We show that the sets in a family with finite VC dimension can be uniformly approximated within a given error by a finite partition. Immediate corollaries include the fact that VC classes have finite bracketing numbers, satisfy uniform laws of averages under strong dependence, and exhibit uniform mixing. Our results are based on recent work concerning uniform laws of averages for VC classes under ergodic sampling.

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

This paper develops automated testing and debugging techniques for answer set solver development. We describe a flexible grammar-based black-box ASP fuzz testing tool which is able to reveal various defects such as unsound and incomplete behavior, i.e. invalid answer sets and inability to find existing solutions, in state-of-the-art answer set solver implementations. Moreover, we develop delta debugging techniques for shrinking failure-inducing inputs on which solvers exhibit defective behavior. In particular, we develop a delta debugging algorithm in the context of answer set solving, and evaluate two different elimination strategies for the algorithm.

Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the gap dimension of F and the uniform convergence of its sample averages under ergodic sampling. In particular, we show that if the gap dimension of F at resolution gamma > 0 is finite, then for every ergodic process the sample averages of functions in F are eventually within 10 gamma of their limiting expectations uniformly over the class F. If the gap dimension of F is finite for every resolution gamma > 0 then the sample averages of functions in F converge uniformly to their limiting expectations. We assume only that F is uniformly bounded and countable (or countably approximable). No smoothness conditions are placed on F, and no assumptions beyond ergodicity are placed on the sampling processes. Our results extend existing work for i.i.d. processes.

Many problems require repeated inference on probabilistic graphical models, with different values for evidence variables or other changes. Examples of such problems include utility maximization, MAP inference, online and interactive inference, parameter and structure learning, and dynamic inference. Since small changes to the evidence typically only affect a small region of the network, repeatedly performing inference from scratch can be massively redundant. In this paper, we propose expanding frontier belief propagation (EFBP), an efficient approximate algorithm for probabilistic inference with incremental changes to the evidence (or model). EFBP is an extension of loopy belief propagation (BP) where each run of inference reuses results from the previous ones, instead of starting from scratch with the new evidence; messages are only propagated in regions of the network affected by the changes. We provide theoretical guarantees bounding the difference in beliefs generated by EFBP and standard BP, and apply EFBP to the problem of expected utility maximization in influence diagrams. Experiments on viral marketing and combinatorial auction problems show that EFBP can converge much faster than BP without significantly affecting the quality of the solutions.

Lifting can greatly reduce the cost of inference on first-order probabilistic graphical models, but constructing the lifted network can itself be quite costly. In online applications (e.g., video segmentation) repeatedly constructing the lifted network for each new inference can be extremely wasteful, because the evidence typically changes little from one inference to the next. The same is true in many other problems that require repeated inference, like utility maximization, MAP inference, interactive inference, parameter and structure learning, etc. In this paper, we propose an efficient algorithm for updating the structure of an existing lifted network with incremental changes to the evidence. This allows us to construct the lifted network once for the initial inference problem, and amortize the cost over the subsequent problems. Experiments on video segmentation and viral marketing problems show that the algorithm greatly reduces the cost of inference without affecting the quality of the solutions.

Research has demonstrated the efficacy of closed-loop control of anesthesia using the bispectral index (BIS) of the electroencephalogram as the controlled variable, and the development of model-based, patient-adaptive systems has considerably improved anesthetic control. To further explore the use of model-based control in anesthesia, we investigated the application of reinforcement learning (RL) in the delivery of patient-specific, propofol-induced hypnosis in human volunteers. When compared to published performance metrics, RL control demonstrated accuracy and stability, indicating that further, more rigorous clinical study is warranted.

We examine the suitability of using decision processes to model real-world systems of intelligent adversaries. Decision processes have long been used to study cooperative multiagent interactions, but their practical applicability to adversarial problems has received minimal study. We address the pros and cons of applying sequential decision-making in this area, using the crime of money laundering as a specific example. Motivated by case studies, we abstract out a model of the money laundering process, using the framework of interactive partially observable Markov decision processes (I-POMDPs). We address why this framework is well suited for modeling adversarial interactions. Particle filtering and value iteration are used to solve the model, with the application of different pruning and look-ahead strategies to assess the tradeoffs between solution quality and algorithmic run time. Our results show that there is a large gap in the level of realism that can currently be achieved by such decision models, largely due to computational demands that limit the size of problems that can be solved. While these results represent solutions to a simplified model of money laundering, they illustrate nonetheless the kinds of agent interactions that cannot be captured by standard approaches such as anomaly detection. This implies that I-POMDP methods may be valuable in the future, when algorithmic capabilities have further evolved.

In this paper, we consider the problem of reinforcement learning in spatial tasks. These tasks have many states that can be aggregated together to improve learning efficiency. In an agent, this aggregation can take the form of selecting appropriate perceptual processes to arrive at a qualitative abstraction of the underlying continuous state. However, for arbitrary problems, an agent is unlikely to have the perceptual processes necessary to discriminate all relevant states in terms of such an abstraction. To help compensate for this, reinforcement learning can be integrated with an imagery system, where simple models of physical processes are applied within a low-level perceptual representation to predict the state resulting from an action. Rather than abstracting the current state, abstraction can be applied to the predicted next state. Formally, it is shown that this integration broadens the class of perceptual abstraction methods that can be used while preserving the underlying problem. Empirically, it is shown that this approach can be used in complex domains, and can be beneficial even when formal requirements are not met.

The work presented in this paper is part of a multidisciplinary team collaborating in the deployment of an autonomous oceanographic probe with the task of exploring marine regions and take phytoplankton samples for their subsequent analysis in a laboratory. We will describe an autonomous system that, from sensor data, is able to characterize phytoplankton structures. Because the system has to work inboard, a main goal of our approach is to dramatically reduce the dimensionality of the problem. Specifically, our development uses two AI techniques, namely Particle Swarm Optimization and Case-Based Reasoning. We report results of experiments performed with simulated environments.