In kernel-based regression learning, optimizing each kernel individually is useful when the data density, curvature of regression surfaces (or decision boundaries) or magnitude of output noise (i.e., heteroscedasticity) varies spatially. Unfortunately, it presents a complex computational problem as the danger of overfitting is high and the individual optimization of every kernel in a learning system may be overly expensive due to the introduction of too many open learning parameters. Previous work has suggested gradient descent techniques or complex statistical hypothesis methods for local kernel shaping, typically requiring some amount of manual tuning of meta parameters. In this paper, we focus on nonparametric regression and introduce a Bayesian formulation that, with the help of variational approximations, results in an EM-like algorithm for simultaneous estimation of regression and kernel parameters. The algorithm is computationally efficient (suitable for large data sets), requires no sampling, automatically rejects outliers and has only one prior to be specified. It can be used for nonparametric regression with local polynomials or as a novel method to achieve nonstationary regression with Gaussian Processes. Our methods are particularly useful for learning control, where reliable estimation of local tangent planes is essential for adaptive controllers and reinforcement learning. We evaluate our methods on several synthetic data sets and on an actual robot which learns a task-level control law.

In many domains, data are distributed among datasets that share only some variables; other recorded variables may occur in only one dataset. There are several asymptotically correct, informative algorithms that search for causal information given a single dataset, even with missing values and hidden variables. There are, however, no such reliable procedures for distributed data with overlapping variables, and only a single heuristic procedure (Structural EM). This paper describes an asymptotically correct procedure, ION, that provides all the information about structure obtainable from the marginal independence relations. Using simulated and real data, the accuracy of ION is compared with that of Structural EM, and with inference on complete, unified data.

Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markovconditional random field (HSCRF), a generalisation of embedded undirected Markov chains to model complex hierarchical, nested Markov processes. It is parameterised in a discriminative framework and has polynomial time algorithms for learning and inference. Importantly, we develop efficient algorithms forlearning and constrained inference in a partially-supervised setting, which is important issue in practice where labels can only be obtained sparsely. We demonstrate the HSCRF in two applications: (i) recognising human activities of daily living (ADLs) from indoor surveillance cameras, and (ii) noun-phrase chunking. We show that the HSCRF is capable of learning rich hierarchical models withreasonable accuracy in both fully and partially observed data cases.

We define a metric for measuring behavior similarity between states in a Markov decision process (MDP), which takes action similarity into account. We show that the kernel of our metric corresponds exactly to the classes of states defined by MDP homomorphisms (Ravindran & Barto, 2003). We prove that the difference inthe optimal value function of different states can be upper-bounded by the value of this metric, and that the bound is tighter than previous bounds provided bybisimulation metrics (Ferns et al. 2004, 2005). Our results hold both for discrete and for continuous actions. We provide an algorithm for constructing approximate homomorphisms, by using this metric to identify states that can be grouped together, as well as actions that can be matched. Previous research on this topic is based mainly on heuristics.

We present a novel mathematical formalism for the idea of a local model,'' a model of a potentially complex dynamical system that makes only certain predictions in only certain situations. As a result of its restricted responsibilities, a local model may be far simpler than a complete model of the system. We then show how one might combine several local models to produce a more detailed model. We demonstrate our ability to learn a collection of local models on a large-scale example and do a preliminary empirical comparison of learning a collection of local models and some other model learning methods."

We introduce the first temporal-difference learning algorithm that is stable with linear function approximation and off-policy training, for any finite Markov decision process, target policy, and exciting behavior policy, and whose complexity scales linearly in the number of parameters. We consider an i.i.d.\ policy-evaluation setting in which the data need not come from on-policy experience. The gradient temporal-difference (GTD) algorithm estimates the expected update vector of the TD(0) algorithm and performs stochastic gradient descent on its L_2 norm. Our analysis proves that its expected update is in the direction of the gradient, assuring convergence under the usual stochastic approximation conditions to the same least-squares solution as found by the LSTD, but without its quadratic computational complexity. GTD is online and incremental, and does not involve multiplying by products of likelihood ratios as in importance-sampling methods.

The Temporal Restricted Boltzmann Machine (TRBM) is a probabilistic model for sequences that is able to successfully model (i.e., generate nice-looking samples of) several very high dimensional sequences, such as motion capture data and the pixels of low resolution videos of balls bouncing in a box. The major disadvantage of the TRBM is that exact inference is extremely hard, since even computing a Gibbs update for a single variable of the posterior is exponentially expensive. This difficulty has necessitated the use of a heuristic inference procedure, that nonetheless was accurate enough for successful learning. In this paper we introduce the Recurrent TRBM, which is a very slight modification of the TRBM for which exact inference is very easy and exact gradient learning is almost tractable. We demonstrate that the RTRBM is better than an analogous TRBM at generating motion capture and videos of bouncing balls.

We develop a statistical framework for the simultaneous, unsupervised segmentation and discovery of visual object categories from image databases. Examining a large set of manually segmented scenes, we use chi--square tests to show that object frequencies and segment sizes both follow power law distributions, which are well modeled by the Pitman--Yor (PY) process. This nonparametric prior distribution leads to learning algorithms which discover an unknown set of objects, and segmentation methods which automatically adapt their resolution to each image. Generalizing previous applications of PY processes, we use Gaussian processes to discover spatially contiguous segments which respect image boundaries. Using a novel family of variational approximations, our approach produces segmentations which compare favorably to state--of--the--art methods, while simultaneously discovering categories shared among natural scenes.

We show how improved sequences for magnetic resonance imaging can be found through automated optimization of Bayesian design scores. Combining recent advances in approximate Bayesian inference and natural image statistics with high-performance numerical computation, we propose the first scalable Bayesian experimental design framework for this problem of high relevance to clinical and brain research. Our solution requires approximate inference for dense, non-Gaussian models on a scale seldom addressed before. We propose a novel scalable variational inference algorithm, and show how powerful methods of numerical mathematics can be modified to compute primitives in our framework. Our approach is evaluated on a realistic setup with raw data from a 3T MR scanner.

We present polynomial-time algorithms for the exact computation of lowest- energy states, worst margin violators, partition functions, and marginals in binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it does not impose any submodularity constraints; instead we require planarity to establish a correspondence with perfect matchings in an expanded dual graph. Maximum-margin parameter estimation for a boundary detection task shows our approach to be efficient and effective.