2006/07/11 by Nick Palmer, Paul W. Goldberg, Palmer, Nick +1
Computer Science · #Algorithms and Data Compression #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Machine Learning and Data Classification
paper · pdf · doi:10.48550/arxiv.cs/0607047
openalex publication_date 2006/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect, the better our estimates of the label class distributions, the better the resulting classifier will be. In this paper we make this observation precise by identifying risk bounds of a classifier in terms of the quality of the estimates of the label class distributions. We show how PAC learnability relates to estimates of the distributions that have a PAC guarantee on their L1 distance from the true distribution, and we bound the increase in negative log likelihood risk in terms of PAC bounds on the KL-divergence. We give an inefficient but general-purpose smoothing method for converting an estimated distribution that is good under the L1 metric into a distribution that is good under the KL-divergence.