Grids with blocked and unblocked cells are often used to represent terrain in robotics and video games. However, paths formed by grid edges can be longer than true shortest paths in the terrain since their headings are artificially constrained. We present two new correct and complete any-angle path-planning algorithms that avoid this shortcoming. Basic Theta* and Angle-Propagation Theta* are both variants of A* that propagate information along grid edges without constraining paths to grid edges. Basic Theta* is simple to understand and implement, fast and finds short paths. However, it is not guaranteed to find true shortest paths. Angle-Propagation Theta* achieves a better worst-case complexity per vertex expansion than Basic Theta* by propagating angle ranges when it expands vertices, but is more complex, not as fast and finds slightly longer paths. We refer to Basic Theta* and Angle-Propagation Theta* collectively as Theta*. Theta* has unique properties, which we analyze in detail. We show experimentally that it finds shorter paths than both A* with post-smoothed paths and Field D* (the only other version of A* we know of that propagates information along grid edges without constraining paths to grid edges) with a runtime comparable to that of A* on grids. Finally, we extend Theta* to grids that contain unblocked cells with non-uniform traversal costs and introduce variants of Theta* which provide different tradeoffs between path length and runtime.

Because reinforcement learning suffers from a lack of scalability, online value (and Q-) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the following features: sample-efficiency, non-linear approximation, non-stationarity handling and uncertainty management. A first KTD-based algorithm is provided for deterministic Markov Decision Processes (MDP) which produces biased estimates in the case of stochastic transitions. Than the eXtended KTD framework (XKTD), solving stochastic MDP, is described. Convergence is analyzed for special cases for both deterministic and stochastic transitions. Related algorithms are experimented on classical benchmarks. They compare favorably to the state of the art while exhibiting the announced features.

Motivated by authentication, intrusion and spam detection applications we consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the learner has a sample from a target distribution and the goal is to construct a classifier capable of distinguishing observations from the target distribution from observations emitted from an unknown other distribution. The ideal SCC classifier must guarantee a given tolerance for the false-positive error (false alarm rate) while minimizing the false negative error (intruder pass rate). Viewing SCC as a two-person zero-sum game we identify both deterministic and randomized optimal classification strategies for different game variants. We demonstrate that randomized classification can provide a significant advantage. In the deterministic setting we show how to reduce SCC to two-class classification where in the two-class problem the other class is a synthetically generated distribution. We provide an efficient and practical algorithm for constructing and solving the two class problem. The algorithm distinguishes low density regions of the target distribution and is shown to be consistent.

The Random Projection Tree structures proposed in [Freund-Dasgupta STOC08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTreeMax and the RPTreeMean data structures. Our result for RPTreeMax gives a near-optimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor $s \geq 2$. We also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds have bounded Local Covariance Dimension. As a consequence we show that RPTreeMean adapts to manifold dimension as well.

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univariate marginals, and apply Kruskal's algorithm to estimate the optimal forest on held out data. We prove an oracle inequality on the excess risk of the resulting estimator relative to the risk of the best forest. For graph estimation, we consider the problem of estimating forests with restricted tree sizes. We prove that finding a maximum weight spanning forest with restricted tree size is NP-hard, and develop an approximation algorithm for this problem. Viewing the tree size as a complexity parameter, we then select a forest using data splitting, and prove bounds on excess risk and structure selection consistency of the procedure. Experiments with simulated data and microarray data indicate that the methods are a practical alternative to Gaussian graphical models.

Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR system as an extension to a SOAR-like problem solving architecture. The work is in a framework in which DR is modeled as a process where subtasks are solved, as appropriate, either by inference from symbolic representations or by interaction with a diagram, i.e., perceiving specified information from a diagram or modifying/creating objects in a diagram in specified ways according to problem solving needs. The perceptions and actions in most DR systems built so far are hand-coded for the specific application, even when the rest of the system is built using the general architecture. The absence of a general framework for executing perceptions/actions poses as a major hindrance to using them opportunistically -- the essence of open-ended search in problem solving. Our goal is to develop a framework for executing a wide variety of specified perceptions and actions across tasks/domains without human intervention. We observe that the domain/task-specific visual perceptions/actions can be transformed into domain/task-independent spatial problems. We specify a spatial problem as a quantified constraint satisfaction problem in the real domain using an open-ended vocabulary of properties, relations and actions involving three kinds of diagrammatic objects -- points, curves, regions. Solving a spatial problem from this specification requires computing the equivalent simplified quantifier-free expression, the complexity of which is inherently doubly exponential. We represent objects as configuration of simple elements to facilitate decomposition of complex problems into simpler and similar subproblems. We show that, if the symbolic solution to a subproblem can be expressed concisely, quantifiers can be eliminated from spatial problems in low-order polynomial time using similar previously solved subproblems. This requires determining the similarity of two problems, the existence of a mapping between them computable in polynomial time, and designing a memory for storing previously solved problems so as to facilitate search. The efficacy of the idea is shown by time complexity analysis. We demonstrate the proposed approach by executing perceptions and actions involved in DR tasks in two army applications.

