We propose a novel information-theoretic approach for Bayesian optimization called Predictive Entropy Search (PES). At each iteration, PES selects the next evaluation point that maximizes the expected information gained with respect to the global maximum. PES codifies this intractable acquisition function in terms of the expected reduction in the differential entropy of the predictive distribution. This reformulation allows PES to obtain approximations that are both more accurate and efficient than other alternatives such as Entropy Search (ES). Furthermore, PES can easily perform a fully Bayesian treatment of the model hyperparameters while ES cannot. We evaluate PES in both synthetic and real-world applications, including optimization problems in machine learning, finance, biotechnology, and robotics. We show that the increased accuracy of PES leads to significant gains in optimization performance.

We introduce a Bayesian solution for the problem in forensic speaker recognition, where there may be very little background material for estimating score calibration parameters. We work within the Bayesian paradigm of evidence reporting and develop a principled probabilistic treatment of the problem, which results in a Bayesian likelihood-ratio as the vehicle for reporting weight of evidence. We show in contrast, that reporting a likelihood-ratio distribution does not solve this problem. Our solution is experimentally exercised on a simulated forensic scenario, using NIST SRE'12 scores, which demonstrates a clear advantage for the proposed method compared to the traditional plugin calibration recipe.

It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate an inference procedure for it. For this approach to be practical, it is important to generate inference code that has reasonable performance. In this paper, we present a probabilistic programming language and compiler for Bayesian networks designed to make effective use of data-parallel architectures such as GPUs. Our language is fully integrated within the Scala programming language and benefits from tools such as IDE support, type-checking, and code completion. We show that the compiler can generate data-parallel inference code scalable to thousands of GPU cores by making use of the conditional independence relationships in the Bayesian network.

Planning under uncertainty poses a complex problem in which multiple objectives often need to be balanced. When dealing with multiple objectives, it is often assumed that the relative importance of the objectives is known a priori. However, in practice human decision makers often find it hard to specify such preferences, and would prefer a decision support system that presents a range of possible alternatives. We propose two algorithms for computing these alternatives for the case of linearly weighted objectives. First, we propose an anytime method, approximate optimistic linear support (AOLS), that incrementally builds up a complete set of ε-optimal plans, exploiting the piecewise linear and convex shape of the value function. Second, we propose an approximate anytime method, scalarised sample incremental improvement (SSII), that employs weight sampling to focus on the most interesting regions in weight space, as suggested by a prior over preferences. We show empirically that our methods are able to produce (near-)optimal alternative sets orders of magnitude faster than existing techniques.

We introduce a family of MDP reduced models characterized by two parameters: the maximum number of primary outcomes per action that are fully accounted for and the maximum number of occurrences of the remaining exceptional outcomes that are planned for in advance. Reduced models can be solved much faster using heuristic search algorithms such as LAO*, benefiting from the dramatic reduction in the number of reachable states. A commonly used determinization approach is a special case of this family of reductions, with one primary outcome per action and zero exceptional outcomes per plan. We present a framework to compute the benefits of planning with reduced models, relying on online planning when the number of exceptional outcomes exceeds the bound. Using this framework, we compare the performance of various reduced models and consider the challenge of generating good ones automatically. We show that each one of the dimensions---allowing more than one primary outcome or planning for some limited number of exceptions---could improve performance relative to standard determinization. The results place recent work on determinization in a broader context and lay the foundation for efficient and systematic exploration of the space of MDP model reductions.

While Markov Decision Processes (MDPs) have been shown to be effective models for planning under uncertainty, the objective to minimize the expected cumulative cost is inappropriate for high-stake planning problems. As such, Yu, Lin, and Yan (1998) introduced the Risk-Sensitive MDP (RS-MDP) model, where the objective is to find a policy that maximizes the probability that the cumulative cost is within some user-defined cost threshold. In this paper, we revisit this problem and introduce new algorithms that are based on classical techniques, such as depth-first search and dynamic programming, and a recently introduced technique called Topological Value Iteration (TVI). We demonstrate the applicability of our approach on randomly generated MDPs as well as domains from the ICAPS 2011 International Probabilistic Planning Competition (IPPC).

Monte-Carlo tree search (MCTS) has been drawing great interest in recent years for planning under uncertainty. One of the key challenges is the trade-off between exploration and exploitation. To address this, we introduce a novel online planning algorithm for large POMDPs using Thompson sampling based MCTS that balances between cumulative and simple regrets. The proposed algorithm  Dirichlet-Dirichlet-NormalGamma based Partially Observable Monte-Carlo Planning (D 2 NG-POMCP) treats the accumulated reward of performing an action from a belief state in the MCTS search tree as a random variable following an unknown distribution with hidden parameters. Bayesian method is used to model and infer the posterior distribution of these parameters by choosing the conjugate prior in the form of a combination of two Dirichlet and one NormalGamma distributions. Thompson sampling is exploited to guide the action selection in the search tree. Experimental results confirmed that our algorithm outperforms the state-of-the-art approaches on several common benchmark problems.

This paper proposes the problem of supply restoration in faulty power distribution systems as a benchmark for planning under uncertainty. This benchmark, which is derived from a significant real-world case, is both simple to understand and easily scalable. The goal is to reconfigure the distribution network to resupply a maximum of consumers affected by the faults.  Due to sensor and actuator uncertainty, the location of the faulty areas and the current network configuration are only partially observable.  This makes the problem very challenging.

Probabilistic graphical models are graphical representations of probability distributions. Graphical models have applications in many fields including biology, social sciences, linguistic, neuroscience. In this paper, we propose directed acyclic graphs (DAGs) learning via bootstrap aggregating. The proposed procedure is named as DAGBag. Specifically, an ensemble of DAGs is first learned based on bootstrap resamples of the data and then an aggregated DAG is derived by minimizing the overall distance to the entire ensemble. A family of metrics based on the structural hamming distance is defined for the space of DAGs (of a given node set) and is used for aggregation. Under the high-dimensional-low-sample size setting, the graph learned on one data set often has excessive number of false positive edges due to over-fitting of the noise. Aggregation overcomes over-fitting through variance reduction and thus greatly reduces false positives. We also develop an efficient implementation of the hill climbing search algorithm of DAG learning which makes the proposed method computationally competitive for the high-dimensional regime. The DAGBag procedure is implemented in the R package dagbag.

Bayesian network structures are usually built using only the data and starting from an empty network or from a naive Bayes structure. Very often, in some domains, like medicine, a prior structure knowledge is already known. This structure can be automatically or manually refined in search for better performance models. In this work, we take Bayesian networks built by specialists and show that minor perturbations to this original network can yield better classifiers with a very small computational cost, while maintaining most of the intended meaning of the original model.