State-space Abstraction for Anytime Evaluation of Probabilistic Networks

One important factor determining the computational complexity of evaluating a probabilistic network is the cardinality of the state spaces of the nodes. By varying the granularity of the state spaces, one can trade off accuracy in the result for computational efficiency. We present an anytime procedure for approximate evaluation of probabilistic networks based on this idea. On application to some simple networks, the procedure exhibits a smooth improvement in approximation quality as computation time increases. This suggests that state-space abstraction is one more useful control parameter for designing real-time probabilistic reasoners.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Some Experiments with Real-Time Decision Algorithms

Real-time Decision algorithms are a class of incremental resource-bounded [Horvitz, 89] or anytime [Dean, 93] algorithms for evaluating influence diagrams. We present a test domain for real-time decision algorithms, and the results of experiments with several Real-time Decision Algorithms in this domain. The results demonstrate high performance for two algorithms, a decision-evaluation variant of Incremental Probabilisitic Inference [D'Ambrosio 93] and a variant of an algorithm suggested by Goldszmidt, [Goldszmidt, 95], PK-reduced. We discuss the implications of these experimental results and explore the broader applicability of these algorithms.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Incremental Tradeoff Resolution in Qualitative Probabilistic Networks

Qualitative probabilistic reasoning in a Bayesian network often reveals tradeoffs: relationships that are ambiguous due to competing qualitative influences. We present two techniques that combine qualitative and numeric probabilistic reasoning to resolve such tradeoffs, inferring the qualitative relationship between nodes in a Bayesian network. The first approach incrementally marginalizes nodes that contribute to the ambiguous qualitative relationships. The second approach evaluates approximate Bayesian networks for bounds of probability distributions, and uses these bounds to determinate qualitative relationships in question. This approach is also incremental in that the algorithm refines the state spaces of random variables for tighter bounds until the qualitative relationships are resolved. Both approaches provide systematic methods for tradeoff resolution at potentially lower computational cost than application of purely numeric methods.Comment: Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998

Abstraction in Belief Networks: The Role of Intermediate States in Diagnostic Reasoning

Bayesian belief networks are bing increasingly used as a knowledge representation for diagnostic reasoning. One simple method for conducting diagnostic reasoning is to represent system faults and observations only. In this paper, we investigate how having intermediate nodes-nodes other than fault and observation nodes affects the diagnostic performance of a Bayesian belief network. We conducted a series of experiments on a set of real belief networks for medical diagnosis in liver and bile disease. We compared the effects on diagnostic performance of a two-level network consisting just of disease and finding nodes with that of a network which models intermediate pathophysiological disease states as well. We provide some theoretical evidence for differences observed between the abstracted two-level network and the full network.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Computational Complexity Reduction for BN2O Networks Using Similarity of States

Although probabilistic inference in a general Bayesian belief network is an NP-hard problem, computation time for inference can be reduced in most practical cases by exploiting domain knowledge and by making approximations in the knowledge representation. In this paper we introduce the property of similarity of states and a new method for approximate knowledge representation and inference which is based on this property. We define two or more states of a node to be similar when the ratio of their probabilities, the likelihood ratio, does not depend on the instantiations of the other nodes in the network. We show that the similarity of states exposes redundancies in the joint probability distribution which can be exploited to reduce the computation time of probabilistic inference in networks with multiple similar states, and that the computational complexity in the networks with exponentially many similar states might be polynomial. We demonstrate our ideas on the example of a BN2O network -- a two layer network often used in diagnostic problems -- by reducing it to a very close network with multiple similar states. We show that the answers to practical queries converge very fast to the answers obtained with the original network. The maximum error is as low as 5% for models that require only 10% of the computation time needed by the original BN2O model.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

A Graph-Theoretic Analysis of Information Value

We derive qualitative relationships about the informational relevance of variables in graphical decision models based on a consideration of the topology of the models. Specifically, we identify dominance relations for the expected value of information on chance variables in terms of their position and relationships in influence diagrams. The qualitative relationships can be harnessed to generate nonnumerical procedures for ordering uncertain variables in a decision model by their informational relevance.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Fast Belief Update Using Order-of-Magnitude Probabilities

We present an algorithm, called Predict, for updating beliefs in causal networks quantified with order-of-magnitude probabilities. The algorithm takes advantage of both the structure and the quantification of the network and presents a polynomial asymptotic complexity. Predict exhibits a conservative behavior in that it is always sound but not always complete. We provide sufficient conditions for completeness and present algorithms for testing these conditions and for computing a complete set of plausible values. We propose Predict as an efficient method to estimate probabilistic values and illustrate its use in conjunction with two known algorithms for probabilistic inference. Finally, we describe an application of Predict to plan evaluation, present experimental results, and discuss issues regarding its use with conditional logics of belief, and in the characterization of irrelevance.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Likelihood Computations Using Value Abstractions

In this paper, we use evidence-specific value abstraction for speeding Bayesian networks inference. This is done by grouping variable values and treating the combined values as a single entity. As we show, such abstractions can exploit regularities in conditional probability distributions and also the specific values of observed variables. To formally justify value abstraction, we define the notion of safe value abstraction and devise inference algorithms that use it to reduce the cost of inference. Our procedure is particularly useful for learning complex networks with many hidden variables. In such cases, repeated likelihood computations are required for EM or other parameter optimization techniques. Since these computations are repeated with respect to the same evidence set, our methods can provide significant speedup to the learning procedure. We demonstrate the algorithm on genetic linkage problems where the use of value abstraction sometimes differentiates between a feasible and non-feasible solution.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000

Max-Entropy Feed-Forward Clustering Neural Network

The outputs of non-linear feed-forward neural network are positive, which could be treated as probability when they are normalized to one. If we take Entropy-Based Principle into consideration, the outputs for each sample could be represented as the distribution of this sample for different clusters. Entropy-Based Principle is the principle with which we could estimate the unknown distribution under some limited conditions. As this paper defines two processes in Feed-Forward Neural Network, our limited condition is the abstracted features of samples which are worked out in the abstraction process. And the final outputs are the probability distribution for different clusters in the clustering process. As Entropy-Based Principle is considered into the feed-forward neural network, a clustering method is born. We have conducted some experiments on six open UCI datasets, comparing with a few baselines and applied purity as the measurement . The results illustrate that our method outperforms all the other baselines that are most popular clustering methods.Comment: This paper has been published in ICANN 201

Learning the Dimensionality of Hidden Variables

A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the relations to other variables in the model and determining the number of states of the hidden variable. In this paper, we address the latter problem in the context of Bayesian networks. We describe an approach that utilizes a score-based agglomerative state-clustering. As we show, this approach allows us to efficiently evaluate models with a range of cardinalities for the hidden variable. We show how to extend this procedure to deal with multiple interacting hidden variables. We demonstrate the effectiveness of this approach by evaluating it on synthetic and real-life data. We show that our approach learns models with hidden variables that generalize better and have better structure than previous approaches.Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001