Decision tree model

About: Decision tree model is a research topic. Over the lifetime, 2256 publications have been published within this topic receiving 38142 citations.

On rank vs. communication complexity

Abstract: This paper concerns the open problem of Lovasz and Saks regarding the relationship between the communication complexity of a boolean function and the rank of the associated matrix. We first give an example exhibiting the largest gap known. We then prove two related theorems.

Lower Bounds in Communication Complexity

Abstract: In the 30 years since its inception, communication complexity has become a vital area of theoretical computer science. The applicability of communication complexity to other areas, including circuit and formula complexity, VLSI design, proof complexity, and streaming algorithms, has meant that it has attracted a lot of interest. Lower Bounds in Communication Complexity focuses on showing lower bounds on the communication complexity of explicit functions. It treats different variants of communication complexity, including randomized, quantum, and multiparty models. Many tools have been developed for this purpose from a diverse set of fields including linear algebra, Fourier analysis, and information theory. As is often the case in complexity theory, demonstrating a lower bound is usually the more difficult task. Lower Bounds in Communication Complexity describes a three-step approach for the development and application of these techniques. This approach can be applied in much the same way for different models, be they randomized, quantum, or multiparty. Lower Bounds in Communication Complexity is an ideal primer for anyone with an interest in this current and popular topic.

Rounds in communication complexity revisited

Abstract: The $k$-round two-party communication complexity was studied in the deterministic model by [14] and [4] and in the probabilistic model by [20] and [6]. We present new lower bounds that give (1) randomization is more powerful than determinism in $k$-round protocols, and (2) an explicit function which exhibits an exponential gap between its $k$ and $(k-1)$-round randomized complexity. We also study the three party communication model, and exhibit an exponential gap in 3-round protocols that differ in the starting player. Finally, we show new connections of these questions to circuit complexity, that motivate further work in this direction.

Efficient algorithms for decision tree cross-validation

Abstract: Cross-validation is a useful and generally applicable technique often employed in machine learning, including decision tree induction. An important disadvantage of straightforward implementation of the technique is its computational overhead. In this paper we show that, for decision trees, the computational overhead of cross-validation can be reduced significantly by integrating the cross-validation with the normal decision tree induction process. We discuss how existing decision tree algorithms can be adapted to this aim, and provide an analysis of the speedups these adaptations may yield. We identify a number of parameters that influence the obtainable speedups, and validate and refine our analysis with experiments on a variety of data sets with two different implementations. Besides cross-validation, we also briefly explore the usefulness of these techniques for bagging. We conclude with some guidelines concerning when these optimizations should be considered.