A longstanding goal of reinforcement learning is to develop non- parametric representations of policies and value functions that support rapid learning without suffering from interference or the curse of di- mensionality. We have developed a trajectory-based approach, in which policies and value functions are represented nonparametrically along tra- jectories. These trajectories, policies, and value functions are updated as the value function becomes more accurate or as a model of the task is up- dated. We have applied this approach to periodic tasks such as hopping and walking, which required handling discount factors and discontinu- ities in the task dynamics, and using function approximation to represent value functions at discontinuities. We also describe extensions of the ap- proach to make the policies more robust to modeling error and sensor noise.

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 algo- rithms for layered Bayesian networks that have superior asymptotic error bounds and very fast computation time.

The inference of hidden graphs from noisy edge appearance data is an important problem with obvious practical application. For example, biologists are currently building networks of all the physical protein-protein interactions (PPI) that occur in particular organisms. The importance of this enterprise is commensurate with its scale: a completed network would be as valuable as a completed genome sequence, and because each organism contains thousands of difierent types of proteins, there are millions of possible types of interactions. However, scalable experimental meth- ods for detecting interactions are noisy, generating many false detections. Motivated by this application, we formulate the general problem of inferring hidden graphs as probabilistic inference in a graphical model, and we introduce an e–cient algorithm that approximates the posterior probability that an edge is present.

Many techniques for complex speech processing such as denoising and deconvolution, time/frequency warping, multiple speaker separation, and multiple microphone analysis operate on sequences of short-time power spectra (spectrograms), a representation which is often well-suited to these tasks. However, a significant problem with algorithms that manipu- late spectrograms is that the output spectrogram does not include a phase component, which is needed to create a time-domain signal that has good perceptual quality. Here we describe a generative model of time-domain speech signals and their spectrograms, and show how an efficient opti- mizer can be used to find the maximum a posteriori speech signal, given the spectrogram. We compare our technique with a standard method using signal-to-noise ratios, but we also provide audio files on the web for the purpose of demonstrating the improvement in perceptual quality that our technique offers.

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 after- current. 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 max- imum likelihood estimation, and show that the computational problem of maximizing the likelihood is tractable.

The detection and pose estimation of people in images and video is made challenging by the variability of human appearance, the complexity of natural scenes, and the high dimensionality of articulated body mod- els. To cope with these problems we represent the 3D human body as a graphical model in which the relationships between the body parts are represented by conditional probability distributions. We formulate the pose estimation problem as one of probabilistic inference over a graphi- cal model where the random variables correspond to the individual limb parameters (position and orientation). Because the limbs are described by 6-dimensional vectors encoding pose in 3-space, discretization is im- practical and the random variables in our model must be continuous- valued. To approximate belief propagation in such a graph we exploit a recently introduced generalization of the particle filter.

We present a Bayesian approach to color constancy which utilizes a non- Gaussian probabilistic model of the image formation process. The pa- rameters of this model are estimated directly from an uncalibrated image set and a small number of additional algorithmic parameters are chosen using cross validation. The algorithm is empirically shown to exhibit RMS error lower than other color constancy algorithms based on the Lambertian surface reflectance model when estimating the illuminants of a set of test images. This is demonstrated via a direct performance comparison utilizing a publicly available set of real world test images and code base.

Principal components analysis (PCA) is one of the most widely used techniques in machine learning and data mining. Minor components analysis (MCA) is less well known, but can also play an important role in the presence of constraints on the data distribution. In this paper we present a probabilistic model for "extreme components analysis" (XCA) which at the maximum likelihood solution extracts an optimal combina- tion of principal and minor components. For a given number of compo- nents, the log-likelihood of the XCA model is guaranteed to be larger or equal than that of the probabilistic models for PCA and MCA. We de- scribe an efficient algorithm to solve for the globally optimal solution.

We introduce an information theoretic method for nonparametric, non- linear dimensionality reduction, based on the infinite cluster limit of rate distortion theory. By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method de- termines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data. Some data sets may not be as complicated as they appear. Consider the set of points on a plane in Figure 1.

When we learn a new motor skill, we have to contend with both the vari- ability inherent in our sensors and the task. The sensory uncertainty can be reduced by using information about the distribution of previously ex- perienced tasks. Here we impose a distribution on a novel sensorimotor task and manipulate the variability of the sensory feedback. We show that subjects internally represent both the distribution of the task as well as their sensory uncertainty. Moreover, they combine these two sources of information in a way that is qualitatively predicted by optimal Bayesian processing.