Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

Phrase-based statistical language generation using graphical models and active learning

Most previous work on trainable language generation has focused on two paradigms: (a) using a statistical model to rank a set of generated utterances, or (b) using statistics to inform the generation decision process. Both approaches rely on the existence of a handcrafted generator, which limits their scalability to new domains. This paper presents BAGEL, a statistical language generator which uses dynamic Bayesian networks to learn from semantically-aligned data produced by 42 untrained annotators. A human evaluation shows that BAGEL can generate natural and informative utterances from unseen inputs in the information presentation domain. Additionally, generation performance on sparse datasets is improved significantly by using certainty-based active learning, yielding ratings close to the human gold standard with a fraction of the data. © 2010 Association for Computational Linguistics.

Reinforcement learning with reference tracking control in continuous state spaces

The contribution described in this paper is an algorithm for learning nonlinear, reference tracking, control policies given no prior knowledge of the dynamical system and limited interaction with the system through the learning process. Concepts from the field of reinforcement learning, Bayesian statistics and classical control have been brought together in the formulation of this algorithm which can be viewed as a form of indirect self tuning regulator. On the task of reference tracking using a simulated inverted pendulum it was shown to yield generally improved performance on the best controller derived from the standard linear quadratic method using only 30 s of total interaction with the system. Finally, the algorithm was shown to work on the simulated double pendulum proving its ability to solve nontrivial control tasks. © 2011 IEEE.

Machine learning for predictive condensed-phase simulation

We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using accurate, correlated quantum chemistry, and predict energies and forces in molecular aggregates ranging from clusters to solid and liquid phases. The widely used electronic-structure methods based on density-functional theory (DFT) give poor accuracy for molecular materials like water, and we show how our techniques can be used to generate systematically improvable corrections to DFT. The resulting corrected DFT scheme gives remarkably accurate predictions for the relative energies of small water clusters and of different ice structures, and greatly improves the description of the structure and dynamics of liquid water.

Determinantal Clustering Processes - A Nonparametric Bayesian Approach to Kernel Based Semi-Supervised Clustering

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input. Dirichlet process mixture models are appealing as they can infer the number of clusters from the data. However, these models do not deal with high dimensional data well and can encounter difficulties in inference. We present a novel nonparameteric Bayesian kernel based method to cluster data points without the need to prespecify the number of clusters or to model complicated densities from which data points are assumed to be generated from. The key insight is to use determinants of submatrices of a kernel matrix as a measure of how close together a set of points are. We explore some theoretical properties of the model and derive a natural Gibbs based algorithm with MCMC hyperparameter learning. The model is implemented on a variety of synthetic and real world data sets.

On-line policy optimisation of Bayesian spoken dialogue systems via human interaction

A partially observable Markov decision process has been proposed as a dialogue model that enables robustness to speech recognition errors and automatic policy optimisation using reinforcement learning (RL). However, conventional RL algorithms require a very large number of dialogues, necessitating a user simulator. Recently, Gaussian processes have been shown to substantially speed up the optimisation, making it possible to learn directly from interaction with human users. However, early studies have been limited to very low dimensional spaces and the learning has exhibited convergence problems. Here we investigate learning from human interaction using the Bayesian Update of Dialogue State system. This dynamic Bayesian network based system has an optimisation space covering more than one hundred features, allowing a wide range of behaviours to be learned. Using an improved policy model and a more robust reward function, we show that stable learning can be achieved that significantly outperforms a simulator trained policy. © 2013 IEEE.

On the Dirichlet Prior and Bayesian Regularization

A common objective in learning a model from data is to recover its network structure, while the model parameters are of minor interest. For example, we may wish to recover regulatory networks from high-throughput data sources. In this paper we examine how Bayesian regularization using a Dirichlet prior over the model parameters affects the learned model structure in a domain with discrete variables. Surprisingly, a weak prior in the sense of smaller equivalent sample size leads to a strong regularization of the model structure (sparse graph) given a sufficiently large data set. In particular, the empty graph is obtained in the limit of a vanishing strength of prior belief. This is diametrically opposite to what one may expect in this limit, namely the complete graph from an (unregularized) maximum likelihood estimate. Since the prior affects the parameters as expected, the prior strength balances a "trade-off" between regularizing the parameters or the structure of the model. We demonstrate the benefits of optimizing this trade-off in the sense of predictive accuracy.

