no code implementations • 28 Oct 2020 • Constantinos Daskalakis, Qinxuan Pan
We show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance $\epsilon$ from an optimal $O(n \ln n/\epsilon^2)$ samples, where $O(\cdot)$ hides an absolute constant which, importantly, does not depend on the model being learned - neither its tree nor the magnitude of its edge strengths, on which we place no assumptions.
no code implementations • 9 Dec 2016 • Constantinos Daskalakis, Qinxuan Pan
As an application of our inequality, we show that distinguishing whether two Bayesian networks $P$ and $Q$ on the same (but potentially unknown) DAG satisfy $P=Q$ vs $d_{\rm TV}(P, Q)>\epsilon$ can be performed from $\tilde{O}(|\Sigma|^{3/4(d+1)} \cdot n/\epsilon^2)$ samples, where $d$ is the maximum in-degree of the DAG and $\Sigma$ the domain of each variable of the Bayesian networks.
