List Sample Compression and Uniform Convergence: Equivalence, Impossibility, and Insights
Core Concepts
Uniform convergence remains equivalent to learnability in list PAC learning, while sample compression faces impossibility challenges.
Abstract
The article explores list learning as a variant of supervised classification.
It investigates the applicability of classical principles like uniform convergence and sample compression in list PAC learning.
Surprising results are revealed regarding sample compression in the list learning setting.
Direct-sum arguments are employed for impossibility results on sample compression.
The equivalence between PAC learning and uniform convergence is confirmed for k-list concept classes.
Detailed definitions of PAC learnability, uniform convergence, and list compressibility are provided.
Technical overview includes combinatorial dimensions like Graph and Daniely-Shwartz dimensions.
Sample compression proofs establish equivalence between learnability and variable-size compressibility.
List Sample Compression and Uniform Convergence
Stats
2-list-learnable classes that cannot be compressed when label space is Y = {0, 1, 2}.
Existence of learnable classes not k-compressible for any arbitrarily large k.
Quotes
"Sample compression schemes offer a more comprehensive manifestation of Occam’s razor."
"We prove an even stronger impossibility result showing there are 2-list-learnable classes that cannot be compressed."