In supervised learning there is a typical presumption that the training and test points are taken from the same distribution. In practice this assumption is commonly violated. The situations where the training and test data are from different distributions is called covariate shift. Recent work has examined techniques for dealing with covariate shift in terms of minimisation of generalisation error. As yet the literature lacks a Bayesian generative perspective on this problem. This paper tackles this issue for regression models. Recent work on covariate shift can be understood in terms of mixture regression. Using this view, we obtain a general approach to regression under covariate shift, which reproduces previous work as a special case. The main advantages of this new formulation over previous models for covariate shift are that we no longer need to presume the test and training densities are known, the regression and density estimation are combined into a single procedure, and previous methods are reproduced as special cases of this procedure, shedding light on the implicit assumptions the methods are making.

Scoring structures of undirected graphical models by means of evaluating the marginal likelihood is very hard. The main reason is the presence of the partition function which is intractable to evaluate, let alone integrate over. We propose to approximate the marginal likelihood by employing two levels of approximation: we assume normality of the posterior (the Laplace approximation) and approximate all remaining intractable quantities using belief propagation and the linear response approximation.

We introduce Coherent Point Drift (CPD), a novel probabilistic method for nonrigid registration of point sets. The registration is treated as a Maximum Likelihood (ML) estimation problem with motion coherence constraint over the velocity field such that one point set moves coherently to align with the second set. We formulate the motion coherence constraint and derive a solution of regularized ML estimation through the variational approach, which leads to an elegant kernel form. We also derive the EM algorithm for the penalized ML optimization with deterministic annealing. The CPD method simultaneously finds both the nonrigid transformation and the correspondence between two point sets without making any prior assumption of the transformation model except that of motion coherence. This method can estimate complex nonlinear nonrigid transformations, and is shown to be accurate on 2D and 3D examples and robust in the presence of outliers and missing points.

This paper introduces adaptor grammars, a class of probabilistic models of language that generalize probabilistic context-free grammars (PCFGs). Adaptor grammars augment the probabilistic rules of PCFGs with "adaptors" that can induce dependencies among successive uses. With a particular choice of adaptor, based on the Pitman-Yor process, nonparametric Bayesian models of language using Dirichlet processes and hierarchical Dirichlet processes can be written as simple grammars. We present a general-purpose inference algorithm for adaptor grammars, making it easy to define and use such models, and illustrate how several existing nonparametric Bayesian models can be expressed within this framework.

We introduce a method for approximate smoothed inference in a class of switching linear dynamical systems, based on a novel form of Gaussian Sum smoother. This class includes the switching Kalman Filter and the more general case of switch transitions dependent on the continuous latent state. The method improves on the standard Kim smoothing approach by dispensing with one of the key approximations, thus making fuller use of the available future information. Whilst the only central assumption required is projection to a mixture of Gaussians, we show that an additional conditional independence assumption results in a simpler but stable and accurate alternative. Unlike the alternative unstable Expectation Propagation procedure, our method consists only of a single forward and backward pass and is reminiscent of the standard smoothing'correction' recursions in the simpler linear dynamical system. The algorithm performs well on both toy experiments and in a large scale application to noise robust speech recognition.

The study of point cloud data sampled from a stratification, a collection of manifolds with possible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality and density of such structures. The framework is based on a maximum likelihood estimation of a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

Data sets involving multiple groups with shared characteristics frequently arise in practice. In this paper we extend hierarchical Dirichlet processes to model such data. Each group is assumed to be generated from a template mixture model with group level variability in both the mixing proportions and the component parameters. Variabilities in mixing proportions across groups are handled using hierarchical Dirichlet processes, also allowing for automatic determination of the number of components. In addition, each group is allowed to have its own component parameters coming from a prior described by a template mixture model. This group-level variability in the component parameters is handled using a random effects model. We present a Markov Chain Monte Carlo (MCMC) sampling algorithm to estimate model parameters and demonstrate the method by applying it to the problem of modeling spatial brain activation patterns across multiple images collected via functional magnetic resonance imaging (fMRI).

Techniques such as probabilistic topic models and latent-semantic indexing have been shown to be broadly useful at automatically extracting the topical or semantic content of documents, or more generally for dimension-reduction of sparse count data. These types of models and algorithms can be viewed as generating an abstraction from the words in a document to a lower-dimensional latent variable representation that captures what the document is generally about beyond the specific words it contains. In this paper we propose a new probabilistic model that tempers this approach by representing each document as a combination of (a) a background distribution over common words, (b) a mixture distribution over general topics, and (c) a distribution over words that are treated as being specific to that document. We illustrate how this model can be used for information retrieval by matching documents both at a general topic level and at a specific word level, providing an advantage over techniques that only match documents at a general level (such as topic models or latent-sematic indexing) or that only match documents at the specific word level (such as TF-IDF).

Everyday inductive reasoning draws on many kinds of knowledge, including knowledge about relationships between properties and knowledge about relationships between objects. Previous accounts of inductive reasoning generally focus on just one kind of knowledge: models of causal reasoning often focus on relationships between properties, and models of similarity-based reasoning often focus on similarity relationships between objects. We present a Bayesian model of inductive reasoning that incorporates both kinds of knowledge, and show that it accounts well for human inferences about the properties of biological species.

We present a robust distributed algorithm for approximate probabilistic inference in dynamical systems, such as sensor networks and teams of mobile robots. Using assumed density filtering, the network nodes maintain a tractable representation of the belief state in a distributed fashion. At each time step, the nodes coordinate to condition this distribution on the observations made throughout the network, and to advance this estimate to the next time step. In addition, we identify a significant challenge for probabilistic inference in dynamical systems: message losses or network partitions can cause nodes to have inconsistent beliefs about the current state of the system. We address this problem by developing distributed algorithms that guarantee that nodes will reach an informative consistent distribution when communication is reestablished. We present a suite of experimental results on real-world sensor data for two real sensor network deployments: one with 25 cameras and another with 54 temperature sensors.