Jul 12, 2020
We study the computational and statistical tradeoffs in inferring the topological structures of high dimensional Ising model. Despite existing research on computationally efficient algorithms for learning the structures of Gaussian graphical model, the optimal algorithm for learning the combinatorial structures of Ising model is still unclear when computational budgets are limited. Our paper focuses on inferring combinatorial structures of the zero-field ferromagnetic Ising model. Under the framework of oracle model, we characterize the computational lower bounds of learning combinatorial structures in polynomial-time via a novel quantity called vertex overlap ratio. Such quantity is shown to be universally valid for the many specific graph structures including cliques and nearest neighbors. On the other side, we attain the optimal rates for these structures by proposing the quadratic testing statistics to match the lower bounds.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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