Above are papers related to the following paper: [Paper_ID] Paper #189721. 	[Title] Sensitivities: An Alternative to Conditional Probabilities for Bayesian Belief Networks [Abstract] We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies between nodes apparent and intuitively easy to understand. We also propose a QR matrix representation for the sensitivities and/or conditional probabilities which is more efficient, in both memory requirements and computational speed, than the traditional representation for computer-based implementations of probabilistic inference. We use sensitivities to show that for a certain class of binary networks, the computation time for approximate probabilistic inference with any positive upper bound on the error of the result is independent of the size of the network. Finally, as an alternative to traditional algorithms that use conditional probabilities, we describe an exact algorithm for probabilistic inference that uses the QR-representation for sensitivities and updates probability distributions of nodes in a network according to messages from the neigh bors. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #189856. 	[Title] State-Space Abstraction for Anytime Evaluation of Probabilistic Networks [Abstract] One important factor determining the computa - tional 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 any - time procedure for approximate evaluation of probabilistic networks based on this idea. On application to some simple networks, the proce - dure exhibits a smooth improvement in approxi - mation quality as computation time increases. This suggests that statespace abstraction is one more useful control parameter for designing real-time probabilistic reasoners. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1123756. 	[Title] Case-Based Probability Factoring in Bayesian Belief Networks [Abstract] Bayesian network inference can be formulated as a combinatorial optimization problem, concerning in the computation of an optimal factoring for the distribution represented in the net. Since the determination of an optimal factoring is a computationally hard problem, heuristic greedy strategies able to find approximations of the optimal factoring are usually adopted. In the present paper we investigate an alternative approach based on a combination of genetic algorithms (GA) and case-based reasoning (CBR). We show how the use of genetic algorithms can improve the quality of the computed factoring in case a static strategy is used (as for the MPE computation), while the combination of GA and CBR can still provide advantages in the case of dynamic strategies. Some preliminary results on different kinds of nets are then reported. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1129518. 	[Title] Computational complexity reduction for BN2O networks using similarity of states [Abstract] Although probabilistic inference in a general Bayesian belief network is an NP-hard problem, inference computation time can be reduced in most practical cases by exploiting domain knowledge and by making appropriate approximations in the knowledge representation. In this paper we introduce the property of similarity of states and a new method for approximate knowledge representation which is based on this property. We define two or more states of a node to be similar when the likelihood ratio of their probabilities 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 computational complexity of probabilistic inference in networks with multiple similar states. For example, we show that a BN2O network|a two layer networks often used in diagnostic problems|can be reduced to a very close network with multiple similar states. Probabilistic inference in the new network can be done in only polynomial time with respect to the size of the network, and the results for queries of practical importance are very close to the results that can be obtained in exponential time with the original network. The error introduced by our reduction converges to zero faster than exponentially with respect to the degree of the polynomial describing the resulting computational complexity. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #124952. 	[Title] Efficient Inference in Bayes Networks As A Combinatorial Optimization Problem [Abstract] A number of exact algorithms have been developed to perform probabilistic inference in Bayesian belief networks in recent years. The techniques used in these algorithms are closely related to network structures and some of them are not easy to understand and implement. In this paper, we consider the problem from the combinatorial optimization point of view and state that efficient probabilistic inference in a belief network is a problem of finding an optimal factoring given a set of probability distributions. From this viewpoint, previously developed algorithms can be seen as alternate factoring strategies. In this paper, we define a combinatorial optimization problem, the optimal factoring problem, and discuss application of this problem in belief networks. We show that optimal factoring provides insight into the key elements of efficient probabilistic inference, and demonstrate simple, easily implemented algorithms with excellent performance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1126011. 	[Title] Algebraic Techniques for Efficient Inference in Bayesian Networks [Abstract] A number of exact algorithms have been developed to perform probabilistic inference in Bayesian belief networks in recent years. These algorithms use graph-theoretic techniques to analyze and exploit network topology. In this paper, we examine the problem of efficient probabilistic inference in a belief network as a combinatorial optimization problem, that of finding an optimal factoring given an algebraic expression over a set of probability distributions. We define a combinatorial optimization problem, the optimal factoring problem, and discuss application of this problem in belief networks. We show that optimal factoring provides insight into the key elements of efficient probabilistic inference, and present simple, easily implemented algorithms with excellent performance. We also show how use of an algebraic perspective permits significant extension to the belief net representation. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1126012. 	[Title] Some Experiments with Real-time Decision Algorithms [Abstract] 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 [DAmbrosio, 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. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1119742. 	[Title] Interpretation of Complex Scenes Using Bayesian Networks [Abstract] In most object recognition systems, interactions between objects in a scene are ignored and the best interpretation is considered to be the set of hypothesized objects that matches the greatest number of image features. We show how image interpretation can be cast as the problem of finding the most probable explanation (MPE) in a Bayesian network that models both visual and physical object interactions. The problem of how to determine exact conditional probabilities for the network is shown to be unimportant, since the goal is to find the most probable configuration of objects, not to calculate absolute probabilities. We furthermore show that evaluating configurations by feature counting is equivalent to calculating the joint probability of the configuration using a restricted Bayesian network, and derive the assumptions about probabilities necessary to make a Bayesian formulation reasonable. Please summarise all the given information.

Paper #189721 has the title `Sensitivities: An Alternative to Conditional Probabilities for Bayesian Belief Networks  
` and the abstract `We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies between nodes apparent and intuitively easy to understand. We also propose a QR matrix representation for the sensitivities and/or conditional probabilities which is more efficient, in both memory requirements and computational speed, than the traditional representation for computer-based implementations of probabilistic inference. We use sensitivities to show that for a certain class of binary networks, the computation time for approximate probabilistic inference with any positive upper bound on the error of the result is independent of the size of the network. Finally, as an alternative to traditional algorithms that use conditional probabilities, we describe an exact algorithm for probabilistic inference that uses the QR-representation for sensitivities and updates probability distributions of nodes in a network according to messages from the neigh bors.
`.
Question: Which category should Paper #189721 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #189721 has the title `Sensitivities: An Alternative to Conditional Probabilities for Bayesian Belief Networks  
` and the abstract `We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies between nodes apparent and intuitively easy to understand. We also propose a QR matrix representation for the sensitivities and/or conditional probabilities which is more efficient, in both memory requirements and computational speed, than the traditional representation for computer-based implementations of probabilistic inference. We use sensitivities to show that for a certain class of binary networks, the computation time for approximate probabilistic inference with any positive upper bound on the error of the result is independent of the size of the network. Finally, as an alternative to traditional algorithms that use conditional probabilities, we describe an exact algorithm for probabilistic inference that uses the QR-representation for sensitivities and updates probability distributions of nodes in a network according to messages from the neigh bors.
`.
Question: Which category should Paper #189721 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods