Paul Dagum and Eric Horvitz. A Bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23:499--516, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a few. Related to the temporal modeling issue is the selection of an appropriate sampling rate and decision horizon. Finally, the problem of intractable inference needs to be addressed. While exact inference methods may be sufficient for models of modest size, approximate inference methods[8, 9] may prove useful for larger models. It is evident that our vision of an ideal alarm depends on effective solutions to modeling and computational challenges that are currently being researched. In this paper, we have presented a general framework for designing alarms that aid in process ....

Paul Dagum and Eric Horvitz. A Bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23:499--516, 1993.

....since its solution would potentially provide a fast computation scheme for inference in belief networks. There is a rich array of stochastic simulation algorithms for approximating inference probabilities in large belief networks, and some of our earlier research has focused on such algorithms [8, 16]. In general, however, both exact and approximate computation in belief networks is NP hard [6, 18] The application of DNMs to complex medical domains exploits the additive decomposition of conditional probabilities to achieve efficiency in inference [11] For large scale applications, however, ....

.... inference has been proven NP hard [6, 18] recent advances in the theory of optimal stopping rules for stochastic simulation have made it possible to perform approximate inference in polynomial time, with a small relative error and failure probability, for a large class of belief networks [16, 17, 48]. We will investigate these improved inference algorithms, and subsequently optimize them for computing and updating the urgency as new data arrive. We will explore various forms of importance sampling to optimize convergence, as well as stratified schemes for sampling. A dynamical system is a ....

Paul Dagum and Eric Horvitz. A bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23:499--516, 1993.

....[42] and Lauritzen and Spiegelhalter [30] Jensen [23] improved aspects of the algorithm which was proposed in [30] With approximate algorithms, based on a simulation of the corresponding Bayesian network. We mention the algorithms introduced by Chavez and Cooper [3] Dagum and Horvitz [6], Fung and Chang [12] Henrion [17] Hryceij [20] Jensen et al. 21] Pearl [36] Shachter and Peot [43] and Shwe and Cooper [44] 4 Our interest in obtaining an optimal decomposition originates in the evidence propagation algorithm proposed by Lauritzen and Spiegelhalter [30] This algorithm ....

P. Dagum and E. Horvitz, A Bayesian analysis of simulation algorithms for inference in belief networks, Networks 23 (5) (1993) 499-516.

.... is a large family, including techniques such as rejection sampling, importance sampling, and Markov chain Monte Carlo methods (MacKay, 1998) Many of these methods have been applied to the problem of approximate probabilistic inference for graphical models and analytic results are available (Dagum Horvitz, 1993). In particular, Shwe and Cooper (1991) proposed a stochastic sampling method known as likelihood weighted sampling for the QMR DT model. Their results are the most promising results to date for inference for the QMR DT they were able to produce reasonably accurate approximations in reasonable ....

....probability models, and we expect that optimal solutions will involve a combination of methods. We return to this point in the discussion section, where we consider various promising hybrids of approximate and exact inference algorithms. The general problem of approximate inference is NP hard (Dagum Luby, 1993) and this provides additional reason to doubt the existence of a single champion approximate inference technique. We think it important to stress, however, that this hardness result, together with Cooper s (1990) hardness result for exact inference cited above, should not be taken to suggest that ....

Dagum, P., & Horvitz, E. (1993). A Bayesian analysis of simulation algorithms for inference in Belief networks. Networks, 23, 499--516.

....Max propagation: DDP90] Daw92] 2.3.2 Linear Programming Formalizations as linear or non linear programming problems: San94] LD94] 2.4 Approximation 2.4. 1 Stochastic Simulation Markov Chain Monte Carlo based techniques (mostly Gibbs Sampling) GG84] CC87] CC90] Pea87b] DC93] DH93] JKK93] DH92] Hry90] Nea93] DKL95] Kja95b] KKR95] MC96] Of these, JKK93, JKK95, MC96, DKL95, JKK93, JKK95, Kja95b] can be viewed as being a combinations of Gibbs sampling and exact propagation. Logic Sampling: Hen88] Likelihood Weighting: FC89] SP89] Backward Simulation: ....

Paul Dagum and Eric Horvitz. A Bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23(5):499--516, August 1993.

....and Spiegelhalter (1988) Jensen (1994) improved aspects of the algorithm which was proposed in Lauritzen and Spiegelhalter (1988) ffl With approximate algorithms, based on a simulation of the corresponding Bayesian network. We mention the algorithms introduced by Chavez and Cooper (1990) Dagum and Horvitz (1993), Fung and Chang (1990) Henrion (1988) Hryceij (1990) Jensen et al. 1993) Pearl (1987) Shachter and Peot (1990) and Shwe and Cooper (1991) We take as point of departure the evidence propagation algorithm proposed by Lauritzen and Spiegelhalter (1988) The first step of this algorithm ....

