Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potentially much more accurate (Bayes-optimal) estimation of node values and node uncertainties from a limited number of simulation trials. We further propose propagating inference in the tree via fast analytic Gaussian approximation methods: this can make the overhead of Bayesian inference manageable in domains such as Go, while preserving high accuracy of expected-value estimates. We find substantial empirical outperformance of UCT in an idealized bandit-tree test environment, where we can obtain valuable insights by comparing with known ground truth. Additionally we rigorously prove on-policy and off-policy convergence of the proposed methods.

We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia.

Most conventional Reinforcement Learning (RL) algorithms aim to optimize decision-making rules in terms of the expected returns. However, especially for risk management purposes, other risk-sensitive criteria such as the value-at-risk or the expected shortfall are sometimes preferred in real applications. Here, we describe a parametric method for estimating density of the returns, which allows us to handle various criteria in a unified manner. We first extend the Bellman equation for the conditional expected return to cover a conditional probability density of the returns. Then we derive an extension of the TD-learning algorithm for estimating the return densities in an unknown environment. As test instances, several parametric density estimation algorithms are presented for the Gaussian, Laplace, and skewed Laplace distributions. We show that these algorithms lead to risk-sensitive as well as robust RL paradigms through numerical experiments.

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters by taking advantage of approximations to the conditional posteriors. We empirically demonstrate (1) the effectiveness of this approximation for improving convergence, (2) the benefits of the Dirichlet process model over alternative clustering techniques for ranked data, and (3) the applicability of the approach to exploring large realworld ranking datasets.

We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions such as the Bayesian algorithm and its approximation, the particle filters. However, these solutions can be very sensitive to model mismatches. In this paper, motivated by online learning, we introduce a new framework for tracking. We provide an efficient tracking algorithm for this framework. We provide experimental results comparing our algorithm to the Bayesian algorithm on simulated data. Our experiments show that when there are slight model mismatches, our algorithm outperforms the Bayesian algorithm.

Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable hierarchies to those with binary branching structure. This limitation, while computationally convenient, is often undesirable. In this paper we explore a Bayesian hierarchical clustering algorithm that can produce trees with arbitrary branching structure at each node, known as rose trees. We interpret these trees as mixtures over partitions of a data set, and use a computationally efficient, greedy agglomerative algorithm to find the rose trees which have high marginal likelihood given the data. Lastly, we perform experiments which demonstrate that rose trees are better models of data than the typical binary trees returned by other hierarchical clustering algorithms.

We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs work with both a topic covariance matrix and a document kernel matrix, learning GPTMs involves a novel component-solving a suitable Sylvester equation capturing both topic and document dependencies. The efficacy of GPTMs is demonstrated with experiments evaluating the quality of both topic modeling and embedding.

The Turing Test (TT) checks for human intelligence, rather than any putative general intelligence. It involves repeated interaction requiring learning in the form of adaption to the human conversation partner. It is a macro-level post-hoc test in contrast to the definition of a Turing Machine (TM), which is a prior micro-level definition. This raises the question of whether learning is just another computational process, i.e. can be implemented as a TM. Here we argue that learning or adaption is fundamentally different from computation, though it does involve processes that can be seen as computations. To illustrate this difference we compare (a) designing a TM and (b) learning a TM, defining them for the purpose of the argument. We show that there is a well-defined sequence of problems which are not effectively designable but are learnable, in the form of the bounded halting problem. Some characteristics of human intelligence are reviewed including it's: interactive nature, learning abilities, imitative tendencies, linguistic ability and context-dependency. A story that explains some of these is the Social Intelligence Hypothesis. If this is broadly correct, this points to the necessity of a considerable period of acculturation (social learning in context) if an artificial intelligence is to pass the TT. Whilst it is always possible to 'compile' the results of learning into a TM, this would not be a designed TM and would not be able to continually adapt (pass future TTs). We conclude three things, namely that: a purely "designed" TM will never pass the TT; that there is no such thing as a general intelligence since it necessary involves learning; and that learning/adaption and computation should be clearly distinguished.

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performance. We propose a generalization of the singular value decomposition (SVD) and principal components analysis (PCA) that is appropriate for massive data sets with structured variables or known two-way dependencies. By finding the best low rank approximation of the data with respect to a transposable quadratic norm, our decomposition, entitled the Generalized least squares Matrix Decomposition (GMD), directly accounts for structural relationships. As many variables in high-dimensional settings are often irrelevant or noisy, we also regularize our matrix decomposition by adding two-way penalties to encourage sparsity or smoothness. We develop fast computational algorithms using our methods to perform generalized PCA (GPCA), sparse GPCA, and functional GPCA on massive data sets. Through simulations and a whole brain functional MRI example we demonstrate the utility of our methodology for dimension reduction, signal recovery, and feature selection with high-dimensional structured data.