2022/11/07 by Moses Charikar, Charikar, Moses, Chirag Pabbaraju +1 · 4 citations
Computer Science · #Data Structures and Algorithms (cs.DS) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Imbalanced Data Classification Techniques #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.2211.04956
openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical result in learning theory shows the equivalence of PAC learnability of binary hypothesis classes and the finiteness of VC dimension. Extending this to the multiclass setting was an open problem, which was settled in a recent breakthrough result characterizing multiclass PAC learnability via the DS dimension introduced earlier by Daniely and Shalev-Shwartz. In this work we consider list PAC learning where the goal is to output a list of k predictions. List learning algorithms have been developed in several settings before and indeed, list learning played an important role in the recent characterization of multiclass learnability. In this work we ask: when is it possible to k-list learn a hypothesis class? We completely characterize k-list learnability in terms of a generalization of DS dimension that we call the k-DS dimension. Generalizing the recent characterization of multiclass learnability, we show that a hypothesis class is k-list learnable if and only if the k-DS dimension is finite.