Motivated by stochastic systems in which observed evidence and conditional dependencies betweenstates of the network change over time, and certain quantities of interest (marginal distributions, likelihood estimates etc.) must be updated, we study the problem of adaptive inference in tree-structured Bayesian networks. We describe an algorithm for adaptive inference that handles a broad range of changes to the network and is able to maintain marginal distributions, MAP estimates, and data likelihoods in all expected logarithmic time. We give an implementation of our algorithm and provide experiments that show that the algorithm can yield up to two orders of magnitude speedups on answering queries and responding to dynamic changesover the sum-product algorithm.

When training and test samples follow different input distributions (i.e., the situation called \emph{covariate shift}), the maximum likelihood estimator is known to lose its consistency. For regaining consistency, the log-likelihood terms need to be weighted according to the \emph{importance} (i.e., the ratio of test and training input densities). Thus, accurately estimating the importance is one of the key tasks in covariate shift adaptation. A naive approach is to first estimate training and test input densities and then estimate the importance by the ratio of the density estimates. However, since density estimation is a hard problem, this approach tends to perform poorly especially in high dimensional cases. In this paper, we propose a direct importance estimation method that does not require the input density estimates. Our method is equipped with a natural model selection procedure so tuning parameters such as the kernel width can be objectively optimized. This is an advantage over a recently developed method of direct importance estimation. Simulations illustrate the usefulness of our approach.

We propose an extended probabilistic model for human perception. We argue that in many circumstances, human observers simultaneously evaluate sensory evidence under different hypotheses regarding the underlying physical process that might have generated the sensory information. Within this context, inference can be optimal if the observer weighs each hypothesis according to the correct belief in that hypothesis. But if the observer commits to a particular hypothesis, the belief in that hypothesis is converted into subjective certainty, and subsequent perceptual behavior is suboptimal, conditioned only on the chosen hypothesis. We demonstrate that this framework can explain psychophysical data of a recently reported decision-estimation experiment. The model well accounts for the data, predicting the same estimation bias as a consequence of the preceding decision step. The power of the framework is that it has no free parameters except the degree of the observer's uncertainty about its internal sensory representation. All other parameters are defined by the particular experiment which allows us to make quantitative predictions of human perception to two modifications of the original experiment.

We give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concave upper bound on the entropy, this gives a new variational inference algorithm for probabilistic inference in discrete Markov Random Fields (MRFs). Valid constraints on the marginal polytope are derived through a series of projections onto the cut polytope. As a result, we obtain tighter upper bounds on the log-partition function. We also show empirically that the approximations of the marginals are significantly more accurate when using the tighter outer bounds. Finally, we demonstrate the advantage of the new constraints for finding the MAP assignment in protein structure prediction.

The resulting model is able to generalize considerably better for users with very few ratings.

This paper describes a new model for human visual classification that enables the recovery of image features that explain human subjects' performance on different visual classification tasks. Unlike previous methods, this algorithm does not model their performance with a single linear classifier operating on raw image pixels. Instead, it models classification as the combination of multiple feature detectors. This approach extracts more information about human visual classification than has been previously possible with other methods and provides a foundation for further exploration.

Web servers on the Internet need to maintain high reliability, but the cause of intermittent failures of web transactions is non-obvious. We use Bayesian inference to diagnose problems with web services. This diagnosis problem is far larger than any previously attempted: it requires inference of 10^4 possible faults from 10^5 observations. Further, such inference must be performed in less than a second. Inference can be done at this speed by combining a variational approximation, a mean-field approximation, and the use of stochastic gradient descent to optimize a variational cost function. We use this fast inference to diagnose a time series of anomalous HTTP requests taken from a real web service. The inference is fast enough to analyze network logs with billions of entries in a matter of hours.

We demonstrate that log-linear grammars with latent variables can be practically trained using discriminative methods. Central to efficient discriminative training is a hierarchical pruning procedure which allows feature expectations to be efficiently approximatedin a gradient-based procedure.

We investigate the problem of learning a widely-used latent-variable model - the Latent Dirichlet Allocation (LDA) or "topic" model - using distributed computation, whereeach of

We propose a Gaussian process (GP) framework for robust inference in which a GP prior on the mixing weights of a two-component noise model augments the standard process over latent function values. This approach is a generalization of the mixture likelihood used in traditional robust GP regression, and a specialization of the GP mixture models suggested by Tresp (2000) and Rasmussen and Ghahramani (2002). The value of this restriction is in its tractable expectation propagation updates, which allow for faster inference and model selection, and better convergence than the standard mixture. An additional benefit over the latter method lies in our ability to incorporate knowledge of the noise domain to influence predictions, and to recover with the predictive distribution information about the outlier distribution via the gating process. The model has asymptotic complexity equal to that of conventional robust methods, but yields more confident predictions on benchmark problems than classical heavy-tailed models and exhibits improved stability for data with clustered corruptions, for which they fail altogether. We show further how our approach can be used without adjustment for more smoothly heteroscedastic data, and suggest how it could be extended to more general noise models. We also address similarities with the work of Goldberg et al. (1998), and the more recent contributions of Tresp, and Rasmussen and Ghahramani.