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For uncertain data, the major challenge is that the data feature or attribute is captured not by a single point value but represented as sample distributions [11].
At last, a theoretical foundation was established on which pruning techniques were derived which can significantly improve the computational efficiency of the distribution-based algorithms for uncertain data.
Robust optimization techniques are developed for uncertain data described by several known distributions including a uniform distribution, a normal distribution, the difference of two normal distributions, a general discrete distribution, a binomial distribution, and a poisson distribution.
Interestingly, the average gap and number of branches performed by CRM2, although not directly comparable with the corresponding one of CRM1, results relatively small, confirming the tightness of the class representative model also for uncertain data.
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Unlike SO, RO generates a solution that is optimal for all realization of uncertain data.
Soyster (1973) was one of the first researchers to propose a RO formulation to produce a solution that is feasible for any realization of uncertain data that belong to a convex set.
Bounded uncertainties on energy hub parameters are taken into account and RO methods are exploited to gain robust solutions which are feasible for all values, or for a selected subset, of uncertain data.
In [105], the authors firstly discussed the sources of data uncertainty and gave some examples and then devised an algorithm for building decision trees from uncertain data using the distribution-based approach.
In this paper, we propose (i) a compact tree structure for capturing uncertain data, (ii) a technique for using our tree structure to tighten upper bounds to expected support, and (iii) an algorithm for mining frequent patterns based on our tightened bounds.
In recent years, tree-based algorithms for mining uncertain data have been developed.
Other tree structures for handling uncertain data may achieve compactness at the expense of loose upper bounds on expected supports.
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