A statistical model for determining whether a pair of documents, a known and a questioned, were written by the same individual is proposed. The model has the following four components: (i) discriminating elements, e.g., global features and characters, are extracted from each document; (ii) differences between corresponding elements from each document are computed; (iii) using conditional probability estimates of each difference, the log-likelihood ratio (LLR) is computed for the hypotheses that the documents were written by the same or different writers; the conditional probability estimates themselves are determined from labeled samples using either Gaussian or gamma estimates for the differences assuming their statistical independence; and (iv) distributions of the LLRs for same and different writer LLRs are analyzed to calibrate the strength of evidence into a standard nine-point scale used by questioned document examiners. The model is illustrated with experimental results for a specific set of discriminating elements.

MOTIVATION: We have used state-space models (SSMs) to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T cell activation. SSMs are a class of dynamic Bayesian networks in which the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be directly measured in a gene expression profiling experiment, for example: genes that have not been included in the microarray, levels of regulatory proteins, the effects of mRNA and protein degradation, etc. RESULTS: We have approached the problem of inferring the model structure of these state-space models using both classical and Bayesian methods. In our previous work, a bootstrap procedure was used to derive classical confidence intervals for parameters representing 'gene-gene' interactions over time. In this article, variational approximations are used to perform the analogous model selection task in the Bayesian context. Certain interactions are present in both the classical and the Bayesian analyses of these regulatory networks. The resulting models place JunB and JunD at the centre of the mechanisms that control apoptosis and proliferation. These mechanisms are key for clonal expansion and for controlling the long term behavior (e.g. programmed cell death) of these cells. AVAILABILITY: Supplementary data is available at http://public.kgi.edu/wild/index.htm and Matlab source code for variational Bayesian learning of SSMs is available at http://www.cse.ebuffalo.edu/faculty/mbeal/software.html.

We propose the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generaliza- tion to new groups. Such grouped clustering problems occur often in practice, e.g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

We describe a Markov chain method for sampling from the distribution of the hidden state sequence in a non-linear dynamical system, given a sequence of observations. This method updates all states in the sequence simultaneously using an embedded Hidden Markov Model (HMM). An update begins with the creation of “pools” of candidate states at each time. We then define an embedded HMM whose states are indexes within these pools. Using a forward-backward dynamic programming algo- rithm, we can efficiently choose a state sequence with the appropriate probabilities from the exponentially large number of state sequences that pass through states in these pools. We illustrate the method in a simple one-dimensional example, and in an example showing how an embed- ded HMM can be used to in effect discretize the state space without any discretization error. We also compare the embedded HMM to a particle smoother on a more substantial problem of inferring human motion from 2D traces of markers.

We present a new approach to modeling and processing multimedia data. This approach is based on graphical models that combine audio and video variables. We demonstrate it by developing a new algorithm for tracking a moving object in a cluttered, noisy scene using two microphones and a camera. Our model uses unobserved variables to describe the data in terms of the process that generates them. It is therefore able to capture and exploit the statistical structure of the audio and video data separately, as well as their mutual dependencies. Model parameters are learned from data via an EM algorithm, and automatic calibration is performed as part of this procedure. Tracking is done by Bayesian inference of the object location from data. We demonstrate successful performance on multimedia clips captured in real world scenarios using off-the-shelf equipment.

We present a self-calibrating algorithm for audio-visual tracking using two microphones and a camera. The algorithm uses a parametrized statistical model which combines simple models of video and audio. Using unobserved variables, the model describes the process that generates the observed data. Hence, it is able to capture and exploit the statistical structure of the audio and video data, as well as their mutual dependencies, The model parameters are estimated by the EM algorithm; object templates are learned and automatic calibration is performed as part of this procedure. Tracking is done by Bayesian inference of the object location using the model. Successful performance is demonstrated on real multimedia clips.

We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected num- ber of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infinite— consider, for example, symbols being possible words appearing in En- glish text.

Variational approximations are becoming a widespread tool for Bayesian learning of graphical models. We provide some theoret(cid:173) ical results for the variational updates in a very general family of conjugate-exponential graphical models. We show how the belief propagation and the junction tree algorithms can be used in the inference step of variational Bayesian learning. Applying these re(cid:173) sults to the Bayesian analysis of linear-Gaussian state-space models we obtain a learning procedure that exploits the Kalman smooth(cid:173) ing propagation, while integrating over all model parameters. We demonstrate how this can be used to infer the hidden state dimen(cid:173) sionality of the state-space model in a variety of synthetic problems and one real high-dimensional data set.