Lower Bounds for Learning Distributions under Communication Constraints via Fisher Information

By Leighton Pate Barnes, Yanjun Han, Ayfer Özgür. 2019

82 citations recorded by the source corpus.

Subfields: Statistical Learning Theory, Information Theory

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Citations in the corpus

Advances and Open Problems in Federated Learning (2019, background): “Characterizing such fundamental trade-offs between accuracy and communication has been of recent interest in theoretical statistics [434, 81, 195, 11, 47, 380].”
Breaking the Communication-Privacy-Accuracy Trilemma (2020, background): “If we further assume X are drawn from some discrete distribution p, then the problem falls into distribution estimation under local differential privacy [9], [13], [34], [36], [42], [43], [44], [45], [46] and limited communication [11], [25], [45], [46], [47], [48], [49], [50].”
rTop-k: A Statistical Estimation Approach to Distributed SGD (2020, methodology): “PROOF OF THEOREM 2 To prove Theorem 2, we use part of Theorem 3 from [35] (see also [26]), reproduced below, which is proved using a Fisher information argument.”
Unified lower bounds for interactive high-dimensional estimation under information constraints (2020, background): “Note that for n ( (e̺ − 1)2 ∧ e̺ ) ≥ d2 and n(2l ∧ d)≥ d2, respectively, our bounds recover those obtained in [7] and [9] under these assumptions.”
Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints (2021, methodology): “…constraints, the optimal convergence rate for discrete distribution estimation was established in (Han et al., 2018b,a; Barnes et al., 2019; Acharya et al., 2019a,b; Chen et al., 2020) for the non-interactive setting, and (Barnes et al., 2019; Acharya et al., 2020) for general interactive models.”