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.

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 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.

Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe a very simple algorithm for solving it. Our algorithm uses a modelbased concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly using a single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from EachMovie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia.

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.

We present an infinite mixture model in which each component comprises a multivariate Gaussian distribution over an input space, and a Gaussian Process model over an output space. Our model is neatly able to deal with non-stationary covariance functions, discontinuities, multimodality and overlapping output signals. The work is similar to that by Rasmussen and Ghahramani [1]; however, we use a full generative model over input and output space rather than just a conditional model. This allows us to deal with incomplete data, to perform inference over inverse functional mappings as well as for regression, and also leads to a more powerful and consistent Bayesian specification of the effective'gating network' for the different experts.

We propose a probabilistic model based on Independent Component Analysis for learning multiple related tasks. In our model the task parameters are assumed to be generated from independent sources which account for the relatedness of the tasks. We use Laplace distributions to model hidden sources which makes it possible to identify the hidden, independent components instead of just modeling correlations. Furthermore, our model enjoys a sparsity property which makes it both parsimonious and robust. We also propose efficient algorithms for both empirical Bayes method and point estimation. Our experimental results on two multi-label text classification data sets show that the proposed approach is promising.

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. Previous results can be used to determine convergence and to estimate convergence rates.

Probabilistic modeling of correlated neural population firing activity is central to understanding the neural code and building practical decoding algorithms. No parametric models currently exist for modeling multivariate correlated neural data and the high dimensional nature of the data makes fully nonparametric methods impractical. To address these problems we propose an energy-based model in which the joint probability of neural activity is represented using learned functions of the 1D marginal histograms of the data. The parameters of the model are learned using contrastive divergence and an optimization procedure for finding appropriate marginal directions. We evaluate the method using real data recorded from a population of motor cortical neurons. In particular, we model the joint probability of population spiking times and 2D hand position and show that the likelihood of test data under our model is significantly higher than under other models. These results suggest that our model captures correlations in the firing activity. Our rich probabilistic model of neural population activity is a step towards both measurement of the importance of correlations in neural coding and improved decoding of population activity.

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.