Projects per year
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution D over [n] and a property P, the goal is to distinguish between D ∈ P and `1(D,P) > ε. We develop a general algorithm for this question, which applies to a large range of “shape-constrained” properties, including monotone,log-concave, t-modal, piecewise-polynomial, and Poisson Binomial distributions. Moreover, for all cases considered, our algorithm has near-optimal sample complexity with regard to the domain size and is computationally efficient. For most of these classes, we provide the first non-trivial tester in the literature. In addition, we also describe a generic method to prove lower bounds for this problem, and use it to show our upper bounds are nearly tight. Finally, we extend some of our techniques to tolerant testing, deriving nearly–tight upper and lower bounds for the corresponding questions.
|Title of host publication||Proceedings of the 33rd International Symposium on Theoretical Aspects of Computer Science (STACS 2016)|
|Publisher||Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany|
|Number of pages||14|
|Publication status||Published - 2016|
|Event||33rd International Symposium on Theoretical Aspects of Computer Science - Orléans, France|
Duration: 17 Feb 2016 → 20 Feb 2016
|Name||Leibniz International Proceedings in Informatics (LIPIcs)|
|Publisher||Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik|
|Conference||33rd International Symposium on Theoretical Aspects of Computer Science|
|Abbreviated title||STACS 2016|
|Period||17/02/16 → 20/02/16|
FingerprintDive into the research topics of 'Testing Shape Restrictions of Discrete Distributions'. Together they form a unique fingerprint.
- 1 Finished
1/09/14 → 31/08/15