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Estimating Gaussian Means under Heteroscedasticity and Anisotropy
Probability| Speaker: | Nikita Zhivotovskiy, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Wed, Mar 15 2023, 10:00AM |
In this talk, we explore two problems related to Gaussian mean estimation in the presence of heteroscedasticity and anisotropy. Firstly, we investigate the problem of estimating the common mean of a set of independent Gaussians with unknown and different standard deviations. We propose an adaptive estimator that provides a confidence interval close to that of the maximum likelihood estimator. Secondly, we consider the problem of multivariate Gaussian mean estimation when a malicious adversary corrupts a fraction of the sample. We introduce a median-based estimator that is statistically optimal in this setup and converges at a rate comparable to that of the Gaussian concentration inequality, which holds when no sample contamination is present. Based on arXiv:2010.11537 and arXiv:2301.09024.