensional image space leading to better estimates of the blur kernel. However, the underlying cost function now involves both integrals with no closed-form solution and complex, function-valued arguments, thus losing the transparency of MAP. Beyond standard Bayesian-inspired intuitions, it thus remains unclear by exactly what mechanism these methods are able to operate, rendering understanding, improvements and extensions more difficult. To elucidate these issues, we demonstrate that the VB methodology can be recast as an unconventional MAP problem with a very particular penalty/prior that couples the image, blur kernel, and noise level in a principled way. This unique penalty has a number of useful characteristics pertaining to relative concavity, local minima avoidance, and scale-invariance that allow us to rigorously explain the success of VB including its existing implementational heuristics and approximations. It also provides strict criteria for choosing the optimal image prior that, perhaps counter-intuitively, need not reflect the statistics of natural scenes. In so doing we challenge the prevailing notion of why VB is successful for blind deconvolution while providing a transparent platform for introducing enhancements.

We extend kernelized matrix factorization with a fully Bayesian treatment and with an ability to work with multiple side information sources expressed as different kernels. Kernel functions have been introduced to matrix factorization to integrate side information about the rows and columns (e.g., objects and users in recommender systems), which is necessary for making out-of-matrix (i.e., cold start) predictions. We discuss specifically bipartite graph inference, where the output matrix is binary, but extensions to more general matrices are straightforward. We extend the state of the art in two key aspects: (i) A fully conjugate probabilistic formulation of the kernelized matrix factorization problem enables an efficient variational approximation, whereas fully Bayesian treatments are not computationally feasible in the earlier approaches. (ii) Multiple side information sources are included, treated as different kernels in multiple kernel learning that additionally reveals which side information sources are informative. Our method outperforms alternatives in predicting drug-protein interactions on two data sets. We then show that our framework can also be used for solving multilabel learning problems by considering samples and labels as the two domains where matrix factorization operates on. Our algorithm obtains the lowest Hamming loss values on 10 out of 14 multilabel classification data sets compared to five state-of-the-art multilabel learning algorithms.

Probabilistic k-nearest neighbour (PKNN) classification has been introduced to improve the performance of original k-nearest neighbour (KNN) classification algorithm by explicitly modelling uncertainty in the classification of each feature vector. However, an issue common to both KNN and PKNN is to select the optimal number of neighbours, $k$. The contribution of this paper is to incorporate the uncertainty in $k$ into the decision making, and in so doing use Bayesian model averaging to provide improved classification. Indeed the problem of assessing the uncertainty in $k$ can be viewed as one of statistical model selection which is one of the most important technical issues in the statistics and machine learning domain. In this paper, a new functional approximation algorithm is proposed to reconstruct the density of the model (order) without relying on time consuming Monte Carlo simulations. In addition, this algorithm avoids cross validation by adopting Bayesian framework. The performance of this algorithm yielded very good performance on several real experimental datasets.

March 22, 2018 Abstract We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Particle Gibbs Sampling method, which alternately samples coalescent times conditioned on coalescent tree structures, and tree structures conditioned on coalescent times via the conditional Sequential Monte Carlo procedure. We implement our algorithm as a C package, and demonstrate its utility via a parameter estimation task in population genetics on both single-and multiple-locus data. The experiment results show that the proposed algorithm performs comparable to or better than several well-developed methods. 1 Introduction Data shows hierarchical structure in many domains. For example, computer vision problems often involve hierarchical representation of images [Lee et al., 2009]. In text mining, documents can be modeled as hierarchical generative processes [Blei et al., 2003, Teh et al., 2006]. Algorithms that can effectively deal with hierarchical structure play an important role in uncovering the intrinsic structures of data.

We introduce 'mixed LICORS', an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data. The new method is implemented in the publicly-available R package "LICORS" (http://cran.r-project.org/web/packages/LICORS/).

A popular approach for large scale data annotation tasks is crowdsourcing, wherein each data point is labeled by multiple noisy annotators. We consider the problem of inferring ground truth from noisy ordinal labels obtained from multiple annotators of varying and unknown expertise levels. Annotation models for ordinal data have been proposed mostly as extensions of their binary/categorical counterparts and have received little attention in the crowdsourcing literature. We propose a new model for crowdsourced ordinal data that accounts for instance difficulty as well as annotator expertise, and derive a variational Bayesian inference algorithm for parameter estimation. We analyze the ordinal extensions of several state-of-the-art annotator models for binary/categorical labels and evaluate the performance of all the models on two real world datasets containing ordinal query-URL relevance scores, collected through Amazon's Mechanical Turk. Our results indicate that the proposed model performs better or as well as existing state-of-the-art methods and is more resistant to'spammy' annotators (i.e., annotators who assign labels randomly without actually looking at the instance) than popular baselines such as mean, median, and majority vote which do not account for annotator expertise. Part of the work was done while at Yandex Labs.

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for probabilistic logic programs. Several such tasks such as computing the marginals given evidence and learning from (partial) interpretations have not really been addressed for probabilistic logic programs before. The first contribution of this paper is a suite of efficient algorithms for various inference tasks. It is based on a conversion of the program and the queries and evidence to a weighted Boolean formula. This allows us to reduce the inference tasks to well-studied tasks such as weighted model counting, which can be solved using state-of-the-art methods known from the graphical model and knowledge compilation literature. The second contribution is an algorithm for parameter estimation in the learning from interpretations setting. The algorithm employs Expectation Maximization, and is built on top of the developed inference algorithms. The proposed approach is experimentally evaluated. The results show that the inference algorithms improve upon the state-of-the-art in probabilistic logic programming and that it is indeed possible to learn the parameters of a probabilistic logic program from interpretations.