Incremental Delta-Shapley: A Standalone Runtime for Predicate Attribution on Sliding Windows

Abstract

Continuous aggregate queries over sliding windows are common in real-time analytics, but most systems report \emph{what} an aggregate is doing without attributing \emph{which} predicates account for the result. A companion paper~\cite{khani2026closedformpredicatelevelshapleyattribution} shows that exact predicate-level Shapley attribution for SUM, COUNT, AVG, and variance needs only three additive predicate summaries with closed-form coefficients. Those results settle the mathematics, not how a runtime maintains summaries across slides, exposes attribution, answers unregistered predicates, or amortizes repeated ad hoc ones. We present \textbf{IDS} (Incremental Delta-Shapley), a standalone single-node runtime that turns those closed forms into a deployable explanation system. IDS consumes window-maintenance deltas, updates global, marginal, and atom summaries, and evaluates any closed form in constant time. Overlapping predicates use atomic refinement, and a restricted SQL-like API exposes attribution and its per-slide change as first-class operators. Unregistered predicates are answered by a retained-state scan, an inverted index, or an amortized sliding-window sample with concentration guarantees; frequent ones are promoted by rebuilding the refinement. On synthetic, adversarial, NEXMark-style, and NYC taxi workloads, attribution matches exhaustive Shapley enumeration to floating-point precision; incremental maintenance is flat in $N$ and up to $4.3\times10^{5}\times$ faster than per-window scans of the same form; and adaptive promotion cuts ad hoc cost by up to $9.2\times$ on Zipfian traces.