| 1. |
- Arnborg, Stefan
(author)
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Robust Bayesian analysis in partially ordered plausibility calculi
- 2016
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In: International Journal of Approximate Reasoning. - : Elsevier. - 0888-613X .- 1873-4731. ; 78, s. 1-14
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Journal article (peer-reviewed)abstract
- In Robust Bayesian analysis one attempts to avoid the 'Dogma of Precision' in Bayesian analysis by entertaining a set of probability distributions instead of exactly one. The algebraic approach to plausibility calculi is inspired by Cox's and Jaynes' analyses of plausibility assessment as a logic of uncertainty. In the algebraic approach one is not so much interested in different ways to prove that precise Bayesian probability is inevitable but rather in how different sets of assumptions are reflected in the resulting plausibility calculus. It has repeatedly been pointed out that a partially ordered plausibility domain is more appropriate than a totally ordered one, but it has not yet been completely resolved exactly what such domains can look like. One such domain is the natural robust Bayesian representation, an indexed family of probabilities. We show that every plausibility calculus embeddable in a partially ordered ring is equivalent to a subring of a product of ordered fields, i.e., the robust Bayesian representation is universal under our assumptions, if extended rather than standard probability is used. We also show that this representation has at least the same expressiveness as coherent sets of desirable gambles with real valued payoffs, for a finite universe.
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| 2. |
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| 3. |
- Bendtsen, Marcus, et al.
(author)
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Gated Bayesian Networks for Algorithmic Trading
- 2016
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In: International Journal of Approximate Reasoning. - Elsevier : Elsevier BV. - 0888-613X .- 1873-4731. ; 69, s. 58-80
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Journal article (peer-reviewed)abstract
- Gated Bayesian networks (GBNs) are a recently introduced extension of Bayesian networks that aims to model dynamical systems consisting of several distinct phases. In this paper, we present an algorithm for semi-automatic learning of GBNs. We use the algorithm to learn GBNs that output buy and sell decisions for use in algorithmic trading systems. We show how using the learnt GBNs can substantially lower risks towards invested capital, while at the same time generating similar or better rewards, compared to the benchmark investment strategy buy-and-hold.
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| 4. |
- Danielson, Mats, et al.
(author)
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Distribution of Belief in Decision Trees
- 2007
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In: International Journal of Approximate Reasoning. - 0888-613X .- 1873-4731. ; 46:2, s. pp. 387-407
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Journal article (peer-reviewed)
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| 5. |
- Danielson, Mats, et al.
(author)
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Distribution of expected utility in decision trees
- 2007
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In: International Journal of Approximate Reasoning. - : Elsevier BV. - 0888-613X .- 1873-4731. ; 46:2, s. 387-407
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Journal article (peer-reviewed)abstract
- Evaluation of decision trees in which uncertain information is present is complicated. Especially when the tree has some depth, i.e. consists of more than one level, the effects of the choice of representation and evaluation procedures are significant. Second-order representation and evaluation may significantly increase a decisionmaker's understanding of a decision situation when handling aggregations of imprecise representations, as is the case in decision trees or influence diagrams, while the use of only first-order results gives an incomplete picture. Furthermore, due to the effects on the distribution of belief over the intervals of expected utilities, the Gamma-maximin decision rule seems to be unnecessarily pessimistic as the belief in neighbourhoods of points near interval boundaries is usually lower than in neighbourhoods near the centre. Due to this, a generalized expected utility is proposed. The results in this paper apply also to approaches which do not explicitly deal with second-order information, such as standard decision trees or probabilistic networks using only first-order concepts, for example upper and lower bounds. Furthermore, the results also apply to other, non-probabilistic weighted trees such as multi-criteria weight trees.
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| 6. |
- Devaraj, Lokesh, et al.
(author)
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Improvements proposed to noisy-OR derivatives for multi-causal analysis: A case study of simultaneous electromagnetic disturbances
- 2024
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In: International Journal of Approximate Reasoning. - 0888-613X .- 1873-4731. ; 164
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Journal article (peer-reviewed)abstract
- In multi-causal analysis, the independence of causal influence (ICI) assumed by the noisy-OR (NOR) model can be used to predict the probability of the effect when several causes are present simultaneously, and to identify (when it fails) inter-causal dependence (ICD) between them. The latter is possible only if the probability of observing the multi-causal effect is available for comparison with a corresponding NOR estimate. Using electromagnetic interference in an integrated circuit as a case study, the data corresponding to the probabilities of observing failures (effect) due to the injection of individual (single cause) and simultaneous electromagnetic disturbances having different frequencies (multiple causes) were collected. This data is initially used to evaluate the NOR model and its existing derivatives, which have been proposed to reduce the error in predictions for higher-order multi-causal interactions that make use of the available information on lower-order interactions. Then, to address the identified limitations of the NOR and its existing derivatives, a new deterministic model called Super-NOR is proposed, which is based on correction factors estimated from the available ICD information.
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| 7. |
- Doherty, Patrick, 1957-, et al.
