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We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d samples. While there have been recent results for specific graph classes, these involve fairly extensive technical arguments that are specialized to each specific graph class. In contrast, we isolate two key graph-structural ingredients that can then be used to specify sample complexity lower-bounds. Presence of these structural properties makes the graph class hard to learn. We derive corollaries of our main result that not only recover existing recent results, but also provide lower bounds for novel graph classes not considered previously. We also extend our framework to the random graph setting and derive corollaries for ErdH{o}s-R{e}nyi graphs in a certain dense setting.
What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly identify the
The overall predictive uncertainty of a trained predictor can be decomposed into separate contributions due to epistemic and aleatoric uncertainty. Under a Bayesian formulation, assuming a well-specified model, the two contributions can be exactly ex
In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under the $m-$ShSBM, we
Learning disentangled representations of natural language is essential for many NLP tasks, e.g., conditional text generation, style transfer, personalized dialogue systems, etc. Similar problems have been studied extensively for other forms of data,
Progress in deep reinforcement learning (RL) research is largely enabled by benchmark task environments. However, analyzing the nature of those environments is often overlooked. In particular, we still do not have agreeable ways to measure the diffic