With ever-increasing available data, predicting individuals' preferences and helping them locate the most relevant information has become a pressing need. Understanding and predicting preferences is also important from a fundamental point of view, as part of what has been called a "new" computational social science. Here, we propose a novel approach based on stochastic block models, which have been developed by sociologists as plausible models of complex networks of social interactions. Our model is in the spirit of predicting individuals' preferences based on the preferences of others but, rather than fitting a particular model, we rely on a Bayesian approach that samples over the ensemble of all possible models. We show that our approach is considerably more accurate than leading recommender algorithms, with major relative improvements between 38% and 99% over industry-level algorithms. Besides, our approach sheds light on decision-making processes by identifying groups of individuals that have consistently similar preferences, and enabling the analysis of the characteristics of those groups.

For such Gaussian graphical models (GGMs), it is usually assumed that a given variable can bepredicted by a small numberof other variables. This assumption implies that the precision matrix is sparse. Therefore estimating Gaussian graphical model can be reduced to the problem of estimating a sparse precision matrix. One approach to sparse precision matrix estimation is covariance selection or neighborhood selection (Dempster, 1972; Meinshausen & Bühlmann, 2006), which tries to estimate each row (or column) of the precision matrix by predicting the corresponding variable using a sparse linear combination of other variables. An alternative formulation is maximum-likelihood estimation method that directly estimate the full precision matrix.

Legislative behavior centers around the votes made by lawmakers. These votes are captured in roll call data, a matrix with lawmakers in the rows and proposed legislation in the columns. We illustrate a sample of roll call votes for the United States Senate in Figure 1. The seminal work of Poole and Rosenthal (1985) introduced the ideal point model, using roll call data to infer the latent political positions of the lawmakers. The ideal point model is a latent factor model of binary data and an application of item-response theory (Lord 1980) to roll call data. It gives each lawmaker a latent political position along a single dimension and then uses these points (called the ideal points) in a model of the votes.

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive results, albeit with some loss of accuracy. Bayesian statistics have been widely used in the development of probability models in machine learning in recent years and these methods have many advantages, including their abilities to avoid overfitting. In this paper, we develop two Bayesian mixture models with the Dirichlet distribution prior and the Dirichlet process (DP) prior to improve the previous non-Bayesian mixture model developed for transaction dataset mining. We implement the inference of both mixture models using two methods: a collapsed Gibbs sampling scheme and a variational approximation algorithm. Experiments in several benchmark problems have shown that both mixture models achieve better performance than a non-Bayesian mixture model. The variational algorithm is the faster of the two approaches while the Gibbs sampling method achieves a more accurate results. The Dirichlet process mixture model can automatically grow to a proper complexity for a better approximation. Once the model is built, it can be very fast to query and run analysis on (typically 10 times faster than Eclat, as we will show in the experiment section). However, these approaches also show that mixture models underestimate the probabilities of frequent itemsets. Consequently, these models have a higher sensitivity but a lower specificity.

We process a large corpus of game records of the board game of Go and propose a way of extracting summary information on played moves. We then apply several basic data-mining methods on the summary information to identify the most differentiating features within the summary information, and discuss their correspondence with traditional Go knowledge. We show statistically significant mappings of the features to player attributes such as playing strength or informally perceived "playing style" (e.g. territoriality or aggressivity), describe accurate classifiers for these attributes, and propose applications including seeding real-work ranks of internet players, aiding in Go study and tuning of Go-playing programs, or contribution to Go-theoretical discussion on the scope of "playing style".

Super-resolution methods form high-resolution images from low-resolution images. In this paper, we develop a new Bayesian nonparametric model for super-resolution. Our method uses a beta-Bernoulli process to learn a set of recurring visual patterns, called dictionary elements, from the data. Because it is nonparametric, the number of elements found is also determined from the data. We test the results on both benchmark and natural images, comparing with several other models from the research literature. We perform large-scale human evaluation experiments to assess the visual quality of the results. In a first implementation, we use Gibbs sampling to approximate the posterior. However, this algorithm is not feasible for large-scale data. To circumvent this, we then develop an online variational Bayes (VB) algorithm. This algorithm finds high quality dictionaries in a fraction of the time needed by the Gibbs sampler.

Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and equispaced inputs (both enable O(N) runtime). However, these GP advances have not been extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests novel extensions of structured GPs to multidimensional inputs. We present new methods for additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. To achieve optimal accuracy-complexity tradeoff, we extend this model with a novel variant of projection pursuit regression. Our primary result -- projection pursuit Gaussian Process Regression -- shows orders of magnitude speedup while preserving high accuracy. The natural second and third steps include non-Gaussian observations and higher dimensional equispaced grid methods. We introduce novel techniques to address both of these necessary directions. We thoroughly illustrate the power of these three advances on several datasets, achieving close performance to the naive Full GP at orders of magnitude less cost.

For the past few decades, man has been trying to create an intelligent computer which can talk and respond like he can. The task of creating a system that can talk like a human being is the primary objective of Automatic Speech Recognition. Various Speech Recognition techniques have been developed in theory and have been applied in practice. This paper discusses the problems that have been encountered in developing Speech Recognition, the techniques that have been applied to automate the task, and a representation of the core problems of present day Speech Recognition by using Fuzzy Mathematics.

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.

Latent feature models are widely used to decompose data into a small number of components. Bayesian nonparametric variants of these models, which use the Indian buffet process (IBP) as a prior over latent features, allow the number of features to be determined from the data. We present a generalization of the IBP, the distance dependent Indian buffet process (dd-IBP), for modeling non-exchangeable data. It relies on distances defined between data points, biasing nearby data to share more features. The choice of distance measure allows for many kinds of dependencies, including temporal and spatial. Further, the original IBP is a special case of the dd-IBP. In this paper, we develop the dd-IBP and theoretically characterize its feature-sharing properties. We derive a Markov chain Monte Carlo sampler for a linear Gaussian model with a dd-IBP prior and study its performance on several non-exchangeable data sets.