Classical statistics assumes that data samples are available in their entirety at one place. But what happens when only limited information is allowed about each sample from a user? The information can be constrained in form of communication constraints as in federated learning or local privacy constraints. We have developed a general framework for design and analysis of statistical and optimization procedures under such distributed information constraints.
J Acharya, C Canonne, and H Tyagi, “Inference under information constraints: Lower Bounds from Chi-Square Contraction,” Proceedings of the Thirty-Second Conference on Learning Theory (COLT), PMLR 99:3-17, 2019.
P Mayekar and H Tyagi, “RATQ: A Universal Fixed-Length Quantizer for Stochastic Optimization” Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 108:1399-1409, 2020.