Anaconda: A Non-Adaptive Conditional Sampling Algorithm for Distribution Testing

Abstract

We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set S to an oracle, which returns a sample from the distribution conditioned on being from S. In the non-adaptive setting, all query sets must be specified in advance of viewing the outcomes.Our main result is the first polylogarithmic-query algorithm for equivalence testing, deciding whether two unknown distributions are equal to or far from each other. This is an exponential improvement over the previous best upper bound, and demonstrates that the complexity of the problem in this model is intermediate to the the complexity of the problem in the standard sampling model and the adaptive conditional sampling model. We also significantly improve the sample complexity for the easier problems of uniformity and identity testing. For the former, our algorithm requires onlyÕ(log n) queries, matching the information-theoretic lower bound up to a O(log log n)-factor.Our algorithm works by reducing the problem from ℓ1-testing to ℓ∞-testing, which enjoys a much cheaper sample complexity. Necessitated by the limited power of the non-adaptive model, our algorithm is very simple to state. However, there are significant challenges in the analysis, due to the complex structure of how two arbitrary distributions may differ.

Oscillatory pattern of glycemic control in patients with diabetes mellitus

“…The predictive model of glycemia. Our predictive model was the convergence of several successive steps to find the best linear models which display a higher and robust adjustment 42,43 . Thus, our algorithm was applied as follow: (i) natural logarithm transformed was applied to the time of the minimum and maximum glycemia; (ii) correlations were made between the variables of minimum and maximum glycemia and minimum and maximum glycemic time with all FFT weights (see "Glycemic oscillatory pattern" section).…”

Greedy Approximation Algorithms for Active Sequential Hypothesis Testing

“…Further, in many problems the theoretical analysis of partially adaptive algorithms turns out to be challenging (e.g. Kamath and Tzamos [2019], Chawla et al [2019]).…”

On Testing of Samplers

“…The sample space is exponential, and for many fundamental distributions, including uniform, it is prohibitively expensive in terms of samples to verify closeness. This led to the development of the conditional sampling model [11,8], which can provide sub-linear or even constant sample complexities for the testing of the above-given properties [1,28,5,9,17]. A detailed discussion on prior work in property testing and their relationship to Barbarik2 is given in Appendix A.…”

“…It is worth noting here that recently conditional sampling and its various variants has been used to design efficient testing and learning algorithms for various other properties of distributions ( [1,28,5,9,17]). Many of these have the potential to be used more efficient and sophisticated testing of samplers and related questions.…”