We present a Bayesian framework for explaining how people reason about and predict the actions of an intentional agent, based on observing its behavior. Action-understanding is cast as a problem of inverting a probabilistic generative model, which assumes that agents tend to act rationally in order to achieve their goals given the constraints of their environment. Working in a simple sprite-world domain, we show how this model can be used to infer the goal of an agent and predict how the agent will act in novel situations or when environmental constraints change. The model provides a qualitative account of several kinds of inferences that preverbal infants have been shown to perform, and also fits quantitative predictions that adult observers make in a new experiment.

We design a new learning algorithm for the Set Covering Machine from a PAC-Bayes perspective and propose a PAC-Bayes risk bound which is minimized for classifiers achieving a non trivial margin-sparsity tradeoff.

We derive a Bayesian Ideal Observer (BIO) for detecting motion and solving the correspondence problem. We obtain Barlow and Tripathy's classic model as an approximation. Our psychophysical experiments show that the trends of human performance are similar to the Bayesian Ideal, but overall human performance is far worse. We investigate ways to degrade the Bayesian Ideal but show that even extreme degradations do not approach human performance. Instead we propose that humans perform motion tasks using generic, general purpose, models of motion. We perform more psychophysical experiments which are consistent with humans using a Slow-and-Smooth model and which rule out an alternative model using Slowness.

We considered a gamma distribution of interspike intervals as a statistical model for neuronal spike generation. The model parameters consist of a time-dependent firing rate and a shape parameter that characterizes spiking irregularities of individual neurons. Because the environment changes with time, observed data are generated from the time-dependent firing rate, which is an unknown function. A statistical model with an unknown function is called a semiparametric model, which is one of the unsolved problem in statistics and is generally very difficult to solve. We used a novel method of estimating functions in information geometry to estimate the shape parameter without estimating the unknown function. We analytically obtained an optimal estimating function for the shape parameter independent of the functional form of the firing rate. This estimation is efficient without Fisher information loss and better than maximum likelihood estimation.

There have been many graph-based approaches for semi-supervised classification. One problem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, transformation of the graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semisupervised classification. Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an inference problem over the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification. The hyperparameters are learned using EM for evidence maximization. We also show that the posterior mean can be written in terms of the kernel matrix, providing a Bayesian classifier to classify new points. Tests on synthetic and real datasets show cases where there are significant improvements in performance over the existing approaches.

We present a competitive analysis of some nonparametric Bayesian algorithms in a worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) and provide bounds on the regret (under the log loss) for commonly used nonparametric Bayesian algorithms -- including Gaussian regression and logistic regression -- which show how these algorithms can perform favorably under rather general conditions. These bounds explicitly handle the infinite dimensionality of these nonparametric classes in a natural way. We also make formal connections to the minimax and minimum description length (MDL) framework. Here, we show precisely how Bayesian Gaussian regression is a minimax strategy.

We discuss a method for obtaining a subject's a priori beliefs from his/her behavior in a psychophysics context, under the assumption that the behavior is (nearly) optimal from a Bayesian perspective. The method is nonparametric in the sense that we do not assume that the prior belongs to any fixed class of distributions (e.g., Gaussian). Despite this increased generality, the method is relatively simple to implement, being based in the simplest case on a linear programming algorithm, and more generally on a straightforward maximum likelihood or maximum a posteriori formulation, which turns out to be a convex optimization problem (with no non-global local maxima) in many important cases. In addition, we develop methods for analyzing the uncertainty of these estimates. We demonstrate the accuracy of the method in a simple simulated coin-flipping setting; in particular, the method is able to precisely track the evolution of the subject's posterior distribution as more and more data are observed. We close by briefly discussing an interesting connection to recent models of neural population coding.

The Octopus arm is a highly versatile and complex limb. How the Octopus controls such a hyper-redundant arm (not to mention eight of them!) is as yet unknown. Robotic arms based on the same mechanical principles may render present day robotic arms obsolete. In this paper, we tackle this control problem using an online reinforcement learning algorithm, based on a Bayesian approach to policy evaluation known as Gaussian process temporal difference (GPTD) learning. Our substitute for the real arm is a computer simulation of a 2-dimensional model of an Octopus arm. Even with the simplifications inherent to this model, the state space we face is a high-dimensional one. We apply a GPTDbased algorithm to this domain, and demonstrate its operation on several learning tasks of varying degrees of difficulty.

We propose a new Bayesian method for spatial cluster detection, the "Bayesian spatial scan statistic," and compare this method to the standard (frequentist) scan statistic approach. We demonstrate that the Bayesian statistic has several advantages over the frequentist approach, including increased power to detect clusters and (since randomization testing is unnecessary) much faster runtime. We evaluate the Bayesian and frequentist methods on the task of prospective disease surveillance: detecting spatial clusters of disease cases resulting from emerging disease outbreaks. We demonstrate that our Bayesian methods are successful in rapidly detecting outbreaks while keeping number of false positives low.

We present a model that learns the influence of interacting Markov chains within a team. The proposed model is a dynamic Bayesian network (DBN) with a two-level structure: individual-level and group-level.