关于原型规则的错误率和压缩率
On Error and Compression Rates for Prototype Rules
摘要：
我们研究了错误和压缩之间的密切相互作用，在非参数多类分类设置的原型学习规则。我们特别关注最近提出的基于压缩的学习规则OptiNet（Kontorovich，Sabato和Urner 2016; Kontorovich，Sabato和Weiss 2017; Hanneke et al. 2021）。除了它的计算优点，这个规则最近被证明是普遍一致的，在任何度量实例空间，承认一个普遍一致的规则-第一个学习算法已知享有此属性。然而，它的错误率和压缩率一直是开放的。在这里，我们得出这样的利率的情况下，实例驻留在欧几里得空间下共同构成的平滑和尾部条件的数据分布。我们首先表明，OptiNet实现非平凡的压缩率，同时享受近最小最优出错率。然后，我们继续研究一种新的通用压缩方案，进一步压缩原型规则，局部适应噪声水平，而不牺牲精度。将其应用于OptiNet，我们表明，在几何余量条件下，实现了压缩率的进一步增益。实验结果比较各种方法的性能。
英文摘要：
We study the close interplay between error and compression in the non-parametric multiclass classification setting in terms of prototype learning rules. We focus in particular on a recently proposed compression-based learning rule termed OptiNet (Kontorovich, Sabato, and Urner 2016; Kontorovich, Sabato, and Weiss 2017; Hanneke et al. 2021). Beyond its computational merits, this rule has been recently shown to be universally consistent in any metric instance space that admits a universally consistent rule--the first learning algorithm known to enjoy this property. However, its error and compression rates have been left open. Here we derive such rates in the case where instances reside in Euclidean space under commonly posed smoothness and tail conditions on the data distribution. We first show that OptiNet achieves non-trivial compression rates while enjoying near minimax-optimal error rates. We then proceed to study a novel general compression scheme for further compressing prototype rules that locally adapts to the noise level without sacrificing accuracy. Applying it to OptiNet, we show that under a geometric margin condition, further gain in the compression rate is achieved. Experimental results comparing the performance of the various methods are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
