The paper presents a new sampling methodology for Bayesian networks that samples only a subset of variables and applies exact inference to the rest. Cutset sampling is a network structure-exploiting application of the Rao-Blackwellisation principle to sampling in Bayesian networks. It improves convergence by exploiting memory-based inference algorithms. It can also be viewed as an anytime approximation of the exact cutset-conditioning algorithm developed by Pearl. Cutset sampling can be implemented efficiently when the sampled variables constitute a loop-cutset of the Bayesian network and, more generally, when the induced width of the network's graph conditioned on the observed sampled variables is bounded by a constant w. We demonstrate empirically the benefit of this scheme on a range of benchmarks.

We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor $M$ from the true distribution $mu$ by the algorithmic complexity of $mu$. Here we assume we are at a time $t>1$ and already observed $x=x_1...x_t$. We bound the future prediction performance on $x_{t+1}x_{t+2}...$ by a new variant of algorithmic complexity of $mu$ given $x$, plus the complexity of the randomness deficiency of $x$. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.

We propose an algorithm that uses Gaussian process regression to learn common hidden structure shared between corresponding sets of heterogenous observations. The observation spaces are linked via a single, reduced-dimensionality latent variable space. We present results from two datasets demonstrating the algorithms's ability to synthesize novel data from learned correspondences. We first show that the method can learn the nonlinear mapping between corresponding views of objects, filling in missing data as needed to synthesize novel views. We then show that the method can learn a mapping between human degrees of freedom and robotic degrees of freedom for a humanoid robot, allowing robotic imitation of human poses from motion capture data.

Neurons can have rapidly changing spike train statistics dictated by the underlying network excitability or behavioural state of an animal. To estimate the time course of such state dynamics from single-or multiple neuron recordings, we have developed an algorithm that maximizes the likelihood of observed spike trains by optimizing the state lifetimes and the state-conditional interspike-interval (ISI) distributions. Our nonparametric algorithm is free of time-binning and spike-counting problems and has the computational complexity of a Mixed-state Markov Model operating on a state sequence of length equal to the total number of recorded spikes. As an example, we fit a two-state model to paired recordings of premotor neurons in the sleeping songbird. We find that the two state-conditional ISI functions are highly similar to the ones measured during waking and singing, respectively.

Given a redundant dictionary of basis vectors (or atoms), our goal is to find maximally sparse representations of signals. Previously, we have argued that a sparse Bayesian learning (SBL) framework is particularly well-suited for this task, showing that it has far fewer local minima than other Bayesian-inspired strategies. In this paper, we provide further evidence for this claim by proving a restricted equivalence condition, based on the distribution of the nonzero generating model weights, whereby the SBL solution will equal the maximally sparse representation. We also prove that if these nonzero weights are drawn from an approximate Jeffreys prior, then with probability approaching one, our equivalence condition is satisfied. Finally, we motivate the worst-case scenario for SBL and demonstrate that it is still better than the most widely used sparse representation algorithms.

We consider criteria for variational representations of non-Gaussian latent variables, and derive variational EM algorithms in general form. We establish a general equivalence among convex bounding methods, evidence based methods, and ensemble learning/Variational Bayes methods, which has previously been demonstrated only for particular cases.

Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. In contrast with most existing models, our approach explicitly captures uncertainty in the number of object instances depicted in a given image. Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DP in which a set of stochastically transformed mixture components are shared between multiple groups of data. For visual scenes, mixture components describe the spatial structure of visual features in an object-centered coordinate frame, while transformations model the object positions in a particular image. Learning and inference in the TDP, which has many potential applications beyond computer vision, is based on an empirically effective Gibbs sampler. Applied to a dataset of partially labeled street scenes, we show that the TDP's inclusion of spatial structure improves detection performance, flexibly exploiting partially labeled training images.

We argue that when objects are characterized by many attributes, clustering them on the basis of a relatively small random subset of these attributes can capture information on the unobserved attributes as well. Moreover, we show that under mild technical conditions, clustering the objects on the basis of such a random subset performs almost as well as clustering with the full attribute set. We prove a finite sample generalization theorems for this novel learning scheme that extends analogous results from the supervised learning setting. The scheme is demonstrated for collaborative filtering of users with movies rating as attributes.

For this purpose, we propose a stochastic procedure, the mirror descent, which performs gradient descent in the dual space. The generated estimates are additionally averaged in a recursive fashion with specific weights. Mirror descent algorithms have been developed in different contexts and they are known to be particularly efficient in high dimensional problems. Moreover their implementation is adapted to the online setting. The main result of the paper is the upper bound on the convergence rate for the generalization error.