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 esti- mates. 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 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. Experiments on synthetic multi-player games and a multi-party meeting corpus show the effectiveness of the proposed model.

We present a Bayesian framework for explaining how people reason about and predict the actions of an intentional agent, based on observ- ing 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 en- vironment. 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 quantita- tive predictions that adult observers make in a new experiment.

An increasing number of projects in neuroscience requires the sta- tistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing or in operating artificial de- vices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classical linear regression approaches are often numerically too fragile in high dimensions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faith- fully reconstructed with linear approaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that auto- matically detects and excludes irrelevant features in the data, reg- ularizing against overfitting. In comparison with ordinary least squares, stepwise regression, partial least squares, LASSO regres- sion and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of reg- ularization against overfitting, computational efficiency and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques.

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.

We extend a previously developed Bayesian framework for perception to account for sensory adaptation. We first note that the perceptual ef- fects of adaptation seems inconsistent with an adjustment of the inter- nally represented prior distribution. Instead, we postulate that adaptation increases the signal-to-noise ratio of the measurements by adapting the operational range of the measurement stage to the input range. We show that this changes the likelihood function in such a way that the Bayesian estimator model can account for reported perceptual behavior. In particu- lar, we compare the model's predictions to human motion discrimination data and demonstrate that the model accounts for the commonly observed perceptual adaptation effects of repulsion and enhanced discriminability.

There have been many graph-based approaches for semi-supervised clas- sification. One problem is that of hyperparameter learning: performance depends greatly on the hyperparameters of the similarity graph, trans- formation of the graph Laplacian and the noise model. We present a Bayesian framework for learning hyperparameters for graph-based semi- supervised classification. Given some labeled data, which can contain inaccurate labels, we pose the semi-supervised classification as an in- ference problem over the unknown labels. Expectation Propagation is used for approximate inference and the mean of the posterior is used for classification.

The Variational Bayesian framework has been widely used to approximate the Bayesian learning. In various applications, it has provided computational tractability and good generalization performance. In this paper, we discuss the Variational Bayesian learning of the mixture of exponential families and provide some additional theoretical support by deriving the asymptotic form of the stochastic complexity. The stochastic complexity, which corresponds to the minimum free energy and a lower bound of the marginal likelihood, is a key quantity for model selection. It also enables us to discuss the effect of hyperparameters and the accuracy of the Variational Bayesian approach as an approximation of the true Bayesian learning.

We show that linear generalizations of Rescorla-Wagner can perform Maximum Likelihood estimation of the parameters of all generative models for causal reasoning. Our approach involves augmenting variables to deal with conjunctions of causes, similar to the agumented model of Rescorla. Our results involve genericity assumptions on the distributions of causes. If these assumptions are violated, for example for the Cheng causal power theory, then we show that a linear Rescorla-Wagner can estimate the parameters of the model up to a nonlinear transformtion. Moreover, a nonlinear Rescorla-Wagner is able to estimate the parameters directly to within arbitrary accuracy.

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g., smoothing, denoising, interpolation) on a new noisy observation. Working in the computation-limited setting, we analyze a joint method in which the same convex variational relaxation is used to construct an M-estimator for fitting parameters, and to perform approximate marginalization for the prediction step. The key result of this paper is that in the computation-limited setting, using an inconsistent parameter estimator (i.e., an estimator that returns the "wrong" model even in the infinite data limit) is provably beneficial, since the resulting errors can partially compensate for errors made by using an approximate prediction technique. En route to this result, we analyze the asymptotic properties of M-estimators based on convex variational relaxations, and establish a Lipschitz stability property that holds for a broad class of variational methods. We show that joint estimation/prediction based on the reweighted sum-product algorithm substantially outperforms a commonly used heuristic based on ordinary sum-product. 1 Keywords: Markov random fields; variational method; message-passing algorithms; sum-product; belief propagation; parameter estimation; learning.