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Full-Text Articles in Physical Sciences and Mathematics
How To Get Beyond Uniform When Applying Maxent To Interval Uncertainty, Songsak Sriboonchitta, Vladik Kreinovich
How To Get Beyond Uniform When Applying Maxent To Interval Uncertainty, Songsak Sriboonchitta, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, the Maximum Entropy (MaxEnt) approach leads to reasonable distributions. However, in an important case when all we know is that the value of a random variable is somewhere within the interval, this approach leads to a uniform distribution on this interval -- while our intuition says that we should have a distribution whose probability density tends to 0 when we approach the interval's endpoints. In this paper, we show that in most cases of interval uncertainty, we have additional information, and if we account for this additional information when applying MaxEnt, we get distributions which are …
Maximum Entropy As A Feasible Way To Describe Joint Distributions In Expert Systems, Thongchai Dumrongpokaphan, Vladik Kreinovich, Hung T. Nguyen
Maximum Entropy As A Feasible Way To Describe Joint Distributions In Expert Systems, Thongchai Dumrongpokaphan, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
In expert systems, we elicit the probabilities of different statements from the experts. However, to adequately use the expert system, we also need to know the probabilities of different propositional combinations of the experts' statements -- i.e., we need to know the corresponding joint distribution. The problem is that there are exponentially many such combinations, and it is not practically possible to elicit all their probabilities from the experts. So, we need to estimate this joint distribution based on the available information. For this purpose, many practitioners use heuristic approaches -- e.g., the t-norm approach of fuzzy logic. However, this …