Distributed Mean Estimation Using Rotated Vector Quantization
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Solution Overview
Problem
Distributed mean estimation in computing systems faces significant communication costs, particularly in scenarios with low-power and low-bandwidth devices, which can be prohibitive for modern applications.
Innovation Solution
The implementation of a computing system that uses random rotation and probabilistic quantization techniques to reduce communication costs, where client devices rotate vectors by a random rotation matrix and perform probabilistic quantization before transmitting them to a centralized server, and the server decodes and aggregates these vectors to estimate the mean.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If distributed mean estimation is performed by transmitting full-precision vectors from clients to server, then estimation accuracy is maintained, but communication cost becomes prohibitive for low-power and low-bandwidth devices
Solution Approach 1:
The patent changes the precision parameter of vector transmission from full-precision to quantized precision. Clients perform probabilistic quantization on rotated vectors, transmitting only quantized values with fewer bits. This parameter change reduces communication bandwidth requirements and energy consumption while maintaining acceptable estimation accuracy through the mathematical properties of the random rotation and probabilistic quantization scheme.
Solution Approach 2:
The patent introduces a rotational dimension by applying random rotation matrices to vectors before quantization. This dimensional transformation rotates the vector into a new coordinate system where probabilistic quantization preserves more information. The rotation adds a stochastic dimension that helps maintain estimation accuracy even after aggressive quantization, effectively using dimensional transformation to bridge the gap between communication efficiency and estimation precision.
2Loss of energy
If quantization is applied directly to original vectors, then communication cost is reduced, but mean square error of estimation increases significantly
Solution Approach 1:
The patent applies preliminary random rotation to vectors before quantization. This preliminary transformation reorients the vector in a stochastic coordinate system where subsequent quantization operations preserve more relevant information for mean estimation. By performing this preparatory rotation action, the system ensures that the quantization step that follows will have minimal impact on estimation accuracy, effectively pre-conditioning the data to withstand quantization better.
Solution Approach 2:
The random rotation matrix acts as an intermediary transformation between the original vector and the quantized representation. Instead of directly quantizing the original vector, the rotation matrix mediates the transformation, creating an intermediate rotated vector that has more favorable properties for quantization. This intermediary step preserves the essential information needed for accurate mean estimation while enabling more aggressive quantization for communication efficiency.
3Reliability
If random rotation matrices are used for privacy protection, then security is improved, but computational complexity increases
Solution Approach 1:
The patent changes the dimensionality parameter of the random rotation matrices to balance privacy protection with computational feasibility. By using rotation matrices with specific dimensional properties (e.g., rotating in random 2D planes rather than full d-dimensional rotations), the system maintains strong privacy guarantees through the randomness while reducing the computational burden on resource-constrained client devices. This parameter adjustment allows low-power devices to perform the necessary cryptographic-style obfuscation without excessive energy consumption.
Data Source
AI summary
The present disclosure provides systems and methods for communication efficient distributed mean estimation. In particular, aspects of the present disclosure can be implemented by a system in which a number of vectors reside on a number of different clients, and a centralized server device seeks to estimate the mean of such vectors. According to one aspect of the present disclosure, a client computing device can rotate a vector by a random rotation matrix and then subsequently perform probabilistic quantization on the rotated vector. According to another aspect of the present disclosure, subsequent to quantization but prior to transmission, the client computing can encode the quantized vector according to a variable length coding scheme (e.g., by computing variable length codes).