text:   Testing with Subcube Conditioning",6,"['New paper on arXiv: Random Restrictions of High-Dimensional Distributions and Uniformity Testing with Subcube Conditioning. With \nClément L. Canonne (@ccanonne_),\xa0Xi Chen,\xa0Amit Levi, and\xa0Erik Waingarten. <LINK> Check out this thread for a summary 1/n <LINK>', ""Say you have a distribution over a discrete support, and you want to test if it's uniform. Birthday paradox says you need sqrt(domain size) samples, and this is achievable. This is sublinear (great), but in high dimensions, the domain is exponentially large (not great) 2/n"", 'Enter the conditional sampling model. You can ask for samples, conditioned on being from some subset of the domain. Canonne, Ron, and Servedio showed that uniformity can be tested with a number of samples independent of the domain size! But the subsets queried may be complex 3/n', 'We study the problem in a weaker model, where you can only condition on ""subcubes"" of the domain. We show the a nearly optimal upper bound of ~sqrt(dimension). That is, sqrt(log(domain size)), and matching the complexity of testing product distributions with vanilla samples 4/n', 'The main technical tool is a structural statement, lower bounding the mean distance after a random restriction by the total variation distance after a random projection. Proved via a ""robust"" (a la Khot-Minzer-Safra) Pisier inequality 5/n', 'A useful subroutine of independent interest is for testing whether a distribution on the hypercube is uniform, or has mean far from zero. Can be done with same ~sqrt(dimension) complexity, generalizing previous results with the same complexity for product distributions. 6/6']",19,11,1603