So, we have a variety of people here with different interests and backgrounds that I asked to talk about not just the key challenges ahead but potential opportunities and promising pathways, trajectories to solving those problems, and their predictions about how R&D might proceed in terms of the timing of various kinds of development over time. I asked the panelists briefly to frame their comments sharing a little bit about fundamental questions, such as, "What is the research goal?" Not everybody stays up late at night hunched over a computer or a simulation or a robotic system, pondering the foundations of intelligence and human-level AI. We have here today Lise Getoor from the University ipate the liability and insurance industry; and the of Maryland; Devika Subramanian, who other one, that it was a human interface problem, comes to us from Rice University; we have Carlos that people don't necessarily want to go and type Guestrin from Carnegie Mellon University (CMU); a bunch of yes/no questions into a computer to get James Hendler from Rensselaer Polytechnic Institute an answer, even with a rule-based explanation, (RPI); Mike Wellman at the University of that if you'd taken that just a step further and Michigan; Henry Kautz at tjhe University of solved the human problem, it might have worked. Rochester; and Joe Konstan, who comes to us from Related to that, I was remembering a bunch of the Midwest, as our Minneapolis person here on these smart house projects. And I have to admit I the panel. I think everyone Joe Konstan: I was actually surprised when you hates smart spaces. I think of myself at the core there's nobody there, do you warn people and give in human-computer interaction. So I went back them a chance to answer? There's no good answer and started looking at what I knew of artificial to this question. I can tell you if that person is in intelligence to try to see where the path forward bed asleep, the answer is no, don't wake them up was, and I was inspired by the past.

IBM Research undertook a challenge to build a computer system that could compete at the human champion level in real time on the American TV Quiz show, Jeopardy! The extent of the challenge includes fielding a real-time automatic contestant on the show, not merely a laboratory exercise. The Jeopardy! Challenge helped us address requirements that led to the design of the DeepQA architecture and the implementation of Watson. After 3 years of intense research and development by a core team of about 20 researches, Watson is performing at human expert-levels in terms of precision, confidence and speed at the Jeopardy! Quiz show. Our results strongly suggest that DeepQA is an effective and extensible architecture that may be used as a foundation for combining, deploying, evaluating and advancing a wide range of algorithmic techniques to rapidly advance the field of QA.

The paper proposes artificial intelligence technique called hill climbing to find numerical solutions of Diophantine Equations. Such equations are important as they have many applications in fields like public key cryptography, integer factorization, algebraic curves, projective curves and data dependency in super computers. Importantly, it has been proved that there is no general method to find solutions of such equations. This paper is an attempt to find numerical solutions of Diophantine equations using steepest ascent version of Hill Climbing. The method, which uses tree representation to depict possible solutions of Diophantine equations, adopts a novel methodology to generate successors. The heuristic function used help to make the process of finding solution as a minimization process. The work illustrates the effectiveness of the proposed methodology using a class of Diophantine equations given by a1. x1 p1 + a2. x2 p2 + ...... + an . xn pn = N where ai and N are integers. The experimental results validate that the procedure proposed is successful in finding solutions of Diophantine Equations with sufficiently large powers and large number of variables.

The paper presents a scheme for computing lower and upper bounds on the posterior marginals in Bayesian networks with discrete variables. Its power lies in its ability to use any available scheme that bounds the probability of evidence or posterior marginals and enhance its performance in an anytime manner. The scheme uses the cutset conditioning principle to tighten existing bounding schemes and to facilitate anytime behavior, utilizing a fixed number of cutset tuples. The accuracy of the bounds improves as the number of used cutset tuples increases and so does the computation time. We demonstrate empirically the value of our scheme for bounding posterior marginals and probability of evidence using a variant of the bound propagation algorithm as a plug-in scheme.