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.

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).

Perceptual Bistability refers to the phenomenon of spontaneously switching between two or more interpretations of an image under continuous viewing. Although switching behavior is increasingly well characterized, the origins remain elusive. We propose that perceptual switching naturally arises from the brain's search for best interpretations while performing Bayesian inference. In particular, we propose that the brain explores a posterior distribution over image interpretations at a rapid time scale via a sampling-like process and updates its interpretation when a sampled interpretation is better than the discounted value of its current interpretation. We formalize the theory, explicitly derive switching rate distributions and discuss qualitative properties of the theory including the effect of changes in the posterior distribution on switching rates. Finally, predictions of the theory are shown to be consistent with measured changes in human switching dynamics to Necker cube stimuli induced by context.

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.

We introduce binary matrix factorization, a novel model for unsupervised matrix decomposition. The decomposition is learned by fitting a nonparametric Bayesian probabilistic model with binary latent variables to a matrix of dyadic data. Unlike bi-clustering models, which assign each row or column to a single cluster based on a categorical hidden feature, our binary feature model reflects the prior belief that items and attributes can be associated with more than one latent cluster at a time. We provide simple learning and inference rules for this new model and show how to extend it to an infinite model in which the number of features is not a priori fixed but is allowed to grow with the size of the data.

The additive clustering model is widely used to infer the features of a set of stimuli from their similarities, on the assumption that similarity is a weighted linear function of common features. This paper develops a fully Bayesian formulation of the additive clustering model, using methods from nonparametric Bayesian statistics to allow the number of features to vary. We use this to explore several approaches to parameter estimation, showing that the nonparametric Bayesian approach provides a straightforward way to obtain estimates of both the number of features used in producing similarity judgments and their importance.

Learning by imitation represents an important mechanism for rapid acquisition of new behaviors in humans and robots. A critical requirement for learning by imitation is the ability to handle uncertainty arising from the observation process as well as the imitator's own dynamics and interactions with the environment. In this paper, we present a new probabilistic method for inferring imitative actions that takes into account both the observations of the teacher as well as the imitator's dynamics. Our key contribution is a nonparametric learning method which generalizes to systems with very different dynamics. Rather than relying on a known forward model of the dynamics, our approach learns a nonparametric forward model via exploration. Leveraging advances in approximate inference in graphical models, we show how the learned forward model can be directly used to plan an imitating sequence. We provide experimental results for two systems: a biomechanical model of the human arm and a 25-degrees-of-freedom humanoid robot. We demonstrate that the proposed method can be used to learn appropriate motor inputs to the model arm which imitates the desired movements. A second set of results demonstrates dynamically stable full-body imitation of a human teacher by the humanoid robot.

Linear Gaussian State-Space Models are widely used and a Bayesian treatment of parameters is therefore of considerable interest. The approximate Variational Bayesian method applied to these models is an attractive approach, used successfully in applications ranging from acoustics to bioinformatics. The most challenging aspect of implementing the method is in performing inference on the hidden state sequence of the model. We show how to convert the inference problem so that standard Kalman Filtering/Smoothing recursions from the literature may be applied. This is in contrast to previously published approaches based on Belief Propagation. Our framework both simplifies and unifies the inference problem, so that future applications may be more easily developed. We demonstrate the elegance of the approach on Bayesian temporal ICA, with an application to finding independent dynamical processes underlying noisy EEG signals.

We present a computational Bayesian approach for Wiener diffusion models, which are prominent accounts of response time distributions in decision-making. We first develop a general closed-form analytic approximation to the response time distributions for one-dimensional diffusion processes, and derive the required Wiener diffusion as a special case. We use this result to undertake Bayesian modeling of benchmark data, using posterior sampling to draw inferences about the interesting psychological parameters. With the aid of the benchmark data, we show the Bayesian account has several advantages, including dealing naturally with the parameter variation needed to account for some key features of the data, and providing quantitative measures to guide decisions about model construction.

A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. The resulting algorithm also allows for the estimation of marginals. We compare our planar decomposition to the tree decomposition method of Wainwright et.