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Dynamic Ranking and Translation Synchronization
In this setup, we are given a sequence of comparison graphs $(G_t)_{t\in \mathcal{T}}$, where $\mathcal{T} \subset [0, 1]$ is a grid representing the time domain, and for each item $i$ and time $t\in \mathcal{T}$ there is an associated unknown strength parameter $z^*_{t, i}\in \mathbb{R}$.
Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method
When $(G_{t'})_{t' \in \mathcal{T}}$ is a sequence of Erd\"os-Renyi graphs, we provide non-asymptotic $\ell_2$ and $\ell_{\infty}$ error bounds for estimating $w_t^*$ which in particular establishes the consistency of this method in terms of $n$, and the grid size $\lvert\mathcal{T}\rvert$.
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