Probabilistic graphical models

Antonucci, Alessandro; Campos, Cassio P. de; Zaffalon, Marco

doi:10.1002/9781118763117.ch9

Cited by 13 publications

(18 citation statements)

References 46 publications

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“…This should affect the computational complexity of evaluation process, thus making necessary the development of specific approximate algorithms. We also intend to apply some ideas proposed in a recent paper [30] about the relations between (sets of) probabilities and (sets of) utilities, to reduce inference in IIDs to inference in credal networks [1,2]. We also intend to extensively test the procedure we proposed for sensitivity analysis in practical IDs and compare it against the methods proposed so far with the same goal.…”

Section: Discussionmentioning

confidence: 94%

“…(2) can be regarded as the expected value of the sum of the utilities when the decision maker takes his/her decisions on the basis of the optimal policies in Eq. (1). These basic concepts are demonstrated in the following example.…”

Section: Ids Evaluation (Definitions)mentioning

confidence: 94%

“…Unlike VE, each step Algorithm 3 ArcRev -Arc reversal scheme. 1: merge utility nodes in U Transformation 1…”

Section: Example 3 (Reversing the Oil Wildcatter's Arcs) Consider Thmentioning

confidence: 99%

“…The early attempts of Fertig and Breese [13] first, and Zaffalon [11] after, to extend these models to non-sharp quantification are among the few works in this direction. 1,2 This sounds unfortunate as the above considerations about the difficulty of assessing sharp estimates for probabilities are even more compelling for utilities, which are supposed to model intrinsically qualitative objects such as preferences. 3 We extend to the interval-valued case the formalism of IDs by keeping the same sensitivity-analysis interpretation of credal networks.…”

Section: Introductionmentioning

confidence: 96%

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Evaluating interval-valued influence diagrams

Cabañas

Antonucci

Cano

et al. 2017

International Journal of Approximate Reasoning

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Influence diagrams are probabilistic graphical models used to represent and solve sequential decision problems under uncertainty. Sharp numerical values are required to quantify probabilities and utilities. This might be an issue with real models, whose parameters are typically obtained from expert judgments or partially reliable data. We consider an interval-valued quantification of the parameters to gain realism in the modeling and evaluate the sensitivity of the inferences with respect to perturbations in the sharp values of the parameters. An extension of the classical influence diagrams formalism to support such interval-valued potentials is presented. The variable elimination and arc reversal inference algorithms are generalized to cope with these models. At the price of an outer approximation, the extension keeps the same complexity as with sharp values. Numerical experiments show improved performances with respect to previous methods. As a natural application, we propose these models for practical sensitivity analysis in traditional influence diagrams. The maximum perturbation level on single or multiple parameters preserving the optimal strategy can be computed. This allows the identification of the parameters deserving a more careful elicitation.

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Section: Discussionmentioning

confidence: 94%

Section: Ids Evaluation (Definitions)mentioning

confidence: 94%

“…Unlike VE, each step Algorithm 3 ArcRev -Arc reversal scheme. 1: merge utility nodes in U Transformation 1…”

Section: Example 3 (Reversing the Oil Wildcatter's Arcs) Consider Thmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Evaluating interval-valued influence diagrams

Cabañas

Antonucci

Cano

et al. 2017

International Journal of Approximate Reasoning

Self Cite

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“…that every variable is strongly independent of its non-descendant non-parents given its parents), and whose projections on local domains lie inside the local credal sets specified in Q, that is, K S is the convex hull of the set of distributions of X whose induced measure satisfies (1) and (5). One can show that the strong extension can be equivalently defined as Antonucci, de Campos, & Zaffalon, 2014)…”

Section: Graph-based Representationmentioning

confidence: 99%

Probabilistic Inference in Credal Networks: New Complexity Results

Mauá¹,

Campos²,

Benavoli³

et al. 2014

jair

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Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

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Quantifying and Analyzing the Uncertainty in Fault Interpretation Using Entropy

Lei

2024

Math Geosci

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Probabilistic graphical models

Cited by 13 publications

References 46 publications

Evaluating interval-valued influence diagrams

Evaluating interval-valued influence diagrams

Probabilistic Inference in Credal Networks: New Complexity Results

Quantifying and Analyzing the Uncertainty in Fault Interpretation Using Entropy

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