Permanent link to this recordhttp://hdl.handle.net/10754/564344
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AbstractIn the paper, authors presents a greedy algorithm for construction of exact and partial decision rules for decision tables with many-valued decisions. Exact decision rules can be 'over-fitted', so instead of exact decision rules with many attributes, it is more appropriate to work with partial decision rules with smaller number of attributes. Based on results for set cover problem authors study bounds on accuracy of greedy algorithm for exact and partial decision rule construction, and complexity of the problem of minimization of decision rule length. © 2011 Springer-Verlag.
Conference/Event name6th International Conference on Rough Sets and Knowledge Technology, RSKT 2011
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Multi-stage optimization of decision and inhibitory trees for decision tables with many-valued decisionsAzad, Mohammad; Moshkov, Mikhail (European Journal of Operational Research, Elsevier BV, 2017-06-16) [Article]We study problems of optimization of decision and inhibitory trees for decision tables with many-valued decisions. As cost functions, we consider depth, average depth, number of nodes, and number of terminal/nonterminal nodes in trees. Decision tables with many-valued decisions (multi-label decision tables) are often more accurate models for real-life data sets than usual decision tables with single-valued decisions. Inhibitory trees can sometimes capture more information from decision tables than decision trees. In this paper, we create dynamic programming algorithms for multi-stage optimization of trees relative to a sequence of cost functions. We apply these algorithms to prove the existence of totally optimal (simultaneously optimal relative to a number of cost functions) decision and inhibitory trees for some modified decision tables from the UCI Machine Learning Repository.
Decision and Inhibitory Trees for Decision Tables with Many-Valued DecisionsAzad, Mohammad (2018-06-06) [Dissertation]
Advisor: Moshkov, Mikhail
Committee members: Bajic, Vladimir B.; Zhang, Xiangliang; Boros, EndreDecision trees are one of the most commonly used tools in decision analysis, knowledge representation, machine learning, etc., for its simplicity and interpretability. We consider an extension of dynamic programming approach to process the whole set of decision trees for the given decision table which was previously only attainable by brute-force algorithms. We study decision tables with many-valued decisions (each row may contain multiple decisions) because they are more reasonable models of data in many cases. To address this problem in a broad sense, we consider not only decision trees but also inhibitory trees where terminal nodes are labeled with “̸= decision”. Inhibitory trees can sometimes describe more knowledge from datasets than decision trees. As for cost functions, we consider depth or average depth to minimize time complexity of trees, and the number of nodes or the number of the terminal, or nonterminal nodes to minimize the space complexity of trees. We investigate the multi-stage optimization of trees relative to some cost functions, and also the possibility to describe the whole set of strictly optimal trees. Furthermore, we study the bi-criteria optimization cost vs. cost and cost vs. uncertainty for decision trees, and cost vs. cost and cost vs. completeness for inhibitory trees. The most interesting application of the developed technique is the creation of multi-pruning and restricted multi-pruning approaches which are useful for knowledge representation and prediction. The experimental results show that decision trees constructed by these approaches can often outperform the decision trees constructed by the CART algorithm. Another application includes the comparison of 12 greedy heuristics for single- and bi-criteria optimization (cost vs. cost) of trees. We also study the three approaches (decision tables with many-valued decisions, decision tables with most common decisions, and decision tables with generalized decisions) to handle inconsistency of decision tables. We also analyze the time complexity of decision and inhibitory trees over arbitrary sets of attributes represented by information systems in the frameworks of local (when we can use in trees only attributes from problem description) and global (when we can use in trees arbitrary attributes from the information system) approaches.
Optimization of decision rule complexity for decision tables with many-valued decisionsAzad, Mohammad; Chikalov, Igor; Moshkov, Mikhail (2013 IEEE International Conference on Systems, Man, and Cybernetics, Institute of Electrical and Electronics Engineers (IEEE), 2013-10) [Conference Paper]We describe new heuristics to construct decision rules for decision tables with many-valued decisions from the point of view of length and coverage which are enough good. We use statistical test to find leaders among the heuristics. After that, we compare our results with optimal result obtained by dynamic programming algorithms. The average percentage of relative difference between length (coverage) of constructed and optimal rules is at most 6.89% (15.89%, respectively) for leaders which seems to be a promising result. © 2013 IEEE.