Extensions of Dynamic Programming: Decision Trees, Combinatorial Optimization, and Data Mining

  • Shahid Hussain

Student thesis: Doctoral Thesis

Abstract

This thesis is devoted to the development of extensions of dynamic programming to the study of decision trees. The considered extensions allow us to make multi-stage optimization of decision trees relative to a sequence of cost functions, to count the number of optimal trees, and to study relationships: cost vs cost and cost vs uncertainty for decision trees by construction of the set of Pareto-optimal points for the corresponding bi-criteria optimization problem. The applications include study of totally optimal (simultaneously optimal relative to a number of cost functions) decision trees for Boolean functions, improvement of bounds on complexity of decision trees for diagnosis of circuits, study of time and memory trade-off for corner point detection, study of decision rules derived from decision trees, creation of new procedure (multi-pruning) for construction of classifiers, and comparison of heuristics for decision tree construction. Part of these extensions (multi-stage optimization) was generalized to well-known combinatorial optimization problems: matrix chain multiplication, binary search trees, global sequence alignment, and optimal paths in directed graphs.
Date of AwardJul 10 2016
Original languageEnglish (US)
Awarding Institution
  • Computer, Electrical and Mathematical Science and Engineering
SupervisorMikhail Moshkov (Supervisor)

Keywords

  • dynamic programming
  • Decision Trees
  • cost functions
  • bi-criteria optimization
  • multi-stage optimization
  • Data Mining

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