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You are here: Home / Seminars / Machine Learning and Signal Processing / How to Estimate Covariance Matrices from One-Bit Samples

How to Estimate Covariance Matrices from One-Bit Samples

Johannes Maly (Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence, LMU Munich)
When May 16, 2024
from 01:00 to 02:00
Attendees Johannes Maly
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Title: How to Estimate Covariance Matrices from One-Bit Samples

Abstract: We consider covariance estimation of any subgaussian distribution from finitely many i.i.d. samples that are quantized to one bit of information per entry. We show how reliable estimators can be constructed for one-bit quantizers with and without dithering. The latter uses uniformly distributed dithers on [−λ,λ] but only enjoys near-minimax optimal, non-asymptotic error estimates in the operator and Frobenius norms if λ is chosen proportional to the largest variance of the distribution. However, this quantity is not known a-priori, and in practice λ needs to be carefully tuned to achieve good performance. To resolve this problem we further introduce a tuning-free variant of this estimator, which replaces λ by a data-driven quantity. We prove that this estimator satisfies the same non-asymptotic error estimates - up to small (logarithmic) losses and a slightly worse probability estimate.   


In Room M7.101 of Monod campus, ENSL.