6 problems

Let $b$ be the parameter in the high-dimensional geometric matching model with dimension $d=\omega(\log n)$ and noise variance $\sigma^2=d/(b\log n)$, and let the maximum likelihoo…

In the Gaussian geometric planted matching setting, let the signal-to-noise ratio be $\frac{d}{\log n\,\sigma^2}$, and consider the greedy inner-product algorithm studied in the ci…

Consider the Gaussian model with $X_1,\dots,X_n\stackrel{\mathrm{iid}}{\sim}\mathcal{N}(0,I_d)$ and $Z_1,\dots,Z_n\stackrel{\mathrm{iid}}{\sim}\mathcal{N}(0,\sigma^2I_d)$, and let…

Let $d$ be fixed, and consider the LSS estimator $\hat{\pi}_{\mathrm{LSS}}$ under the assumptions of the fixed-dimensional model. Its error upper bound has the form … where…

Let $n$ particles move in $d$ dimensions, sampled at intervals of length $\delta$, and let $\widehat{\pi}_k$ be the estimator at time step $k$. Let $T_{\max}$ denote the maximum tr…

Let $n$ be the number of points, $d$ the dimension, $\sigma^2$ the noise parameter, and $\mathcal{E}$ the set of errors made by the maximum-likelihood estimator. Write…