Talha Amin

Dynamic Programming Approach for Exact Decision Rule Optimization

This chapter is devoted to the study of an extension of dynamic programming approach that allows sequential optimization of exact decision rules relative to the length and coverage. It contains also results of experiments with decision tables from UCI Machine Learning Repository.

Optimization and analysis of decision trees and rules: dynamic programming approach

Abstract This paper is devoted to the consideration of software system Dagger created in KAUST. This system is based on extensions of dynamic programming. It allows sequential optimization of decision trees and rules relative to different cost functions, derivation of relationships between two cost functions (in particular, between number of misclassifications and depth of decision trees), and between cost and uncertainty of decision trees. We describe features of Dagger and consider examples of this system’s work on decision tables from UCI Machine Learning Repository. We also use Dagger to compare 16 different greedy algorithms for decision tree construction.

Dynamic Programming Approach for Partial Decision Rule Optimization

This paper is devoted to the study of an extension of dynamic programming approach which allows optimization of partial decision rules relative to the length or coverage. We introduce an uncertainty measure J(T) which is the difference between number of rows in a decision table T and number of rows with the most common decision for T. For a nonnegative real number γ, we consider γ-decision rules (partial decision rules) that localize rows in subtables of T with uncertainty at most γ. Presented algorithm constructs a directed acyclic graph Δγ(T) which nodes are subtables of the decision table T given by systems of equations of the kind “attribute = value”. This algorithm finishes the partitioning of a subtable when its uncertainty is at most γ. The graph Δγ(T) allows us to describe the whole set of so-called irredundant γ-decision rules. We can optimize such set of rules according to length or coverage. This paper contains also results of experiments with decision tables from UCI Machine Learning Repository.

Optimization of Decision Rules Based on Dynamic Programming Approach

This chapter is devoted to the study of an extension of dynamic programming approach which allows optimization of approximate decision rules relative to the length and coverage. We introduce an uncertainty measure that is the difference between number of rows in a given decision table and the number of rows labeled with the most common decision for this table divided by the number of rows in the decision table. We fix a threshold γ, such that 0 ≤ γ < 1, and study so-called γ-decision rules (approximate decision rules) that localize rows in subtables which uncertainty is at most γ. Presented algorithm constructs a directed acyclic graph Δγ T which nodes are subtables of the decision table T given by pairs “attribute = value”. The algorithm finishes the partitioning of a subtable when its uncertainty is at most γ. The chapter contains also results of experiments with decision tables from UCI Machine Learning Repository.

Relationships Between Length and Coverage of Decision Rules

The paper describes a new tool for study relationships between length and coverage of exact decision rules. This tool is based on dynamic programming approach. We also present results of experiments with decision tables from UCI Machine Learning Repository.

Optimization of approximate decision rules relative to number of misclassifications: comparison of greedy and dynamic programming approaches

In the paper, we present a comparison of dynamic programming and greedy approaches for construction and optimization of approximate decision rules relative to the number of misclassifications. We use an uncertainty measure that is a difference between the number of rows in a decision table T and the number of rows with the most common decision for T. For a nonnegative real number γ, we consider γ-decision rules that localize rows in subtables of T with uncertainty at most γ. Experimental results with decision tables from the UCI Machine Learning Repository are also presented.

Dynamic Programming Approach for Construction of Association Rule Systems

In the paper, an application of dynamic programming approach for optimization of association rules from the point of view of knowledge representation is considered. Experimental results present cardinality of the set of association rules constructed for information system and lower bound on minimum possible cardinality of rule set based on the information obtained during algorithm work.

Totally optimal decision rules

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 rules 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.

Element Partition Trees: Main Notions

This chapter starts by formally defining the class of meshes under study. We describe the notion of element partition tree and present an abstract way of defining optimization criteria of element partition trees in terms of cost functions. A definition of a cost function is provided in addition to a few examples of cost functions under study along with some of their properties.

Multi-stage Optimization of Element Partition Trees

This chapter presents tools and applications of multi-stage optimization of element partition trees. It starts by describing how the set of element partition trees can be represented compactly in the form of a directed acyclic graph (DAG). It then suggests algorithms to count the number of element partition trees represented by a DAG and to optimize the corresponding set of element partition trees with respect to some criterion. The latter algorithm can be used for multi-stage optimization of element partition trees relative to a sequence of cost functions and for the study of totally optimal element partition trees that are optimal with respect to multiple criteria simultaneously. Finally, we present results of experiments on three different classes of adaptive meshes.