Dynamic estimation of slowly varying sequences
We consider the problem of sequentially approximating functions of each element in a slowly-varying sequence, i.e. one where the magnitude $α_i$ of the difference between the elements at positions $i$ and $i-1$ is small. Recent work on implicit trace estimation shows that when $α_t$ is small, reusing queries to past sequence elements can reduce the overall cost [Dharangutte \& Musco, NeurIPS~2021; Woodruff et al., NeurIPS~2022]. We introduce a framework generalizing this to a variety of linear and nonlinear functions on diverse vector spaces, obtaining novel sequential estimation results for matrix powers, spectral densities, Monte Carlo integration, and a boundary value problem from part...
| Authors | Prashant Gokhale, Mikhail Khodak, Sandeep Silwal |
|---|---|
| Primary category | cs.LG |
| Published | 22 June 2026 |
| Last updated at source | 22 June 2026 |
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