Budgeted optimization involves optimizing an unknown function that is costly to evaluate by requesting a limited number of function evaluations at intelligently selected inputs. Typical problem formulations assume that experiments are selected one at a time with a limited total number of experiments, which fail to capture important aspects of many real-world problems. This paper defines a novel problem formulation with the following important extensions: 1) allowing for concurrent experiments; 2) allowing for stochastic experiment durations; and 3) placing constraints on both the total number of experiments and the total experimental time. We develop both offline and online algorithms for selecting concurrent experiments in this new setting and provide experimental results on a number of optimization benchmarks. The results show that our algorithms produce highly effective schedules compared to natural baselines.

We propose a novel class of Bayesian nonparametric models for sequential data called fragmentation-coagulation processes (FCPs). FCPs model a set of sequences using a partition-valued Markov process which evolves by splitting and merging clusters. An FCP is exchangeable, projective, stationary and reversible, and its equilibrium distributions are given by the Chinese restaurant process. As opposed to hidden Markov models, FCPs allow for flexible modelling of the number of clusters, and they avoid label switching non-identifiability problems. We develop an efficient Gibbs sampler for FCPs which uses uniformization and the forward-backward algorithm. Our development of FCPs is motivated by applications in population genetics, and we demonstrate the utility of FCPs on problems of genotype imputation with phased and unphased SNP data.

In this paper, we derive a method to refine a Bayes network diagnostic model by exploiting constraints implied by expert decisions on test ordering. At each step, the expert executes an evidence gathering test, which suggests the test's relative diagnostic value. We demonstrate that consistency with an expert's test selection leads to non-convex constraints on the model parameters. We incorporate these constraints by augmenting the network with nodes that represent the constraint likelihoods. Gibbs sampling, stochastic hill climbing and greedy search algorithms are proposed to find a MAP estimate that takes into account test ordering constraints and any data available. We demonstrate our approach on diagnostic sessions from a manufacturing scenario.

Modern classification tasks usually involve many class labels and can be informed by a broad range of features. Many of these tasks are tackled by constructing a set of classifiers, which are then applied at test time and then pieced together in a fixed procedure determined in advance or at training time. We present an active classification process at the test time, where each classifier in a large ensemble is viewed as a potential observation that might inform our classification process. Observations are then selected dynamically based on previous observations, using a value-theoretic computation that balances an estimate of the expected classification gain from each observation as well as its computational cost. The expected classification gain is computed using a probabilistic model that uses the outcome from previous observations. This active classification process is applied at test time for each individual test instance, resulting in an efficient instance-specific decision path. We demonstrate the benefit of the active scheme on various real-world datasets, and show that it can achieve comparable or even higher classification accuracy at a fraction of the computational costs of traditional methods.

Applications such as robot control and wireless communication require planning under uncertainty. Partially observable Markov decision processes (POMDPs) plan policies for single agents under uncertainty and their decentralized versions (DEC-POMDPs) find a policy for multiple agents. The policy in infinite-horizon POMDP and DEC-POMDP problems has been represented as finite state controllers (FSCs). We introduce a novel class of periodic FSCs, composed of layers connected only to the previous and next layer. Our periodic FSC method finds a deterministic finite-horizon policy and converts it to an initial periodic infinite-horizon policy. This policy is optimized by a new infinite-horizon algorithm to yield deterministic periodic policies, and by a new expectation maximization algorithm to yield stochastic periodic policies. Our method yields better results than earlier planning methods and can compute larger solutions than with regular FSCs.

Variational Message Passing (VMP) is an algorithmic implementation of the Variational Bayes (VB) method which applies only in the special case of conjugate exponential family models. We propose an extension to VMP, which we refer to as Non-conjugate Variational Message Passing (NCVMP) which aims to alleviate this restriction while maintaining modularity, allowing choice in how expectations are calculated, and integrating into an existing message-passing framework: Infer.NET. We demonstrate NCVMP on logistic binary and multinomial regression. In the multinomial case we introduce a novel variational bound for the softmax factor which is tighter than other commonly used bounds whilst maintaining computational tractability.

Many applications in computer vision measure the similarity between images or image patches based on some statistics such as oriented gradients. These are often modeled implicitly or explicitly with a Gaussian noise assumption, leading to the use of the Euclidean distance when comparing image descriptors. In this paper, we show that the statistics of gradient based image descriptors often follow a heavy-tailed distribution, which undermines any principled motivation for the use of Euclidean distances. We advocate for the use of a distance measure based on the likelihood ratio test with appropriate probabilistic models that fit the empirical data distribution. We instantiate this similarity measure with the Gamma-compound-Laplace distribution, and show significant improvement over existing distance measures in the application of SIFT feature matching, at relatively low computational cost.

Kernel-based reinforcement-learning (KBRL) is a method for learning a decision policy from a set of sample transitions which stands out for its strong theoretical guarantees. However, the size of the approximator grows with the number of transitions, which makes the approach impractical for large problems. In this paper we introduce a novel algorithm to improve the scalability of KBRL. We resort to a special decomposition of a transition matrix, called stochastic factorization, to fix the size of the approximator while at the same time incorporating all the information contained in the data. The resulting algorithm, kernel-based stochastic factorization (KBSF), is much faster but still converges to a unique solution. We derive a theoretical upper bound for the distance between the value functions computed by KBRL and KBSF. The effectiveness of our method is illustrated with computational experiments on four reinforcement-learning problems, including a difficult task in which the goal is to learn a neurostimulation policy to suppress the occurrence of seizures in epileptic rat brains. We empirically demonstrate that the proposed approach is able to compress the information contained in KBRL's model. Also, on the tasks studied, KBSF outperforms two of the most prominent reinforcement-learning algorithms, namely least-squares policy iteration and fitted Q-iteration.

A sizable literature has focused on the problem of estimating a low-dimensional feature space capturing a neuron's stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to a neuron's output spike rate. Here, we use a Gaussian process (GP) prior over the infinite-dimensional space of nonlinear functions to obtain Bayesian estimates of the "nonlinearity" in the linear-nonlinear-Poisson (LNP) encoding model. This offers flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). Most importantly, we develop a framework for optimal experimental design based on uncertainty sampling. This involves adaptively selecting stimuli to characterize the nonlinearity with as little experimental data as possible, and relies on a method for rapidly updating hyperparameters using the Laplace approximation. We apply these methods to data from color-tuned neurons in macaque V1. We estimate nonlinearities in the 3D space of cone contrasts, which reveal that V1 combines cone inputs in a highly nonlinear manner. With simulated experiments, we show that optimal design substantially reduces the amount of data required to estimate this nonlinear combination rule.

Latent tree graphical models are natural tools for expressing long range and hierarchical dependencies among many variables which are common in computer vision, bioinformatics and natural language processing problems. However, existing models are largely restricted to discrete and Gaussian variables due to computational constraints; furthermore, algorithms for estimating the latent tree structure and learning the model parameters are largely restricted to heuristic local search. We present a method based on kernel embeddings of distributions for latent tree graphical models with continuous and non-Gaussian variables. Our method can recover the latent tree structures with provable guarantees and perform local-minimum free parameter learning and efficient inference. Experiments on simulated and real data show the advantage of our proposed approach.