Approximate Decision Trees Research Articles

Advancing synthesis of decision tree-based multiple classifier systems: an approximate computing case study

So far, multiple classifier systems have been increasingly designed to take advantage of hardware features, such as high parallelism and computational power. Indeed, compared to software implementations, hardware accelerators guarantee higher throughput and lower latency. Although the combination of multiple classifiers leads to high classification accuracy, the required area overhead makes the design of a hardware accelerator unfeasible, hindering the adoption of commercial configurable devices. For this reason, in this paper, we exploit approximate computing design paradigm to trade hardware area overhead off for classification accuracy. In particular, starting from trained DT models and employing precision-scaling technique, we explore approximate decision tree variants by means of multiple objective optimization problem, demonstrating a significant performance improvement targeting field-programmable gate array devices.

Totally optimal decision trees for Boolean functions

We study decision trees which are totally optimal relative to different sets of complexity parameters for Boolean functions. A totally optimal tree is an optimal tree relative to each parameter from the set simultaneously. We consider the parameters characterizing both time (in the worst- and average-case) and space complexity of decision trees, i.e., depth, total path length (average depth), and number of nodes. We have created tools based on extensions of dynamic programming to study totally optimal trees. These tools are applicable to both exact and approximate decision trees, and allow us to make multi-stage optimization of decision trees relative to different parameters and to count the number of optimal trees. Based on the experimental results we have formulated the following hypotheses (and subsequently proved): for almost all Boolean functions there exist totally optimal decision trees (i) relative to the depth and number of nodes, and (ii) relative to the depth and average depth.

The binary identification problem for weighted trees

The Binary Identification Problem for weighted trees asks for the minimum cost strategy (decision tree) for identifying a vertex in an edge weighted tree via testing edges. Each edge has assigned a different cost, to be paid for testing it. Testing an edge e reveals in which component of T−e lies the vertex to be identified. We give a complete characterization of the computational complexity of this problem with respect to both tree diameter and degree. In particular, we show that it is strongly NP-hard to compute a minimum cost decision tree for weighted trees of diameter at least 6, and for trees having degree three or more. For trees of diameter five or less, we give a polynomial time algorithm. Moreover, for the degree 2 case, we significantly improve the straightforward O(n3) dynamic programming approach, and provide an O(n2) time algorithm. Finally, this work contains the first approximate decision tree construction algorithm that breaks the barrier of factor logn.

Evaluating system dynamics models of risky projects using decision trees: alternative energy projects as an illustrative example

AbstractMany important risky projects are characterized by stochastic processes embedded in nonlinear, feedback structures with delays. System dynamics models may be used to estimate the cash flow resulting from these projects for any given predetermined sequence of decisions. However, using system dynamics models to evaluate these cash flows when management has the flexibility to change its decisions in the face of future information often remains difficult in practice. To remedy this, we leverage the decision analysis literature to propose a methodology that transforms the system dynamics model into an approximate decision tree. The methodology then evaluates that tree to account for the value of managerial flexibility in executing a project. This approach has the virtue of combining system dynamics' capability to cope with dynamic complexity with that of decision analysis to model managerial flexibility. We illustrate this method with a model drawn from the wind power industry, which is characterized by numerous uncertainties and high managerial flexibility. We conclude with a discussion describing the limitations of this approach and the conditions under which its use would be most appropriate. Copyright © 2010 John Wiley & Sons, Ltd.