Paper Info
Title
Sample and Computationally Efficient Learning Algorithms under S-Concave Distributions.
Abstract
We provide new results for noise-tolerant and sample-efficient learning algorithms under s-concave distributions. The new class of s-concave distributions is a broad and natural generalization of log-concavity, and includes many important additional distributions, e.g., the Pareto distribution and t-distribution. This class has been studied in the context of efficient sampling, integration, and optimization, but much remains unknown about the geometry of this class of distributions and their applications in the context of learning. The challenge is that unlike the commonly used distributions in learning (uniform or more generally log-concave distributions), this broader class is not closed under the marginalization operator and many such distributions are fat-tailed. In this work, we introduce new convex geometry tools to study the properties of s-concave distributions and use these properties to provide bounds on quantities of interest to learning including the probability of disagreement between two halfspaces, disagreement outside a band, and the disagreement coefficient. We use these results to significantly generalize prior results for margin-based active learning, disagreement-based active learning, and passive learning of intersections of halfspaces. Our analysis of geometric properties of s-concave distributions might be of independent interest to optimization more broadly.
Year
Venue
Field
2017
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 30 (NIPS 2017)
Convex geometry,Mathematical optimization,Active learning,Pareto distribution,Computer science,Algorithm,Operator (computer programming),Sampling (statistics),Artificial intelligence,Passive learning,Machine learning
DocType
Volume
ISSN
Conference
30
1049-5258
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Maria-Florina Balcan11445105.01
Hongyang Zhang21108.33