Published experiments on spidering the Web suggest that, given training data in the form of a (relatively small) subgraph of the Web containing a subset of a selected class of target pages, it is possible to conduct a directed search and find additional target pages significantly faster (with fewer page retrievals) than by performing a blind or uninformed random or systematic search, e.g., breadth-first search. If true, this claim motivates a number of practical applications. Unfortunately, these experiments were carried out in specialized domains or under conditions that are difficult to replicate. We present and apply an experimental framework designed to reexamine and resolve the basic claims of the earlier work, so that the supporting experiments can be replicated and built upon. We provide high-performance tools for building experimental spiders, make use of the ground truth and static nature of the WT10g TREC Web corpus, and rely on simple well understand machine learning techniques to conduct our experiments. In this paper, we describe the basic framework, motivate the experimental design, and report on our findings supporting and qualifying the conclusions of the earlier research.

Precision achieved by stochastic sampling algorithms for Bayesian networks typically deteriorates in face of extremely unlikely evidence. To address this problem, we propose the Evidence Pre-propagation Importance Sampling algorithm (EPIS-BN), an importance sampling algorithm that computes an approximate importance function by the heuristic methods: loopy belief Propagation and e-cutoff. We tested the performance of e-cutoff on three large real Bayesian networks: ANDES, CPCS, and PATHFINDER. We observed that on each of these networks the EPIS-BN algorithm gives us a considerable improvement over the current state of the art algorithm, the AIS-BN algorithm. In addition, it avoids the costly learning stage of the AIS-BN algorithm.

A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most commonly discussed frequentist notions are pointwise consistency and uniform consistency. Uniform consistency is in general preferred to pointwise consistency because the former allows us to control the worst case error bounds with a finite sample size. In the sense of pointwise consistency, several reliable causal inference algorithms have been established under the Markov and Faithfulness assumptions [Pearl 2000, Spirtes et al. 2001]. In the sense of uniform consistency, however, reliable causal inference is impossible under the two assumptions when time order is unknown and/or latent confounders are present [Robins et al. 2000]. In this paper we present two natural generalizations of the Faithfulness assumption in the context of structural equation models, under which we show that the typical algorithms in the literature (in some cases with modifications) are uniformly consistent even when the time order is unknown. We also discuss the situation where latent confounders may be present and the sense in which the Faithfulness assumption is a limiting case of the stronger assumptions.

The paper explores the power of two systematic Branch and Bound search algorithms that exploit partition-based heuristics, BBBT (a new algorithm for which the heuristic information is constructed during search and allows dynamic variable/value ordering) and its predecessor BBMB (for which the heuristic information is pre-compiled) and compares them against a number of popular local search algorithms for the MPE problem as well as against the recently popular iterative belief propagation algorithms. We show empirically that the new Branch and Bound algorithm, BBBT demonstrates tremendous pruning of the search space far beyond its predecessor, BBMB which translates to impressive time saving for some classes of problems. Second, when viewed as approximation schemes, BBBT/BBMB together are highly competitive with the best known SLS algorithms and are superior, especially when the domain sizes increase beyond 2. The results also show that the class of belief propagation algorithms can outperform SLS, but they are quite inferior to BBMBIBBBT. As far as we know, BBBT/BBMB are currently among the best performing algorithms for solving the MPE task.

The property of perfectness plays an important role in the theory of Bayesian networks. First, the existence of perfect distributions for arbitrary sets of variables and directed acyclic graphs implies that various methods for reading independence from the structure of the graph (e.g., Pearl, 1988; Lauritzen, Dawid, Larsen & Leimer, 1990) are complete. Second, the asymptotic reliability of various search methods is guaranteed under the assumption that the generating distribution is perfect (e.g., Spirtes, Glymour & Scheines, 2000; Chickering & Meek, 2002). We provide a lower-bound on the probability of sampling a non-perfect distribution when using a fixed number of bits to represent the parameters of the Bayesian network. This bound approaches zero exponentially fast as one increases the number of bits used to represent the parameters. This result implies that perfect distributions with fixed-length representations exist. We also provide a lower-bound on the number of bits needed to guarantee that a distribution sampled from a uniform Dirichlet distribution is perfect with probability greater than 1/2. This result is useful for constructing randomized reductions for hardness proofs.

