Above are papers related to the following paper: [Paper_ID] Paper #683355. 	[Title] Using Qualitative Relationships for Bounding Probability Distributions [Abstract] We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction operations that are guaranteed to bound the distributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distributions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1129994. 	[Title] Sonderforschungsbereich 314 K unstliche Intelligenz Wissensbasierte Systeme KI-Labor am Lehrstuhl f ur Informatik IV Numerical [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #683404. 	[Title] Incremental Tradeoff Resolution in Qualitative Probabilistic Networks [Abstract] 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. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #159897. 	[Title] Robustness Analysis of Bayesian Networks with Finitely Generated Convex Sets of Distributions [Abstract] This paper presents exact solutions and convergent approximations for inferences in Bayesian networks associated with finitely generated convex sets of distributions. Robust Bayesian inference is the calculation of bounds on posterior values given perturbations in a probabilistic model. The paper presents exact inference algorithms and analyzes the circumstances where exact inference becomes intractable. Two classes of algorithms for numeric approximations are developed through transformations on the original model. The first transformation reduces the robust inference problem to the estimation of probabilistic parameters in a Bayesian network. The second transformation uses Lavine's bracketing algorithm to generate a sequence of maximization problems in a Bayesian network. The analysis is extended to the *-contaminated, the lower density bounded, the belief function, the sub-sigma, the density bounded, the total variation and the density ratio classes of distributions. c fl1996 Carnegie Mellon University Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #28957. 	[Title] Operations for Learning with Graphical Models decomposition techniques and the demonstration that graphical models provide [Abstract] This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. 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 #50337. 	[Title] Recursive algorithms for approximating probabilities in graphical models [Abstract] MIT Computational Cognitive Science Technical Report 9604 Abstract We develop a recursive node-elimination formalism for efficiently approximating large probabilistic networks. No constraints are set on the network topologies. Yet the formalism can be straightforwardly integrated with exact methods whenever they are/become applicable. The approximations we use are controlled: they maintain consistently upper and lower bounds on the desired quantities at all times. We show that Boltzmann machines, sigmoid belief networks, or any combination (i.e., chain graphs) can be handled within the same framework. The accuracy of the methods is verified exper imentally. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #50336. 	[Title] Computing upper and lower bounds on likelihoods in intractable networks [Abstract] We present deterministic techniques for computing upper and lower bounds on marginal probabilities in sigmoid and noisy-OR networks. These techniques become useful when the size of the network (or clique size) precludes exact computations. We illustrate the tightness of the bounds by numerical experi ments. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #6818. 	[Title] Exploiting Tractable Substructures in Intractable Networks [Abstract] We develop a refined mean field approximation for inference and learning in probabilistic neural networks. Our mean field theory, unlike most, does not assume that the units behave as independent degrees of freedom; instead, it exploits in a principled way the existence of large substructures that are computationally tractable. To illustrate the advantages of this framework, we show how to incorporate weak higher order interactions into a first-order hidden Markov model, treating the corrections (but not the first order structure) within mean field theory. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #108962. 	[Title] BUCKET ELIMINATION: A UNIFYING FRAMEWORK FOR PROBABILISTIC INFERENCE [Abstract] Probabilistic inference algorithms for belief updating, finding the most probable explanation, the maximum a posteriori hypothesis, and the maximum expected utility are reformulated within the bucket elimination framework. This emphasizes the principles common to many of the algorithms appearing in the probabilistic inference literature and clarifies the relationship of such algorithms to nonserial dynamic programming algorithms. A general method for combining conditioning and bucket elimination is also presented. For all the algorithms, bounds on complexity are given as a function of the problem's structure. 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 #108983. 	[Title] Exploiting Causal Independence in Bayesian Network Inference [Abstract] A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as or, sum or max, on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #189623. 	[Title] Localized Partial Evaluation of Belief Networks [Abstract] in the network. Often, however, an application will not need information about every node in the network nor will it need exact probabilities. We present the localized partial evaluation (LPE) propagation algorithm, which computes interval bounds on the marginal probability of a specified query node by examining a subset of the nodes in the entire network. Conceptually, LPE ignores parts of the network that are "too far away" from the queried node to have much impact on its value. LPE has the "anytime" property of being able to produce better solutions (tighter intervals) given more time to consider more of the network. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #36802. 	[Title] Dynamic Belief Networks for Discrete Monitoring [Abstract] We describe the development of a monitoring system which uses sensor observation data about discrete events to construct dynamically a probabilistic model of the world. This model is a Bayesian network incorporating temporal aspects, which we call a Dynamic Belief Network; it is used to reason under uncertainty about both the causes and consequences of the events being monitored. The basic dynamic construction of the network is data-driven. However the model construction process combines sensor data about events with externally provided information about agents' behaviour, and knowledge already contained within the model, to control the size and complexity of the network. This means that both the network structure within a time interval, and the amount of history and detail maintained, can vary over time. We illustrate the system with the example domain of monitoring robot vehicles and people in a restricted dynamic environment using light-beam sensor data. In addition to presenting a generic network structure for monitoring domains, we describe the use of more complex network structures which address two specific monitoring problems, sensor validation and the Data Association Problem. