Plato: Approximate Analytics over Compressed Time Series with Tight Deterministic Error Guarantees

TL;DR

Plato enables fast, approximate time series analytics with tight, deterministic error guarantees by precomputing compressed representations and error measures, supporting complex expressions like correlation with high accuracy.

Contribution

This work introduces a novel framework for providing tight deterministic error guarantees over compressed time series, including new estimation families and the AI property for amplitude-independent bounds.

Findings

AI guarantees often certified results within 1% of true values

Vector Space and Linear Scalable Families lead to high-quality error bounds

Experimental results confirm the effectiveness of AI guarantees on real datasets

Abstract

Plato provides fast approximate analytics on time series, by precomputing and storing compressed time series. Plato's key novelty is the delivery of tight deterministic error guarantees for time series analytics. Plato evaluates any time series expression composed by the linear algebra operators over vectors, along with arithmetic operators. This large scope of possible expressions includes common use cases such as correlation and cross-correlation expressions. Each time series is segmented either by fixed-length segmentation or by (a usually more effective) variable-length segmentation. Each segment is compressed by an estimation/compression function that approximates the actual values and is coming from a user-chosen function family, as taught by many prior works. The novelty is that Plato associates to each segment 1 to 3 (depending on the case) precomputed error measures and, using them, Plato computes tight deterministic error guarantees for analytics over the compressions. Importantly, some compression families lead to much better deterministic error guarantees. This work identifies two broad estimation function family groups (Vector Space (VS) and Linear Scalable Family (LSF)), which lead to theoretically and practically high-quality guarantees, even for expressions (eg correlation) that combine multiple time series that have been independently compressed and may, thus, use misaligned segmentations. The theoretical aspect of "high quality" is crisply captured by the Amplitude Independence (AI) property: An AI guarantee does not depend on the amplitude of the involved time series, even when we combine multiple time series. The experiments on four real-life datasets showed that when the novel AI guarantees were applicable, the approximate query results were certified to be very close (typically 1%) to the true results.