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Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models. (arXiv:2206.02455v3 [math.ST] UPDATED)
Oct. 13, 2022, 1:13 a.m. | Yihan Zhang, Nir Weinberger
cs.LG updates on arXiv.org arxiv.org
We consider a high-dimensional mean estimation problem over a binary hidden
Markov model, which illuminates the interplay between memory in data, sample
size, dimension, and signal strength in statistical inference. In this model,
an estimator observes $n$ samples of a $d$-dimensional parameter vector
$\theta_{*}\in\mathbb{R}^{d}$, multiplied by a random sign $ S_i $ ($1\le i\le
n$), and corrupted by isotropic standard Gaussian noise. The sequence of signs
$\{S_{i}\}_{i\in[n]}\in\{-1,1\}^{n}$ is drawn from a stationary homogeneous
Markov chain with flip probability $\delta\in[0,1/2]$. As …
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