The Dempster-Shafer theory of evidence accumulation is one of the main tools for combining data obtained from multiple sources. In this paper a special case of combination of two bodies of evidence with non-zero conflict coefficient is considered. It is shown that application of the Dempster-Shafer rule of combination in this case leads to an evaluation of masses of the combined bodies that is different from the evaluation of the corresponding probabilities obtained by application of the law of total probability. This finding supports the view that probabilistic interpretation of results of the Dempster-Shafer analysis in the general case is not appropriate.

In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is pi ^2 /6 the number of cities goes to infinity. In addition, we show that the average computational cost of the well-known branch-and-bound subtour elimination algorithm for the problem also exhibits a thrashing behavior, transitioning from easy to difficult as the distance precision increases. These results answer positively an open question regarding the existence of phase transitions in the ATSP, and provide guidance on how difficult ATSP problem instances should be generated.

We propose a model for errors in sung queries, a variant of the hidden Markov model (HMM). This is a solution to the problem of identifying the degree of similarity between a (typically error-laden) sung query and a potential target in a database of musical works, an important problem in the field of music information retrieval. Similarity metrics are a critical component of query-by-humming (QBH) applications which search audio and multimedia databases for strong matches to oral queries. Our model comprehensively expresses the types of error or variation between target and query: cumulative and non-cumulative local errors, transposition, tempo and tempo changes, insertions, deletions and modulation. The model is not only expressive, but automatically trainable, or able to learn and generalize from query examples. We present results of simulations, designed to assess the discriminatory potential of the model, and tests with real sung queries, to demonstrate relevance to real-world applications.

This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We focus on six prominent prediction algorithms, including Context Tree Weighting (CTW), Prediction by Partial Match (PPM) and Probabilistic Suffix Trees (PSTs). We discuss the properties of these algorithms and compare their performance using real life sequences from three domains: proteins, English text and music pieces. The comparison is made with respect to prediction quality as measured by the average log-loss. We also compare classification algorithms based on these predictors with respect to a number of large protein classification tasks. Our results indicate that a "decomposed" CTW (a variant of the CTW algorithm) and PPM outperform all other algorithms in sequence prediction tasks. Somewhat surprisingly, a different algorithm, which is a modification of the Lempel-Ziv compression algorithm, significantly outperforms all algorithms on the protein classification problems.

We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases, which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously, we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective, while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem.

In this paper, we confront the problem of applying reinforcement learning to agents that perceive the environment through many sensors and that can perform parallel actions using many actuators as is the case in complex autonomous robots. We argue that reinforcement learning can only be successfully applied to this case if strong assumptions are made on the characteristics of the environment in which the learning is performed, so that the relevant sensor readings and motor commands can be readily identified. The introduction of such assumptions leads to strongly-biased learning systems that can eventually lose the generality of traditional reinforcement-learning algorithms. In this line, we observe that, in realistic situations, the reward received by the robot depends only on a reduced subset of all the executed actions and that only a reduced subset of the sensor inputs (possibly different in each situation and for each action) are relevant to predict the reward. We formalize this property in the so called 'categorizability assumption' and we present an algorithm that takes advantage of the categorizability of the environment, allowing a decrease in the learning time with respect to existing reinforcement-learning algorithms. Results of the application of the algorithm to a couple of simulated realistic-robotic problems (landmark-based navigation and the six-legged robot gait generation) are reported to validate our approach and to compare it to existing flat and generalization-based reinforcement-learning approaches.

The difficulty in solving optimally such problems arises when the agents lack full observability of the global state of the system when they operate. The general problem has been shown to be NEXP-complete. In this paper, we identify classes of decentralized control problems whose complexity ranges between NEXP and P. In particular, we study problems characterized by independent transitions, independent observations, and goal-oriented objective functions. Two algorithms are shown to solve optimally useful classes of goal-oriented decentralized processes in polynomial time. This paper also studies information sharing among the decision-makers, which can improve their performance. We distinguish between three ways in which agents can exchange information: indirect communication, direct communication and sharing state features that are not controlled by the agents. Our analysis shows that for every class of problems we consider, introducing direct or indirect communication does not change the worst-case complexity. The results provide a better understanding of the complexity of decentralized control problems that arise in practice and facilitate the development of planning algorithms for these problems.

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space.

Argumentation is based on the exchange and valuation of interacting arguments, followed by the selection of the most acceptable of them (for example, in order to take a decision, to make a choice). Starting from the framework proposed by Dung in 1995, our purpose is to introduce 'graduality' in the selection of the best arguments, i.e., to be able to partition the set of the arguments in more than the two usual subsets of 'selected' and 'non-selected' arguments in order to represent different levels of selection. Our basic idea is that an argument is all the more acceptable if it can be preferred to its attackers. First, we discuss general principles underlying a 'gradual' valuation of arguments based on their interactions. Following these principles, we define several valuation models for an abstract argumentation system. Then, we introduce 'graduality' in the concept of acceptability of arguments. We propose new acceptability classes and a refinement of existing classes taking advantage of an available 'gradual' valuation.

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas.