M. P. Wellman and C. L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI94, pp. 567 -- 574, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....time and solution quality, making it possible to compute approximate solutions to complex problems under time constraints. Anytime algorithms are being used increasingly in a range of practical domains that include planning and scheduling [2,38] belief network and influence diagram evaluation [12,16, 36], database query processing [31,33] and information gathering [10] By itself, however, an anytime algorithm does not provide a complete solution to Simon s challenge to make the best return decision, net of computational costs. To achieve this, a meta level control procedure in needed that ....

M.P. Wellman, C.-L. Liu, State-space abstraction for anytime evaluation of probabilistic networks, in: Proc. 10th Conference on Uncertainty in Artificial Intelligence, Seattle, WA, 1994, pp. 567--574.

.... algorithm removes selected nodes from networks [Dr95] Bounded conditioning ignores some cutset instances to compute probability bounds and considers more instances to improve the accuracy [HSC89] The state space abstraction algorithm reduces the cardinality of CPTs to simplify the model [WL94]. Variational approach introduces variational transformations and delinks nodes from the graph one by one until the graph is sparse enough that the exact method is feasible [JJ99, JGJS99] Sarkar s algorithm approximates the Bayesian network by finding the optimal tree decomposable representation ....

....algorithms. 4. 1 Anytime BN Inference Algorithms Theoretically, any Bayesian networks inference algorithm that temporarily ignores partial information contained in a BN, and recovers those ignored information whenever the allocated computational time allowed, is an anytime inference algorithm [WL94]. This partial information could be partial instantiations [Po96, SS96, SS98] partial nodes [Dr95] partial edges [Kj94, En97] partial probabilities in CPTs [JA90] partial node states [WL94] and partial cutset or other computational items [HSC89] Therefore, most approximate inference ....

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M. P. Wellman and C. L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI '94, pp. 567 -- 574, 1994.

....et al. [10] and Shafer and Shenoy [20] Unfortunately, there are applications that CTP cannot deal with or where it is too slow (e.g. 18] Much recent effort has been spent on speeding up inference. The efforts can be classified into those that approximate (e.g. 15] 2] 9] 6] 7] 17] [22], 11] and [19] and those that exploit structures in the probability tables (e.g. 3] 1] We are interested in exploiting structures in the probability tables induced by independence of causal influence (ICI) The concept of ICI was first introduced by Heckerman [3] under the name causal ....

M. P. Wellman, C. -L. Liu (1994), State-Space abstraction for anytime evaluation of probabilistic networks, in Proc. of tenth Conference on Uncertainty in Artificial Intelligence, pp. 567-574.

....heuristics achieve impressive speedups that allow to analyze linkage problems that could not be dealt with using the prior state of the art procedures. In the language of Bayesian networks these heuristics can be understood as finding Value abstractions (reminiscent of the abstractions studied by [15]) These abstractions are found in an evidence specific manner to save computations for a specific training example. In the remainder of this paper we review genetic linkage analysis problems. Then we develop a method to find value abstractions that generalizes the ideas of [11] in a manner that ....

M. P. Wellman and C.-L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI 1994.

....for designing straw models through various other elimination methods or the use of other (automatic or semi automatic) approximations and abstractions, such as, e.g. ffl Eliminate variables for which one value is much more probable than the others. ffl Eliminate certain states in variables [Wellman, 1994]. ffl Combine certain variables into one. 2. This approach should be tested on more realistic models. 3. Conditions under which bipartite straw models are better than independent straw models should be investigated. We expect he bipartite straw model to be more accurate than the independent ....

Wellman, M.P. and C.-L. Liu. "StateSpace Abstraction for Any-Time Evaluation of Probabilistic Networks." Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference. San Mateo, CA: Morgan-Kaufmann, 567--574.

....part of the hidden variable detection algorithm FindHidden on synthetic and real life data and showed improved performance as well as more appealing structures. Several works are related to our approach. Several authors examined operations of value abstraction and refinement in Bayesian networks [2, 16, 15, 19]. These works were mostly concerned with the ramifications of these operations on inference and decision making. Decisions about cardinality also appear in the context of discretization. Although the data is observable, the introduction of a discretized variable can be modeled as adding a hidden ....

M. P. Wellman and C.-L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI '94, pp. 567 -- 574, 1994.

....technique is optimal and demonstrates its applicability. Introduction Anytime algorithms are being used increasingly for timecritical problem solving in domains such as planning and scheduling (Boddy Dean 1994; Zilberstein 1996) belief network evaluation (Horvitz, Suermondt, Cooper 1989; Wellman Liu 1994), database query processing (Shekhar Dutta 1989; Smith Liu 1989) and others. The defining property of an anytime algorithm is that it can be stopped at any time to provide a solution, such that the quality of the solution increases with computation time. This property allows a tradeoff ....

Wellman, M.P., and Liu, C.-L. 1994. State-space abstraction for anytime evaluation of probabilistic networks. Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, 567-574.

.... that simply enumerate instantiations are presented in [23] enumeration of complete instantiations) and in [33] partial, IB assignments) Another such algorithm considers terms, rather than instantiations [16] Deterministic approximation algorithms that do not fit into this pattern are [35, 14]. The above approximation algorithms perform better if the conditional distributions are heavily skewed [6, 23] 1 . Encouraging theoretical results presented in [8] state that even for weak skewness, a small fraction of the instantiations is expected to hold most of the probability mass. ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Uncertainty in AI, Proceedings of the Tenth Conference, pages 567--574, July 1994.

....topologically. An exact algorithm is then run on the approximate network, to produce an approximate answer [25] Another source of complexity is the large number of states per node in various applications. To alleviate that problem, an approximation based on merging states was suggested [46]. The scheme begins by making all variables unary valued, and successively refining the states of variables, while performing probability updating on the approximate network and thus getting a successively better approximation in each step. Another category of deterministic approximation ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Uncertainty in AI, Proceedings of the Tenth Conference, pages 567--574, July 1994. 35

....reviews previous work and casts the problem in a new framework from which some improved monitoring strategies emerge. 1 Introduction Anytime algorithms are being used increasingly for timecritical problem solving in domains such as planning and scheduling [1] 5] belief network evaluation [9][18], database query processing [16] 17] and others. The defining property of an anytime algorithm is that it can be stopped at any time to provide a solution, where the quality of the solution increases with computation time. This property allows a tradeoff between computation time and solution ....

M.P. Wellman and C.-L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, pp. 567-574, 1994.

.... may take is the removal of low probability values from the action state space, as described in [1] An example of the third approach is Wellman and Liu s use of abstraction for the approximate evaluation of BNs when the state space is prohibitive or when a real time response is required [14]. They trade off accuracy in the result for computational efficiency by varying the granularity of the variable state spaces. This is done by merging values that are adjacent in the enumeration of the variable s state space. This approach can be effective when such values are similar , but is not ....

M.P. Wellman and C.L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI94 -- Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, pages 567--574, Seattle, Washington, 1994.

....of these states into a group of similar states. We then make probabilistic inference with these states as a group. We show that the resulting model provides a good estimate of the probabilistic inference results as compared to the original BN2O model and is better than the state abstraction method [Wellman and Liu, 1994] used for approximate inference. The paper is organized as follows. In Section 2 we clarify the notations and conventions we use throughout the paper. In Section 3 we introduce BN2O networks and review the approaches to make probabilistic inference in them tractable. In Section 4 we define the ....

....a finding node x f j and the aggregated similar state. As we can see, the computation to transform the model to a reduced model involves simple summations over the base states. The computational requirements in this state aggregation model are thus the same as in the state space abstraction model [Wellman and Liu, 1994] in which the answer to a query is inferred by summing over the base states only and completely ignoring the rest of the states. Our model accounts for some of the ignored probability mass via the coefficients ff(d i ) Let us now see how the state space aggregation model helps to increase the ....

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Wellman, M. P. and Liu, C.- L. (1994). State-space abstraction for anytime evaluation of probabilistic networks. In Lopez de Montara, R. and Poole, D., editors, Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, pages 567 -- 574. Morgan Kaufmann.

....and translates into constraints on edge directions. Other types of background knowledge include constraints on edge existence and constraints on whether a node must be a root or may have parents. Researchers have also examined the task of discretizing variable values in Bayesian network learning [6, 11, 15]. The objective is to nd an appropriate discretization of a continuous variable, or an appropriate partitioning for an ordinal variable, that will lead to a higher scoring network (which one hopes, in turn, will translate into improved generalization performance) Another line of research has ....

....this research are relevant to our approach. Friedman and Goldszmidt [6] present a Minimum Description Length (MDL) based approach for discretizing variables during Bayesian network learning. Monti and Cooper [11] use a latent variable model to perform multivariate discretization. Wellman and Liu [15] describe a statistical approach for creating abstract variable values by combining neighboring values of ordinal variables in a Bayesian network essentially discretization via aggregation for integer valued variables. Tree Structured CPTs (TCPTs) and other representations for CPTs that take ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Proceedings of the Ninth Conference on Uncertainty in Articial Intelligence (UAI-93), pages 567-574, 1994.

....3.5 4.5 0 0.5 1.5 2.5 3 3.5 4 Iterations (x 50) LS LW Test network L6: 99 nodes, 131 arcs. Above: evidence = 1 root node; query = all leaves (35) Below: evidence = 1 leaf node; query = all root nodes (29) Lecture 3 Nicholson and Korb 30 Other approximation methods ffl State space abstraction (Wellman Liu, 1994). ffl Localised Partial Evaluation (Draper, 1995) ffl Weak arc removal (Kjrulff, 1994) ffl Using a mutual information measure to guide approximate evaluation. Jitnah, 1999) ffl And others Lecture 3 Nicholson and Korb 31 Dynamic Belief Networks Obs t 1 Obs t 2 Obs State t 2 State t 1 State ....

M. P. Wellman and C. Liu, "State-Space abstraction for anytime evaluation of probabilistic networks", in Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence, pp. 567-574, 1994.

....[6] One class of approximate inference algorithms is based on stochastic simulation; a number of variations have been proposed. Another way to reduce the computational complexity is by approximating (i.e. simplifying) the model, for example by removing arcs [19] or abstracting the state space [28]. Other algorithms reduce the complexity by computing probability intervals rather than exact probabilities, or do not update beliefs for all nodes in the network, only those of interest (e.g. 10] When new belief updating algorithms, or variants on existing algorithms, are presented in the ....

....nodes and of their children are recomputed. For each state of a child of an abstracted node, the new conditional probability is assigned as an sum of the original conditional probabilities weighted by the prior probability of the abstracted states. No empirical performance results are given. In [28, 21], Wellman and Liu use the same technique of state space abstraction, but instead they set the new conditional probabilities of children of an abstracted node as an average of the original conditional probabilities. This version of state space abstraction is tested on a set of example networks and ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Proc. of UAI-94, pages 567--574, 1994.

.... may take is the removal of low probability values from the action state space, as described in [1] An example of the third approach is Wellman and Liu s use of abstraction for the approximate evaluation of BNs when the state space is prohibitive or when a real time response is required [14]. They trade off accuracy in the result for computational efficiency by varying the granularity of the variable state spaces. This is done by merging values that are adjacent in the enumeration of the variable s state space. This approach can be effective when such values are similar , but is not ....

M.P. Wellman and C.L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI94 -- Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, pages 567--574, Seattle, Washington, 1994.

....Operations A detailed influence view may be too complicated to solve or understand; abstraction on the model is sometimes necessary to omit or suppress detail, for computational tractability and for comprehensibility. Unlike most of the existing work which focus on abstracting the state space [3, 15], we focus on abstracting and refining the network P i 1 = n state t state t 1 M(t 1) R(t 1) M(t) R(t) structure, including abstracting and refining a group of event variables based on concept taxonomies, and summarizing the influence path based on node reduction. In the following ....

