We study the maximum possible sign rank of $N \times N$ sign matrices with a given VC dimension $d$. For $d=1$, this maximum is $3$. For $d=2$, this maximum is $\tilde{\Theta}(N^{1/2})$. Similar (slightly less accurate) statements hold for $d>2$ as well. We discuss the tightness of our methods, and describe ... more >>>

We initiate the study of the *randomness complexity* of differential privacy, i.e., how many random bits an algorithm needs in order to generate accurate differentially private releases. As a test case, we focus on the task of releasing the results of $d$ counting queries, or equivalently all one-way marginals on ... more >>>