Abstract
In the monitoring problem, the input is an unbounded stream P = p1, p2 · · · 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. minc∈C cost(P, c) + λ(c), where cost(P, c) = -ni=1 sin2(2πN pic), 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 | American English |
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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 |
All Science Journal Classification (ASJC) codes
- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability