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 #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 #35778. 	[Title] Context-Specific Independence in Bayesian Networks [Abstract] Bayesiannetworks provide a languagefor qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation schemetree-structured CPTs for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #108963. 	[Title] Topological Parameters for time-space tradeoff [Abstract] In this paper we propose a family of algorithms combining tree-clustering with conditioning that trade space for time. Such algorithms are useful for reasoning in probabilistic and deterministic networks as well as for accomplishing optimization tasks. By analyzing the problem structure it will be possible to select from a spectrum the algorithm that best meets a given time-space specifica tion. 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 #108974. 	[Title] Global Conditioning for Probabilistic Inference in Belief Networks [Abstract] In this paper we propose a new approach to probabilistic inference on belief networks, global conditioning, which is a simple generalization of Pearl's (1986b) method of loop-cutset conditioning. We show that global conditioning, as well as loop-cutset conditioning, can be thought of as a special case of the method of Lauritzen and Spiegelhalter (1988) as refined by Jensen et al (1990a; 1990b). Nonetheless, this approach provides new opportunities for parallel processing and, in the case of sequential processing, a tradeoff of time for memory. We also show how a hybrid method (Suermondt and others 1990) combining loop-cutset conditioning with Jensen's method can be viewed within our framework. By exploring the relationships between these methods, we develop a unifying framework in which the advantages of each approach can be combined successfully. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1095507. 	[Title] Generalized Queries on Probabilistic Context-Free Grammars  on Pattern Analysis and Machine Intelligence [Abstract]  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 #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 #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 #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.

Paper #310653 has the title `Robustness Analysis of Bayesian Networks with Global Neighborhoods  
` and the 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
`.
Question: Which category should Paper #310653 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #310653 has the title `Robustness Analysis of Bayesian Networks with Global Neighborhoods  
` and the 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
`.
Question: Which category should Paper #310653 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