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We revisit the well-studied problem of efficiently learning the underlying structure and parameters of an Ising model from data. Current algorithmic approaches achieve essentially optimal sample complexity when samples are generated i.i.d. from the ...

We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under pairwise ...

The theory of influences in product measures has profound applications in theoretical computer science, combinatorics, and discrete probability. This deep theory is intimately connected to functional inequalities and to the Fourier analysis of discrete ...

We show how to use parallelization to speed up sampling from an arbitrary distribution µ on a product space [q]ⁿ, given oracle access to counting queries: ℙ_{X∼ µ}[X_S=σ_S] for any S⊆ [n] and σ_S ∈ [q]^S. Our algorithm takes O(n^2/3· polylog(n,q)) parallel time, ...

The random geometric graph RGG(n,S^d−1,p) is formed by sampling n i.i.d. vectors {V_i}_{i = 1}ⁿ uniformly on S^d−1 and placing an edge between pairs of vertices i and j for which ⟨ V_i,V_j⟩ ≥ τ_d^p, where τ_d^p is such that the expected density is p. We study the ...