Optimization of Decision Rules Based on Dynamic Programming Approach

Zielosko, Beata; Chikalov, Igor; Moshkov, Mikhail; Amin, Talha

doi:10.1007/978-3-319-01866-9_12

Cited by 5 publications

(3 citation statements)

References 16 publications

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“…For each heuristic method H and each table T ∈ Φ m−v (I), we first compute the average length of rules for system of rules constructed by H for T , denoted by length greedy. Second, we compute the average length of rules for optimal relative to length system of rules constructed by dynamic programming algorithm for T (see [25,26,27,28] for decision tables with single-valued decisions and [29] for decision tables with many-valued decisions), denoted by length min. Finally, we calculate for each T ∈ Φ m−v (I) the relative difference length greedy−length min length min (we assume that 0 0 = 0), and then sum the relative differences and average the summation over |Φ m−v (I)|.…”

Section: Resultsmentioning

confidence: 99%

Comparison of Heuristics for Optimization of Association Rules

Alsolami

Amin

Moshkov

et al. 2019

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In this paper, seven greedy heuristics for construction of association rules are compared from the point of view of the length and coverage of constructed rules. The obtained rules are compared also with optimal ones constructed by dynamic programming algorithms. The average relative difference between length of rules constructed by the best heuristic and minimum length of rules is at most 4%. The same situation is with coverage.

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Section: Resultsmentioning

confidence: 99%

Comparison of Heuristics for Optimization of Association Rules

Alsolami

Amin

Moshkov

et al. 2019

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“…There are many different ways to design and analyze decision rules, such as brute force, genetic algorithms [25], boolean reasoning [21], derivation from decision trees [23,18], sequential covering procedures [9,13], greedy algorithms [17], and dynamic programming [2,26]. Implementations of many of these methods can be found in programs such as LERS [14], RSES [5], Rosetta [20], Weka [15], TRS Library [24], and DAGGER [1].…”

Section: Introductionmentioning

confidence: 99%

Totally optimal decision rules

Amin

Moshkov

2018

Discrete Applied Mathematics

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Optimality of decision rules (patterns) can be measured in many ways. One of these is referred to as length. Length signifies the number of terms in a decision rule and is optimally minimized. Another, coverage, represents the width of a rule's applicability and generality. As such, it is desirable to maximize coverage. A totally optimal decision rule is a decision rule that has the minimum possible length and the maximum possible coverage. This paper presents a method for determining the presence of totally optimal decision rules for "complete" decision tables (representations of total functions in which different variables can have domains of differing values). Depending on the cardinalities of the domains, we can either guarantee for each tuple of values of the function that totally optimal rules exist for each row of the table (as in the case of total Boolean functions where the cardinalities are equal to 2) or, for each row, we can find a tuple of values of the function for which totally optimal rules do not exist for this row.

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“…We consider here extensions of dynamic programming approach and greedy approach that allow us to derive a system of decision rules directly from a input dataset. In Amin et al (2013); Zielosko et al (2014) the authors considered an optimization algorithm relative to only a single objective function (either length or coverage), whereas here we consider bi-criteria optimization. The authors in Azad et al (2013) considered the average relative difference measure to evaluate the quality of the rule heuristics relative to a given cost function.…”

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confidence: 99%

Bi-criteria optimization problems for decision rules

et al. 2018

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We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems -minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion -we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria -we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.

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Optimization of Decision Rules Based on Dynamic Programming Approach

Cited by 5 publications

References 16 publications

Comparison of Heuristics for Optimization of Association Rules

Comparison of Heuristics for Optimization of Association Rules

Totally optimal decision rules

Bi-criteria optimization problems for decision rules

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