Click here to return to the main page of the workshop.
In the past several years, there has been a revival of interest in the field of distribution testing, with a flurry of results showing how to test and estimate properties with a sample complexity which is sublinear in the domain size. Indeed the number of recent works may even feel overwhelming to the casual observer, and the literature hard to navigate. The goal of this workshop is to catch the community up in recent developments, and highlight some of the most interesting frontiers in distribution testing.
The workshop included an Open Problems session (see the schedule below)
, which resulted in a list of 12 open questions and directions to tackle and explore. Nine of those have been posted to the Sublinear.info
website; the tenth was also posed at a previous workshop
, in Baltimore; the last two, more open-ended, are described below.
- Problem 1: Rényi Entropy Estimation
- Problem 2: Beyond Identity Testing
- Problem 3: Instance-Specific Hellinger Testing
- Problem 4: Efficient Profile Maximum Likelihood Computation
- Problem 5: Sample Stretching (or “how to create samples out of thin air”)
- Problem 6: Equivalence Testing Lower Bound via Communication Complexity
- Problem 7: Equivalence Testing with Conditional Samples (or “how to remove that pesky quadratic gap”)
- Problem 8: Separating PDF and CDF Query Models (or “with more power comes... more power. Right?”)
- Problem 9: AM vs. NP for Proofs of Proximity in Distribution Testing (or “do we need that Merlin anyway?”)
- Problem 10: Correcting Independence of Distributions (or “how to create independence out of thin air”)
- Problem 11: There has recently been some work on testing Ising models, Bayes nets, and Markov chains under the viewpoint of distribution testing. What other models, assumptions, or families are natural to study distribution testing of high-dimensional probability distributions? (asked by Costis Daskalakis).
- Problem 12: in Phylogenetics, the question of testing whether a set of species, given their genomes, can be organized as a family tree (or whether, instead, some cross-relations between species happened) is a crucial problem. How to formalize a relevant and natural version of this problem, and study it rigorously either under the model of distribution testing, or a suitable variant thereof? (asked by Costis Daskalakis).
Organizers and support
This workshop was organized by Clément Canonne and Gautam "G" Kamath, with the support of the FOCS Tutorial and Workshop chairs James R. Lee and Aleksander Mądry.