Honest compressions and their application to compression schemes

Roi Livni, Pierre Simon

Research output: Contribution to journalConference articlepeer-review

14 Scopus citations


The existence of a compression scheme for every concept class with bounded VC-dimension is one of the oldest open problems in statistical learning theory. Here we demonstrate the existence of such compression schemes under stronger assumptions than finite VC-dimension. Specifically, for each concept class we associate a family of concept classes that we call the alternating concept classes. Under the assumption that these concept classes have bounded VC-dimension, we prove existence of a compression scheme. This result is motivated by recent progress in the field of model theory with respect to an analogues problem. In fact, our proof can be considered as a constructive proof of these advancements. This means that we describe the reconstruction function explicitly. Not less important, the theorems and proofs we present are in purely combinatorial terms and are available to the reader who is unfamiliar with model theory. Also, using tools from model theory, we apply our results and prove existence of compression schemes in interesting cases such as concept classes defined by hyperplanes, polynomials, exponentials, restricted analytic functions and compositions, additions and multiplications of all of the above.

Original languageEnglish (US)
Pages (from-to)77-92
Number of pages16
JournalJournal of Machine Learning Research
StatePublished - 2013
Event26th Conference on Learning Theory, COLT 2013 - Princeton, NJ, United States
Duration: Jun 12 2013Jun 14 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


  • Compression Conjecture
  • Compression Scheme
  • NIP Structures


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