Learning Classes Correlated to a Hierarchy

Trees are a common way of organizing large amounts of information by placing items with similar characteristics near one another in the tree. We introduce a classification problem where a given tree structure gives us information on the best way to label nearby elements. We suggest there are many practical problems that fall under this domain. We propose a way to map the classification problem onto a standard Bayesian inference problem. We also give a fast, specialized inference algorithm that incrementally updates relevant probabilities. We apply this algorithm to web-classification problems and show that our algorithm empirically works well.

A Framework for the Scoring of Operators on the Search Space of Equivalence Classes of Bayesian Network Structures

R. Daly and Q. Shen. A Framework for the Scoring of Operators on the Search Space of Equivalence Classes of Bayesian Network Structures. Proceedings of the 2005 UK Workshop on Computational Intelligence, pages 67-74.

Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. The model structure setup and parameter learning are done using a variational Bayesian approach, which enables automatic Bayesian model structure selection, hence solving the problem of over-fitting. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Spatio-temporal Bayesian network models with latent variables for revealing trophic dynamics and functional networks in fisheries ecology

Ecosystems consist of complex dynamic interactions among species and the environment, the understanding of which has implications for predicting the environmental response to changes in climate and biodiversity. However, with the recent adoption of more explorative tools, like Bayesian networks, in predictive ecology, few assumptions can be made about the data and complex, spatially varying interactions can be recovered from collected field data. In this study, we compare Bayesian network modelling approaches accounting for latent effects to reveal species dynamics for 7 geographically and temporally varied areas within the North Sea. We also apply structure learning techniques to identify functional relationships such as prey–predator between trophic groups of species that vary across space and time. We examine if the use of a general hidden variable can reflect overall changes in the trophic dynamics of each spatial system and whether the inclusion of a specific hidden variable can model unmeasured group of species. The general hidden variable appears to capture changes in the variance of different groups of species biomass. Models that include both general and specific hidden variables resulted in identifying similarity with the underlying food web dynamics and modelling spatial unmeasured effect. We predict the biomass of the trophic groups and find that predictive accuracy varies with the models' features and across the different spatial areas thus proposing a model that allows for spatial autocorrelation and two hidden variables. Our proposed model was able to produce novel insights on this ecosystem's dynamics and ecological interactions mainly because we account for the heterogeneous nature of the driving factors within each area and their changes over time. Our findings demonstrate that accounting for additional sources of variation, by combining structure learning from data and experts' knowledge in the model architecture, has the potential for gaining deeper insights into the structure and stability of ecosystems. Finally, we were able to discover meaningful functional networks that were spatially and temporally differentiated with the particular mechanisms varying from trophic associations through interactions with climate and commercial fisheries.

Computational learning of the conditional phase-type (C-Ph) distribution: Learning C-Ph distributions

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a dataset as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output.The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.

Hierarchical Bayesian models in ecology: Reconstructing species interaction networks from non-homogeneous species abundance data

The relationships among organisms and their surroundings can be of immense complexity. To describe and understand an ecosystem as a tangled bank, multiple ways of interaction and their effects have to be considered, such as predation, competition, mutualism and facilitation. Understanding the resulting interaction networks is a challenge in changing environments, e.g. to predict knock-on effects of invasive species and to understand how climate change impacts biodiversity. The elucidation of complex ecological systems with their interactions will benefit enormously from the development of new machine learning tools that aim to infer the structure of interaction networks from field data. In the present study, we propose a novel Bayesian regression and multiple changepoint model (BRAM) for reconstructing species interaction networks from observed species distributions. The model has been devised to allow robust inference in the presence of spatial autocorrelation and distributional heterogeneity. We have evaluated the model on simulated data that combines a trophic niche model with a stochastic population model on a 2-dimensional lattice, and we have compared the performance of our model with L1-penalized sparse regression (LASSO) and non-linear Bayesian networks with the BDe scoring scheme. In addition, we have applied our method to plant ground coverage data from the western shore of the Outer Hebrides with the objective to infer the ecological interactions. (C) 2012 Elsevier B.V. All rights reserved.