For a given problem, the optimal Markov policy can be considerred as a conditional or contingent plan containing a (potentially large) number of branches. Unfortunately, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. For example, it may be that plans must later undergo more detailed simulation to verify correctness and safety, or that they must be simple enough to be understood and analyzed by humans. As a result, it may be necessary to limit consideration to plans with only a small number of branches. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning (OKP). It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a Partially Observable Markov Decision Process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.

The aim of this research is to develop a reasoning under uncertainty strategy in the context of the Fuzzy Inductive Reasoning (FIR) methodology. FIR emerged from the General Systems Problem Solving developed by G. Klir. It is a data driven methodology based on systems behavior rather than on structural knowledge. It is a very useful tool for both the modeling and the prediction of those systems for which no previous structural knowledge is available. FIR reasoning is based on pattern rules synthesized from the available data. The size of the pattern rule base can be very large making the prediction process quite difficult. In order to reduce the size of the pattern rule base, it is possible to automatically extract classical Sugeno fuzzy rules starting from the set of pattern rules. The Sugeno rule base preserves pattern rules knowledge as much as possible. In this process some information is lost but robustness is considerably increased. In the forecasting process either the pattern rule base or the Sugeno fuzzy rule base can be used. The first option is desirable when the computational resources make it possible to deal with the overall pattern rule base or when the extracted fuzzy rules are not accurate enough due to uncertainty associated to the original data. In the second option, the prediction process is done by means of the classical Sugeno inference system. If the amount of uncertainty associated to the data is small, the predictions obtained using the Sugeno fuzzy rule base will be very accurate. In this paper a mixed pattern/fuzzy rules strategy is proposed to deal with uncertainty in such a way that the best of both perspectives is used. Areas in the data space with a higher level of uncertainty are identified by means of the so-called error models. The prediction process in these areas makes use of a mixed pattern/fuzzy rules scheme, whereas areas identified with a lower level of uncertainty only use the Sugeno fuzzy rule base. The proposed strategy is applied to a real biomedical system, i.e., the central nervous system control of the cardiovascular system.

This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus exploring different good local optima. When greediness is set at maximum, KES corresponds to the greedy equivalence search algorithm (GES). When greediness is kept at minimum, we prove that under mild assumptions KES asymptotically returns any inclusion optimal BN with nonzero probability. Experimental results for both synthetic and real data are reported showing that KES often finds a better local optima than GES. Moreover, we use KES to experimentally confirm that the number of different local optima is often huge.

Group elevator scheduling is an NPhard sequential decision-making problem with unbounded state spaces and substantial uncertainty. Decision-theoretic reasoning plays a surprisingly limited role in fielded systems. A new opportunity for probabilistic methods has opened with the recent discovery of a tractable solution for the expected waiting times of all passengers in the building, marginalized over all possible passenger itineraries [Nikovski and Brand, 2003]. Though commercially competitive, this solution does not contemplate future passengers. Yet in up-peak traffic, the effects of future passengers arriving at the lobby and entering elevator cars can dominate all waiting times. We develop a probabilistic model of how these arrivals affect the behavior of elevator cars at the lobby, and demonstrate how this model can be used to very significantly reduce the average waiting time of all passengers.

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of structural solutions for MAP are not only exponential in the network treewidth, but in a larger parameter known as the "constrained" treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computing posterior probabilities or MPE. This paper introduces a new, simple upper bound on the probability of a MAP solution, which admits a tradeoff between the bound quality and the time needed to compute it. The bound is shown to be generally much tighter than those of other methods of comparable complexity. We use this proposed upper bound to develop a branch-and-bound search algorithm for solving MAP exactly. Experimental results demonstrate that the search algorithm is able to solve many problems that are far beyond the reach of any structure-based method for MAP. For example, we show that the proposed algorithm can compute MAP exactly and efficiently for some networks whose constrained treewidth is more than 40.