Low-Precision Streaming PCA

2025-10-25

AI Summary

This work addresses streaming principal component analysis (PCA) under low-precision constraints, aiming to efficiently track the dominant eigenvectors of data streams with extremely low quantization resolution—suitable for resource-constrained real-time applications. Methodologically, we first derive an information-theoretic lower bound on the quantization resolution required to achieve a prescribed estimation accuracy. Then, we propose novel variants of Oja’s algorithm incorporating linear and nonlinear stochastic quantization: both weight storage and update steps employ unbiased randomized quantization, balancing computational efficiency and statistical fidelity. We theoretically establish that, under mild conditions, these algorithms achieve optimal convergence rates, with quantization error nearly independent of ambient dimension. Empirically, on synthetic data streams, our methods closely match the performance of full-precision Oja’s algorithm while substantially reducing memory footprint and arithmetic cost.

Technology Category

• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Data Mining & Knowledge Management: Data Stream Mining

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Abstract

Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantization resolution required to achieve a target accuracy for the leading eigenvector. We study Oja's algorithm for streaming PCA under linear and nonlinear stochastic quantization. The quantized variants use unbiased stochastic quantization of the weight vector and the updates. Under mild moment and spectral-gap assumptions on the data distribution, we show that a batched version achieves the lower bound up to logarithmic factors under both schemes. This leads to a nearly dimension-free quantization error in the nonlinear quantization setting. Empirical evaluations on synthetic streams validate our theoretical findings and demonstrate that our low-precision methods closely track the performance of standard Oja's algorithm.

Problem

• Estimate top principal component in streaming data
• Establish quantization resolution lower bounds for accuracy
• Analyze Oja's algorithm under stochastic quantization schemes

Innovation

• Uses stochastic quantization for streaming PCA
• Achieves near-dimension-free quantization error
• Validates performance matching standard Oja's algorithm