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #35922. 	[Title] Mean Field Theory for Sigmoid Belief Networks [Abstract] We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition|the classification of handwritten digits. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #13269. 	[Title] database [Abstract] MIT Computational Cognitive Science Technical Report 9701 Abstract We describe variational approximation methods for efficient probabilistic reasoning, applying these methods to the problem of diagnostic inference in the QMR-DT database. The QMR-DT database is a large-scale belief network based on statistical and expert knowledge in internal medicine. The size and complexity of this network render exact probabilistic diagnosis infeasible for all but a small set of cases. This has hindered the development of the QMR- DT network as a practical diagnostic tool and has hindered researchers from exploring and critiquing the diagnostic behavior of QMR. In this paper we describe how variational approximation methods can be applied to the QMR network, resulting in fast diagnostic inference. We evaluate the accuracy of our methods on a set of standard diagnostic cases and compare to stochastic sampling methods. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #683360. 	[Title] Some Varieties of Qualitative Probability [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #390894. 	[Title] A variational approach to Bayesian logistic regression models and their extensions [Abstract] We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that accurate variational techniques can be used to obtain a closed form posterior distribution over the parameters given the data thereby yielding a posterior predictive model. The results are readily extended to (binary) belief networks. For belief networks we also derive closed form posteriors in the presence of missing values. Finally, we show that the dual of the regression problem gives a latent variable density model, the variational formulation of which leads to exactly solvable EM updates. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #310653. 	[Title] Robustness Analysis of Bayesian Networks with Global Neighborhoods [Abstract] This paper presents algorithms for robustness analysis of Bayesian networks with global neighborhoods. Robust Bayesian inference is the calculation of bounds on posterior values given perturbations in a probabilistic model. We present algorithms for robust inference (including expected utility, expected value and variance bounds) with global perturbations that can be modeled by *-contaminated, constant density ratio, constant density bounded and total variation classes of distributions. c fl1996 Carnegie Mellon University Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #189566. 	[Title] Introduction to the Special Section on Knowledge-Based Construction of Probabilistic and Decision Models (IEEE Transactions [Abstract] Modeling techniques developed recently in the AI and uncertain reasoning communities permit significantly more flexible specifications of probabilistic knowledge. Specifically, graphical decision-modeling formalisms|belief networks, influence diagrams, and their variants|provide compact representation of probabilistic relationships, and support inference algorithms that automatically exploit the dependence structure in such models [1, 3, 4]. These advances have brought on a resurgence of interest in computational decision systems based on normative theories of belief and preference. However, graphical decision-modeling languages are still quite limited for purposes of knowledge representation because, while they can describe the relationships among particular event instances, they cannot capture general knowledge about probabilistic relationships across classes of events. The inability to capture general knowledge is a serious impediment for those AI tasks in which the relevant factors of a decision problem cannot be enumerated in advance. A graphical decision model encodes a particular set of probabilistic dependencies, a predefined set of decision alternatives, and a specific mathematical form for a utility function. Given a properly specified model, there exist relatively efficient algorithms for calculating posterior probabilities and optimal decision policies. A range of similar cases may be handled by parametric variations of the original model. However, if the structure of dependencies, the set of available alternatives, or the form of utility function changes from situation to situation, then a fixed network representation is no longer adequate. An ideal computational decision system would possess general, broad knowledge of a domain, but would have the ability to reason about the particular circumstances of any given decision problem within the domain. One obvious approach|which we call call knowledge-based model construction (KBMC)|is to generate a decision model dynamically at run-time, based on the problem description and information received thus far. Model construction consists of selection, instantiation, and assembly of causal and associational relationships from a broad knowledge base of general relationships among domain concepts. For example, suppose we wish to develop a system to recommend appropriate actions for maintaining a computer network. The natural graphical decision model would include chance Please summarise all the given information.

Paper #683355 has the title `Using Qualitative Relationships for Bounding Probability Distributions  
` and the abstract `We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction operations that are guaranteed to bound the distributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distributions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well. 
`.
Question: Which category should Paper #683355 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #683355 has the title `Using Qualitative Relationships for Bounding Probability Distributions  
` and the abstract `We exploit qualitative probabilistic relationships among variables for computing bounds of conditional probability distributions of interest in Bayesian networks. Using the signs of qualitative relationships, we can implement abstraction operations that are guaranteed to bound the distributions of interest in the desired direction. By evaluating incrementally improved approximate networks, our algorithm obtains monotonically tightening bounds that converge to exact distributions. For supermodular utility functions, the tightening bounds monotonically reduce the set of admissible decision alternatives as well. 
`.
Question: Which category should Paper #683355 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