Wellman, M. P. and Liu, C.: State-Space Abstraction for Anytime Evaluation of Probabilistic Networks. Uncertainty in Artificial Intelligence: Proceedings of the Tenth Conference, pages 567-574. Morgan Kaufmann (1994)

....children representing nodes in the second level. Although the resulting cluster node has exponentially many states (in the number of the first layer nodes) we can aggregate some of these states into a group of similar states (as opposed to eliminating them in the state space abstraction method [Wellman and Liu, 1994]) We show that the resulting model provides a good estimate of the probabilistic inference results as compared to the original BN2O model. Since we Submitted to the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI 96) August 1 3, 1996, Portland, Oregon, USA can make ....

....present at the same time is less or equal to some number d max , and the other is the subset of N oe = 2 n 1 Gamma N b states with the number of diseases present at the same time greater than d max . The latter states are the ones we make similar. While in the state space abstraction method [Wellman and Liu, 1994] we would eliminate the states with the number of diseases present more than d max completely, in our approach we always have a non zero contribution from the subset of similar states. According to the definition of the similar states, the ratio of the probability contribution to any single ....

[Article contains additional citation context not shown here]

Wellman, M. P. and Liu, C.-L. (1994). State-space abstraction for anytime evaluation of probabilistic networks. In Lopez de Montara, R. and Poole, D., editors, Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, pages 567 -- 574. Morgan Kaufmann.

....into a tree structure with a query node at the root of the tree. Estimates for the belief of the query node are iteratively computed by traversing the tree. This incremental evaluation results in a form of anytime algorithm. Other researchers have developed anytime algorithms for BN evaluation [5, 19, 13] and proposed the use of tree representations for efficient representation of evaluation of a BN [8, 4] Sect. 2) in this paper we combine these approaches. The representation, construction and tree traversal evaluation of a treeNet is described in Sect. 3. A best first tree traversal ....

....the algorithm has an anytime flavour. The rate at which this distance decreases is obviously important. Simulation approaches [5] are classified as anytime algorithms because the accuracy of results improves as the sample size grows. Other anytime algorithms for BN evaluation have been developed [13, 19] and compared [16] In Wellman and Liu s state Space abstraction [19] the states of selected nodes are merged; the subsequent size reduction of the CPDs allows faster evaluation of the BN. By iteratively refining the merged states and re2 evaluating the BN, a progressively more accurate result is ....

[Article contains additional citation context not shown here]

M. Wellman and C. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Proc. of 10th Conf. on UAI, pages 567--574, 1994.

.... [14] Influence diagrams offer a concise graphical representation for complex decisions and they can be evaluated using efficient existing algorithms [23] In addition, several techniques for anytime evaluation of belief networks have been developed by Horvitz et al. 12] and by Wellman and Liu [30]. We anticipate that a large number of influence diagrams representing typical tasks can be constructed and stored in a library for future reuse. We also expect that in many cases minimal modification of existing decision models would be required in order to tailor them to fit particular user s ....

M. P. Wellman and C.-L. Liu. State-Space Abstraction for Anytime Evaluation of Probabilistic Networks. In Proc. 10th Conference on Uncertainty in Artificial Intelligence, pp. 567--574, Seattle, Washington, 1994.

....[FC89] SP89] Backward Simulation: FDF94] Mean Field Theory: SJ95] SJJ96] Monte Carlo for DempsterShafer: Wil91] MCMC for Dempster Shafer: MW94] 2.4. 2 Structure Alteration or Abstraction Simplifying the network structure to obtain an approximation: Kja93] Kja94] PFH94] WL94] Pro93b] Sar93] Lam94] Removal of Small Probabilities: JA90] CBS95] Quality of an Abstraction: KV95] Las91] Las93] LL94] 2.4.3 Approximation of Cutset Conditioning By taking only a subsample of the conditioning variables values: Dar94b, GD95] 2.4.4 Heuristic Searching for ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, San Mateo, Calif., 1994. Morgan Kaufmann.

