Nested sampling is a new Monte Carlo method by Skilling [1] intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.

The observed physiological dynamics of an infant receiving intensive care are affected by many possible factors, including interventions to the baby, the operation of the monitoring equipment and the state of health. The Factorial Switching Kalman Filter can be used to infer the presence of such factors from a sequence of observations, and to estimate the true values where these observations have been corrupted. We apply this model to clinical time series data and show it to be effective in identifying a number of artifactual and physiological patterns.

Long-distance language modeling is important not only in speech recognition and machine translation, but also in high-dimensional discrete sequence modeling in general. However, the problem of context length has almost been neglected so far and a naïve bag-of-words history has been employed in natural language processing. In contrast, in this paper we view topic shifts within a text as a latent stochastic process to give an explicit probabilistic generative model that has partial exchangeability. We propose an online inference algorithm using particle filters to recognize topic shifts to employ the most appropriate length of context automatically. Experiments on the BNC corpus showed consistent improvement over previous methods involving no chronological order.

We measure the ability of human observers to predict the next datum in a sequence that is generated by a simple statistical process undergoing change at random points in time. Accurate performance in this task requires the identification of changepoints. We assess individual differences between observers both empirically, and using two kinds of models: a Bayesian approach for change detection and a family of cognitively plausible fast and frugal models. Some individuals detect too many changes and hence perform sub-optimally due to excess variability. Other individuals do not detect enough changes, and perform sub-optimally because they fail to notice short-term temporal trends.

This paper presents a new filter for online data association problems in high-dimensional spaces. The key innovation is a representation of the data association posterior in information form, in which the "proximity" of objects and tracks are expressed by numerical links. Updating these links requires linear time, compared to exponential time required for computing the exact posterior probabilities. The paper derives the algorithm formally and provides comparative results using data obtained by a real-world camera array and by a large-scale sensor network simulation.

Desirable Characteristics of a model include good representation of objects, fast and efficient learning algorithms that require as little supervised information as possible.

This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of Gaussian process regression.

We describe a hierarchy of motif-based kernels for multiple alignments of biological sequences, particularly suitable to process regulatory regions ofgenes. The kernels incorporate progressively more information, with the most complex kernel accounting for a multiple alignment of orthologous regions, the phylogenetic tree relating the species, and the prior knowledge that relevant sequence patterns occur in conserved motif blocks.These kernels can be used in the presence of a library of known transcription factor binding sites, or de novo by iterating over all k-mers of a given length. In the latter mode, a discriminative classifier builtfrom such a kernel not only recognizes a given class of promoter regions,but as a side effect simultaneously identifies a collection of relevant, discriminative sequence motifs. We demonstrate the utility of the motif-based multiple alignment kernels by using a collection ofaligned promoter regions from five yeast species to recognize classes of cell-cycle regulated genes.

The classical Bayes rule computes the posterior model probability from the prior probability and the data likelihood. We generalize this rule to the case when the prior is a density matrix (symmetric positive definite and trace one) and the data likelihood a covariance matrix. The classical Bayes rule is retained as the special case when the matrices are diagonal. In the classical setting, the calculation of the probability of the data is an expected likelihood, where the expectation is over the prior distribution. In the generalized setting, this is replaced by an expected variance calculation where the variance is computed along the eigenvectors of the prior density matrix and the expectation is over the eigenvalues of the density matrix (which form a probability vector).The variances along any direction is determined by the covariance matrix. Curiously enough this expected variance calculationis a quantum measurement where the covariance matrix specifies the instrument and the prior density matrix the mixture state of the particle. We motivate both the classical and the generalized Bayes rule with a minimum relative entropy principle, wherethe Kullbach-Leibler version gives the classical Bayes rule and Umegaki's quantum relative entropy the new Bayes rule for density matrices.

We present a family of approximation techniques for probabilistic graphical models,based on the use of graphical preconditioners developed in the scientific computing literature. Our framework yields rigorous upper and lower bounds on event probabilities and the log partition function of undirected graphical models, using non-iterative procedures that have low time complexity. As in mean field approaches, the approximations are built upon tractable subgraphs; however, we recast the problem of optimizing thetractable distribution parameters and approximate inference in terms of the well-studied linear systems problem of obtaining a good matrix preconditioner. Experiments are presented that compare the new approximation schemes to variational methods.