Dagum, P. and Horvitz, E. (1993) A Bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23, 499-516.

....determining the value of a variable; however, for determining the value of a variable x, its probability table need to be looked up which may be relatively expensive if x has many parents. In general, estimates of beliefs become more accurate when the number of samples increases. Dagum and Horvitz [4] showed that for the likelihood weighting scheme, to output a belief in a value of a variable x that with probability higher than 1 Gamma ffi has relative error less than ffl, at least a: ln(4=ffi) ffl 2 Bel(x) samples are required where a is the maximum value of the weighting distribution. ....

P. Dagum and E. Horvitz. A Bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23:499--516, 1993.

.... is a large family, including techniques such as rejection sampling, importance sampling, and Markov chain Monte Carlo methods (MacKay, 1998) Many of these methods have been applied to the problem of approximate probabilistic inference for graphical models and analytic results are available (Dagum Horvitz, 1993). In particular, Shwe and Cooper (1991) proposed a stochastic sampling method known as likelihood weighted sampling for the QMR DT model. Their results are the most promising results to date for inference for the QMR DT they were able to produce reasonably accurate approximations in reasonable ....

....probability models, and we expect that optimal solutions will involve a combination of methods. We return to this point in the discussion section, where we consider various promising hybrids of approximate and exact inference algorithms. The general problem of approximate inference is NP hard (Dagum Luby, 1993) and this provides additional reason to doubt the existence of a single champion approximate inference technique. We think it important to stress, however, that this hardness result, together with Cooper s (1990) hardness result for exact inference cited above, should not be taken to suggest that ....

Dagum, P. and Horvitz, E. (1993). A Bayesian analysis of simulation algorithms for inference in Belief networks. In Networks 23: 499-516.

.... see [68, 76, 72] Inference methods can be divided into two broad classes exact methods, or methods that exploit the conditional independence revealed when the graph structure is relatively sparse [128] and approximation methods, or stochastic simulation and Monte Carlo sampling techniques [34]. A further classification of the approximation methods is found in [68] while a further classification of exact methods is found in [81] In the latter paper, Jensen, Olesen, and Andersen define the static and dynamic components of an algorithm and characterize several exact inference methods in ....

P. Dagum and E. Horvitz. A Bayesian Analysis of Simulation Algorithms for Inference in Belief Networks. Networks, 23:499-516, 1993.

.... logic sampling [Henrion, 1988] and randomized approximation schemes [Chavez Cooper, 1990] Many variations of these algorithms have been reported that improve on the run times [Fung Chang, 1990; Fung Del Favero, 1994; Hulme, 1995; Shachter Peot, 1990; Shwe Cooper, 1991] Dagum and Luby [Dagum Luby, 1993] showed that the general problem of approximate inference in belief networks with evidence is also NP hard. There are, however, restricted classes of networks in which approximate inference is provably amenable to a polynomial time solution. Dagum Chavez, 1993] In this paper we present two ....

....Before describing the likelihood weighting algorithm we will review different types of approximation algorithms, in particular we make clear the distinction between relative and absolute error bounds. 2. 1 A CATEGORIZATION OF APPROXIMATION ALGORITHMS The following discussion is modeled after [Dagum Luby, 1993]. INSTANCE: A real value between 0 and 1, a belief network with binary valued nodes, V, arcs A, conditional probabilities Pr, two nodes X and E in V instantiated to x and e, respectively. e d e page 2 ABSOLUTE APPROXIMATION: An estimate such that . RELATIVE APPROXIMATION: An estimate such ....

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Dagum, P. & Horvitz, E. (1993). A Bayesian analysis of simulation algorithms for inference in belief networks.

....and searchbased approximations. Simulation based algorithms use a source of random bits to generate random samples of the solution space. Simulation based algorithms include straight simulation [25, 26] forward simulation, 15] likelihood weighting [13, 33] and randomized approximation schemes [3, 4, 7, 8]. Variants of these methods such as backward simulation [14] exist; Neal [23] provides a good overview of the theory of simulation based algorithms. Search based algorithms search the space of alternative instantiations to find the most probable instantiation. These methods yield upper and lower ....

P. Dagum and E. Horvitz. A Bayesian analysis of simulation algorithms for inference in belief networks. Networks, 23:499--516, 1993.

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P. Dagum and E. Horvitz, A Bayesian analysis of simulation algorithms for inference in belief networks, Networks 23 (5) (1993) 499-516.

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Dagum, P., and Horvitz, E., A bayesian analysis of simulation algorithms for inference in belief networks, Networks, 23, 499#516, 1993.

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