....topologically. An exact algorithm is then run on the approximate network, to produce an approximate answer [24] Another source of complexity is the large number of states per node in various applications. To alleviate that problem, an approximation based on merging states was suggested [43]. The scheme begins by making all variables unary valued, and succesively refining the states of variables, while performing probability updating on the approximate network and thus getting a successively better approximation in each step. Another category of deterministic approximation algorithms ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Uncertainty in AI, Proceedings of the Tenth Conference, pages 567--574, July 1994.

....3.1 Library of Tasks First, we consider the library of tasks, lots, in more detail. Clearly, from our discussions in Section 2, reasoning with Bayesian networks is quite difficult. Although there are a number of approaches available, only a few of them address the issue of anytime computations [10, 33] and none have been combined together to work in a cooperative fashion. Exact algorithms are generally exponential time, but are efficient for certain classes of network (usually dependent on topology) Nondeterministic methods, on the other hand, are usually anytime, but cannot guarantee that ....

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Uncertainty in AI, Proceedings of the Tenth Conference, pages 567--574, July 1994.

.... relationships is rarely required, and that in many cases purely qualitative information (for some conception of qualitative ) is sufficient (Goldszmidt 1994) In consequence, the literature has admitted numerous schemes attempting to capture various forms of qualitative relationships (Wellman 1994), useful for various uncertain reasoning tasks. Unfortunately, we generally lack a robust mapping from tasks to the levels of precision required, and indeed, necessary precision is inevitably variable across problem instances. As long as some potential problem might require precision not captured ....

....Abstraction Approximate evalu ation of Bayesian networks is a common strategy for time critical problems. For qualitative inference, approximated distributions can be particularly useful if the qualitative relationships between nodes are preserved in the approximations. In previous research (Wellman Liu 1994), we have proposed iterative state space abstraction (ISSA) as a technique for approximate evaluation of Bayesian networks. ISSA iteratively refines the state spaces of the nodes whose states are aggregated at the initial step of the algorithm. Approximated distributions get closer and closer to ....

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Wellman, M. P., and Liu, C.-L. 1994. State-space abstraction for anytime evaluation of probabilistic networks.

....been shown that even approximating a conditional probability to a fixed degree of accuracy is NP hard [10] This work was supported in part by Grant F49620 94 10027 from the Air Force Office of Scientific Research, and an NSF National Young Investigator award. This paper contains material from [28]. restricting network structure, and employing heuristic methods to improve average performance. The problem might be finessed when networks are handcrafted by knowledge engineers to serve as the core of a consultation system. In this case, speed vs. accuracy tradeoffs can be resolved at design ....

....strategies, with widely varying profiles of computational value over time. Thus, we cannot really get away without some sort of metalevel evaluation, even if it is only an off line design time analysis. In this paper, we explore another variety of anytime algorithm for evaluating Bayesian networks [28]. Specifically, we consider the possibility of modulating precision in the state space of variables in order to generate results of progressively improving approximation as computation time increases. This approach is motivated by the observation that state space cardinality can have a large ....

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Wellman, M. P., and C.-L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence, Seattle, WA, Morgan Kaufmann, pp. 567-574, 1994.

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M. P. Wellman and C. L. Liu. State-space abstraction for anytime evaluation of probabilistic networks. In UAI94, pp. 567 -- 574, 1994.

No context found.

Michael P. Wellman and Chao-Lin Liu. State-space abstraction for anytime evaluation of probabilistic networks. In Proceedings of AAAI-94, pages 567--574, Seattle, WA, 1994.

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Wellman, M. & Lui, C. (1994). State-space abstraction for anytime evaluation of probabilistic networks. In Proceedings of the 10 th Conference on Uncertainty in AI, Seattle WA.

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