  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.
