Collaborative Learning of Distributions under Heterogeneity and
Communication Constraints
- URL: http://arxiv.org/abs/2206.00707v1
- Date: Wed, 1 Jun 2022 18:43:06 GMT
- Title: Collaborative Learning of Distributions under Heterogeneity and
Communication Constraints
- Authors: Xinmeng Huang, Donghwan Lee, Edgar Dobriban, Hamed Hassani
- Abstract summary: In machine learning, users often have to collaborate to learn distributions that generate the data.
We propose a novel two-stage method named SHIFT: First, the users collaborate by communicating with the server to learn a central distribution.
Then, the learned central distribution is fine-tuned to estimate the individual distributions of users.
- Score: 35.82172666266493
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In modern machine learning, users often have to collaborate to learn
distributions that generate the data. Communication can be a significant
bottleneck. Prior work has studied homogeneous users -- i.e., whose data follow
the same discrete distribution -- and has provided optimal
communication-efficient methods. However, these methods rely heavily on
homogeneity, and are less applicable in the common case when users' discrete
distributions are heterogeneous. Here we consider a natural and tractable model
of heterogeneity, where users' discrete distributions only vary sparsely, on a
small number of entries. We propose a novel two-stage method named SHIFT:
First, the users collaborate by communicating with the server to learn a
central distribution; relying on methods from robust statistics. Then, the
learned central distribution is fine-tuned to estimate the individual
distributions of users. We show that SHIFT is minimax optimal in our model of
heterogeneity and under communication constraints. Further, we provide
experimental results using both synthetic data and $n$-gram frequency
estimation in the text domain, which corroborate its efficiency.
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