讨论组:算法、复杂性及密码组
标题:Attribute-efficient learning and weight-degree tradeoffs for polynomial threshol
演讲人: Liyang Tan University
时间: 2012-04-20 14:00-2012-04-20 15:30
地点:FIT 1-222

内容:

 We study the challenging problem of learning decision lists attribute-efficiently, giving both positive and negative results.

Our main positive result is a new tradeoff between the running time and mistake bound for learning length-k decision lists over n Boolean variables. When the allowed running time is relatively high, our new mistake bound improves significantly on the mistake bound of the best previous algorithm of Klivans and Servedio.

Our main negative result is a new lower bound on the weight of any degree-d polynomial threshold function (PTF) that computes a particular decision list over k variables. This lower bound establishes strong limitations on the effectiveness of the Klivans and Servedio approach and suggests that it may be difficult to improve on our positive result. The main tool used in our lower bound is a new variant of Markov's classical inequality which may be of independent interest; it provides a bound on the derivative of a univariate polynomial in terms of both its degree and the size of its coefficients.

Joint work with Rocco Servedio and Justin Thaler



人物介绍: