  In this paper, we study two well known methods of Ising structure learning,
namely the pseudolikelihood approach and the interaction screening approach, in
the context of tensor recovery in $k$-spin Ising models. We show that both
these approaches, with proper regularization, retrieve the underlying
hypernetwork structure using a sample size logarithmic in the number of network
nodes, and exponential in the maximum interaction strength and maximum
node-degree. We also track down the exact dependence of the rate of tensor
recovery on the interaction order $k$, that is allowed to grow with the number
of samples and nodes, for both the approaches. We then provide a comparative
discussion of the performance of the two approaches based on simulation
studies, which also demonstrates the exponential dependence of the tensor
recovery rate on the maximum coupling strength. Our tensor recovery methods are
then applied on gene data taken from the Curated Microarray Database (CuMiDa),
where we focus on understanding the important genes related to hepatocellular
carcinoma.
