Dynamic estimation of slowly varying sequences (opens in new tab)

We consider the problem of sequentially approximating functions of each element in a slowly-varying sequence, i.e. one where the magnitude $\alpha_i$ of the difference between the elements at positions $i$ and $i-1$ is small. Recent work on implicit trace estimation shows that when $\alpha_t$ is small, reusing queries to past sequence elements can reduce the overall cost [Dharangutte \& Musco, NeurIPS~2021; Woodruff et al., NeurIPS~2022]. We int...