低精度流式PCA在有限精度下高效估算主成分，逼近理论极限。
Low-Precision Streaming PCA
- 采用随机量化更新权重与梯度，保持无偏性
- 批量版本在两种量化下逼近信息论下界，误差近似无关维度
- 适合资源受限场景下的实时主成分分析
低精度流式PCA在精度受限条件下，对流数据中的主成分进行估计。本文建立了实现目标精度所需量化分辨率的信息论下界。研究了在线性与非线性随机量化下对奥卡算法的改进，通过无偏随机量化权重向量和更新量，在数据分布满足弱矩与谱隙假设的前提下，批量版本在两种方案下均达到下界（仅差对数因子）。这使得在非线性量化下，量化误差几乎不随维度增长。合成数据流上的实验验证了理论结果，表明低精度方法性能接近标准奥卡算法。
原文摘要 · Abstract (English)
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.
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