High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization. (arXiv:2202.13157v2 [stat.ML] UPDATED)

In this paper, we propose a uniformly dithered one-bit quantization scheme
for high-dimensional statistical estimation. The scheme contains truncation,
dithering, and quantization as typical steps. As canonical examples, the
quantization scheme is applied to three estimation problems: sparse covariance
matrix estimation, sparse linear regression, and matrix completion. We study
both sub-Gaussian and heavy-tailed regimes, with the underlying distribution of
heavy-tailed data assumed to possess bounded second or fourth moment. For each
model we propose new estimators based on one-bit quantized …

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