# Optimal SQ Lower Bounds for Robustly Learning Discrete Product Distributions and Ising Models

@inproceedings{Diakonikolas2022OptimalSL, title={Optimal SQ Lower Bounds for Robustly Learning Discrete Product Distributions and Ising Models}, author={Ilias Diakonikolas and Daniel M. Kane and Yuxin Sun}, booktitle={COLT}, year={2022} }

We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efﬁcient SQ algorithm with access to an (cid:15) -corrupted binary product distribution can learn its mean within (cid:96) 2 -error o ( (cid:15) (cid:112) log(1 /(cid:15) )) . Similarly, we show that no efﬁcient SQ algorithm with access to an (cid:15) -corrupted ferromagnetic high-temperature Ising model can learn the model to…

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