Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent aftercurrent. This model is a biophysically plausible alternative to models with Poisson (memory-less) spiking, and has been shown to effectively reproduce various spiking statistics of neurons in vivo. However, the problem of estimating the model from extracellular spike train data has not been examined in depth. We formulate the problem in terms of maximum likelihood estimation, and show that the computational problem of maximizing the likelihood is tractable.

We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting--which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts.

The bootstrap has become a popular method for exploring model (structure) uncertainty. Our experiments with artificial and realworld data demonstrate that the graphs learned from bootstrap samples can be severely biased towards too complex graphical models. Accounting for this bias is hence essential, e.g., when exploring model uncertainty. We find that this bias is intimately tied to (well-known) spurious dependences induced by the bootstrap. The leading-order bias-correction equals one half of Akaike's penalty for model complexity. We demonstrate the effect of this simple bias-correction in our experiments. We also relate this bias to the bias of the plugin estimator for entropy, as well as to the difference between the expected test and training errors of a graphical model, which asymptotically equals Akaike's penalty (rather than one half).

In this paper we present Discriminative Random Fields (DRF), a discriminative framework for the classification of natural image regions by incorporating neighborhood spatial dependencies in the labels as well as the observed data. The proposed model exploits local discriminative models and allows to relax the assumption of conditional independence of the observed data given the labels, commonly used in the Markov Random Field (MRF) framework. The parameters of the DRF model are learned using penalized maximum pseudo-likelihood method. Furthermore, the form of the DRF model allows the MAP inference for binary classification problems using the graph min-cut algorithms. The performance of the model was verified on the synthetic as well as the real-world images. The DRF model outperforms the MRF model in the experiments.

When we model a higher order functions, such as learning and memory, we face a difficulty of comparing neural activities with hidden variables that depend on the history of sensory and motor signals and the dynamics of the network. Here, we propose novel method for estimating hidden variables of a learning agent, such as connection weights from sequences of observable variables. Bayesian estimation is a method to estimate the posterior probability of hidden variables from observable data sequence using a dynamic model of hidden and observable variables. In this paper, we apply particle filter for estimating internal parameters and metaparameters of a reinforcement learning model. We verified the effectiveness of the method using both artificial data and real animal behavioral data.

In this paper we obtain convergence bounds for the concentration of Bayesian posterior distributions (around the true distribution) using a novel method that simplifies and enhances previous results. Based on the analysis, we also introduce a generalized family of Bayesian posteriors, and show that the convergence behavior of these generalized posteriors is completely determined by the local prior structure around the true distribution. This important and surprising robustness property does not hold for the standard Bayesian posterior in that it may not concentrate when there exist "bad" prior structures even at places far away from the true distribution.

We develop a framework based on Bayesian model averaging to explain how animals cope with uncertainty about contingencies in classical conditioning experiments. Traditional accounts of conditioning fit parameters within a fixed generative model of reinforcer delivery; uncertainty over the model structure is not considered. We apply the theory to explain the puzzling relationship between second-order conditioning and conditioned inhibition, two similar conditioning regimes that nonetheless result in strongly divergent behavioral outcomes. According to the theory, second-order conditioning results when limited experience leads animals to prefer a simpler world model that produces spurious correlations; conditioned inhibition results when a more complex model is justified by additional experience.

We describe a nonparametric Bayesian approach to generalizing from few labeled examples, guided by a larger set of unlabeled objects and the assumption of a latent tree-structure to the domain. The tree (or a distribution over trees) may be inferred using the unlabeled data. A prior over concepts generated by a mutation process on the inferred tree(s) allows efficient computation of the optimal Bayesian classification function from the labeled examples. We test our approach on eight real-world datasets.

Loopy belief propagation (BP) has been successfully used in a number of difficult graphical models to find the most probable configuration of the hidden variables. In applications ranging from protein folding to image analysis one would like to find not just the best configuration but rather the top M. While this problem has been solved using the junction tree formalism, in many real world problems the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations when exact inference is impossible. We start by developing a new exact inference algorithm for calculating the best configurations that uses only max-marginals. For approximate inference, we replace the max-marginals with the beliefs calculated using max-product BP and generalized BP. We show empirically that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.

We present an analysis of concentration-of-expectation phenomena in layered Bayesian networks that use generalized linear models as the local conditional probabilities. This framework encompasses a wide variety of probability distributions, including both discrete and continuous random variables. We utilize ideas from large deviation analysis and the delta method to devise and evaluate a class of approximate inference algorithms for layered Bayesian networks that have superior asymptotic error bounds and very fast computation time.