We consider the problem of approximate belief-state monitoring using particle filtering for the purposes of implementing a policy for a partially-observable Markov decision process (POMDP). While particle filtering has become a widely-used tool in AI for monitoring dynamical systems, rather scant attention has been paid to their use in the context of decision making. Assuming the existence of a value function, we derive error bounds on decision quality associated with filtering using importance sampling. We also describe an adaptive procedure that can be used to dynamically determine the number of samples required to meet specific error bounds. Empirical evidence is offered supporting this technique as a profitable means of directing sampling effort where it is needed to distinguish policies.

We propose a new approach to value-directed belief state approximation for POMDPs. The value-directed model allows one to choose approximation methods for belief state monitoring that have a small impact on decision quality. Using a vector space analysis of the problem, we devise two new search procedures for selecting an approximation scheme that have much better computational properties than existing methods. Though these provide looser error bounds, we show empirically that they have a similar impact on decision quality in practice, and run up to two orders of magnitude more quickly.

There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be intractable for many nonrecursive models and impossible in the general case for recursive problems, several research groups are actively developing computational techniques for recursive stochastic languages. We have developed an extension to the traditional lambda-calculus as a framework for families of Turing complete stochastic languages. We have also developed a class of exact inference algorithms based on the traditional reductions of the lambda-calculus. We further propose that using the deBruijn notation (a lambda-calculus notation with nameless dummies) supports effective caching in such systems (caching being an essential component of efficient computation). Finally, our extension to the lambda-calculus offers a foundation and general theory for the construction of recursive stochastic modeling languages as well as promise for effective caching and efficient approximation algorithms for inference.

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what circumstances are the marginal distributions over the conditioning variables sufficient to determine the probability ofthe conditioned variable?Sufficiency in this sense is equivalent to additive separability ofthe conditional probability distribution.Such separability structure is natural and can be exploited forefficient inference.Separability has a natural generalization to conditional separability.Separability provides a precise notion of weaklyinteracting subsystems in temporal probabilistic models.Given a system that is decomposed into separable subsystems, exactmarginal probabilities over subsystems at future points in time can becomputed by propagating marginal subsystem probabilities, rather thancomplete system joint probabilities.Thus, separability can make exact prediction tractable.However, observations can break separability,so exact monitoring of dynamic systems remains hard.

The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given evidence. Unlike computing marginals, posteriors, and MPE (a special case of MAP), the time and space complexity of MAP is not only exponential in the network treewidth, but also in a larger parameter known as the "constrained" treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computingposteriors or MPE. Thus, practitioners generally avoid MAP computations, resorting instead to approximating them by the most likely value for each MAP variableseparately, or by MPE.We present a method for approximating MAP using local search. This method has space complexity which is exponential onlyin the treewidth, as is the complexity of each search step. We investigate the effectiveness of different local searchmethods and several initialization strategies and compare them to otherapproximation schemes.Experimental results show that local search provides a much more accurate approximation of MAP, while requiring few search steps.Practically, this means that the complexity of local search is often exponential only in treewidth as opposed to the constrained treewidth, making approximating MAP as efficient as other computations.

A standard approach to approximate inference in state-space models isto apply a particle filter, e.g., the Condensation Algorithm.However, the performance of particle filters often varies significantlydue to their stochastic nature.We present a class of algorithms, called lattice particle filters, thatcircumvent this difficulty by placing the particles deterministicallyaccording to a Quasi-Monte Carlo integration rule.We describe a practical realization of this idea, discuss itstheoretical properties, and its efficiency.Experimental results with a synthetic 2D tracking problem show that thelattice particle filter is equivalent to a conventional particle filterthat has between 10 and 60% more particles, depending ontheir "sparsity" in the state-space.We also present results on inferring 3D human motion frommoving light displays.

Most successful Bayesian network (BN) applications to datehave been built through knowledge elicitation from experts.This is difficult and time consuming, which has lead to recentinterest in automated methods for learning BNs from data. We present a case study in the construction of a BN in anintelligent tutoring application, specifically decimal misconceptions. Wedescribe the BN construction using expert elicitation and then investigate how certainexisting automated knowledge discovery methods might support the BN knowledge engineering process.

The Factored Frontier (FF) algorithm is a simple approximate inferencealgorithm for Dynamic Bayesian Networks (DBNs). It is very similar tothe fully factorized version of the Boyen-Koller (BK) algorithm, butinstead of doing an exact update at every step followed bymarginalisation (projection), it always works with factoreddistributions. Hence it can be applied to models for which the exactupdate step is intractable. We show that FF is equivalent to (oneiteration of) loopy belief propagation (LBP) on the original DBN, andthat BK is equivalent (to one iteration of) LBP on a DBN where wecluster some of the nodes. We then show empirically that byiterating, LBP can improve on the accuracy of both FF and BK. Wecompare these algorithms on two real-world DBNs: the first is a modelof a water treatment plant, and the second is a coupled HMM, used tomodel freeway traffic.

We propose using recognition networks for approximate inference inBayesian networks (BNs). A recognition network is a multilayerperception (MLP) trained to predict posterior marginals given observedevidence in a particular BN. The input to the MLP is a vector of thestates of the evidential nodes. The activity of an output unit isinterpreted as a prediction of the posterior marginal of thecorresponding variable. The MLP is trained using samples generated fromthe corresponding BN.We evaluate a recognition network that was trained to do inference ina large Bayesian network, similar in structure and complexity to theQuick Medical Reference, Decision Theoretic (QMR-DT). Our networkis a binary, two-layer, noisy-OR network containing over 4000 potentially observable nodes and over 600 unobservable, hidden nodes. Inreal medical diagnosis, most observables are unavailable, and there isa complex and unknown bias that selects which ones are provided. Weincorporate a very basic type of selection bias in our network: a knownpreference that available observables are positive rather than negative.Even this simple bias has a significant effect on the posterior. We compare the performance of our recognition network tostate-of-the-art approximate inference algorithms on a large set oftest cases. In order to evaluate the effect of our simplistic modelof the selection bias, we evaluate algorithms using a variety ofincorrectly modeled observation biases. Recognition networks performwell using both correct and incorrect observation biases.