(author)
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Rough set reasoning using answer set programs
- 2021
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In: International Journal of Approximate Reasoning. - : Elsevier. - 0888-613X .- 1873-4731. ; 130:March, s. 126-149
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Journal article (peer-reviewed)abstract
- Reasoning about uncertainty is one of the main cornerstones of Knowledge Representation. Formal representations of uncertainty are numerous and highly varied due to different types of uncertainty intended to be modeled such as vagueness, imprecision and incompleteness. There is a rich body of theoretical results that has been generated for many of these approaches. It is often the case though, that pragmatic tools for reasoning with uncertainty lag behind this rich body of theoretical results. Rough set theory is one such approach for modeling incompleteness and imprecision based on indiscernibility and its generalizations. In this paper, we provide a pragmatic tool for constructively reasoning with generalized rough set approximations that is based on the use of Answer Set Programming (Asp). We provide an interpretation of answer sets as (generalized) approximations of crisp sets (when possible) and show how to use Asp solvers as a tool for reasoning about (generalized) rough set approximations situated in realistic knowledge bases. The paper includes generic Asp templates for doing this and also provides a case study showing how these techniques can be used to generate reducts for incomplete information systems. Complete, ready to run clingo Asp code is provided in the Appendix, for all programs considered. These can be executed for validation purposes in the clingo Asp solver.
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| 8. |
- Dunin-Keplicz, Barbara, et al.
(author)
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Tractable approximate knowledge fusion using the Horn fragment of serial propositional dynamic logic
- 2010
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In: International Journal of Approximate Reasoning. - : Elsevier. - 0888-613X .- 1873-4731. ; 51:3, s. 346-362
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Journal article (peer-reviewed)abstract
- In this paper we investigate a technique for fusing approximate knowledge obtained from distributed, heterogeneous information sources. This issue is substantial, e.g., in modeling multiagent systems, where a group of loosely coupled heterogeneous agents cooperate in achieving a common goal. Information exchange, leading ultimately to knowledge fusion, is a natural and vital ingredient of this process. We use a generalization of rough sets and relations [30], which depends on allowing arbitrary similarity relations. The starting point of this research is [6], where a framework for knowledge fusion in multiagent systems is introduced. Agents individual perceptual capabilities are represented by similarity relations, further aggregated to express joint capabilities of teams, This aggregation, expressing a shift from individual to social level of agents activity, has been formalized by means of dynamic logic. The approach of Doherty et al. (2007) [6] uses the full propositional dynamic logic, which does not guarantee tractability of reasoning. Our idea is to adapt the techniques of Nguyen [26-28] to provide an engine for tractable approximate database querying restricted to a Horn fragment of serial dynamic logic. We also show that the obtained formalism is quite powerful in applications.
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| 9. |
- Ekenberg, Love, et al.
(author)
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Value Differences using Second Order Distributions
- 2005
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In: International Journal of Approximate Reasoning. - : Elsevier. - 0888-613X .- 1873-4731. ; 38:1, s. 81-97
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Journal article (peer-reviewed)abstract
- Most decision models for handling vague and imprecise information are unnecessarily restrictive since they do not admit for discrimination between different beliefs in different values. This is true for classical utility theory as well as for the various interval methods that have prevailed. To allow for more refined estimates, we suggest a framework designed for evaluating decision situations considering beliefs in sets of epistemically possible utility and probability functions, as well as relations between them. The various beliefs are expressed using different kinds of belief distributions. We show that the use of such distributions allows for representation principles not requiring too hard data aggregation, but still admitting efficient evaluation of decision situations.
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| 10. |
- Etminani, Kobra, et al.
(author)
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DemocraticOP : A Democratic way of aggregating Bayesian network parameters
- 2013
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In: International Journal of Approximate Reasoning. - : Elsevier. - 0888-613X .- 1873-4731. ; 54:5, s. 602-614
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Journal article (peer-reviewed)abstract
- When there are several experts in a specific domain, each may believe in a different Bayesian network (BN) representation of the domain. In order to avoid having to work with several BNs, it is desirable to aggregate them into a single BN. One way of finding the aggregated BN is to start by finding the structure, and then find the parameters. In this paper, we focus on the second step, assuming that the structure has been found by some previous method.DemocraticOP is a new way of combining experts’ parameters in a model. The logic behind this approach is borrowed from the concept of democracy in the real world. We assume that there is a ground truth and that each expert represents a deviation from it - the goal is to try to find the ground truth based on the experts’ opinions. If the experts do not agree, then taking a simple average of their opinions (as occurs in classical aggregation functions such as LinOP and LogOP) is flawed. Instead, we believe it is better to identify similar opinions through clustering, and then apply averaging, or any other aggregation function, over the cluster with the highest number of members to obtain the aggregated parameters that are closest to the ground truth. In other words, respect the majority as is done in democratic societies instead of averaging over all experts’ parameters. The new approach is implemented and tested over several BNs with different numbers of variables and parameters, and with different numbers of experts. The results show that DemocraticOP outperforms two commonly used methods, LinOP and LogOP, in three key metrics: the average of absolute value of the difference between the true probability distribution and the one corresponding to the aggregated parameters, Kullback-Leibler divergence, and running time.
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