## Abstract

In the monitoring problem, the input is an unbounded stream P = p_{1}, p_{2} · · · of integers in [N]:= {1, · · ·, N}, that are obtained from a sensor (such as GPS or heart beats of a human). The goal (e.g., for anomaly detection) is to approximate the n points received so far in P by a single frequency sin, e.g. min_{c}∈_{C} cost(P, c) + λ(c), where cost(P, c) = -n_{i=1} sin^{2}(2π_{N} p_{i}c), C ⊆ [N] is a feasible set of solutions, and λ is a given regularization function. For any approximation error ε > 0, we prove that every set P of n integers has a weighted subset S ⊆ P (sometimes called core-set) of cardinality |S| ∈ O(log(N)^{O(1)}) that approximates cost(P, c) (for every c ∈ [N]) up to a multiplicative factor of 1 ±ε. Using known coreset techniques, this implies streaming algorithms using only O((log(N) log(n))^{O(1)}) memory. Our results hold for a large family of functions. Experimental results and open source code are provided.

Original language | English |
---|---|

Pages (from-to) | 10622-10639 |

Number of pages | 18 |

Journal | Proceedings of Machine Learning Research |

Volume | 151 |

State | Published - 2022 |

Event | 25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain Duration: 28 Mar 2022 → 30 Mar 2022 |

### Bibliographical note

Publisher Copyright:Copyright © 2022 by the author(s)

## ASJC Scopus subject areas

- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability