Closed-Form Predicate-Level Shapley Attribution for Sliding-Window Aggregates

Pouya Khani; Ira Assent

Home/Archive/arXiv

arXiv · 2608.23087

Closed-Form Predicate-Level Shapley Attribution for Sliding-Window Aggregates

Pouya Khani·Ira Assent

View original source ↗Read source document ↗Export metadata ↓

Abstract

Streaming engines report sliding-window aggregates in real time, but they do not explain \emph{why} an aggregate takes its current value. A natural target is the Shapley value from cooperative game theory, which axiomatically distributes an aggregate among the tuples in the window. Practitioners, however, ask predicate-level questions (e.g., how much a region or customer tier contributed to an average or variance spike). Exact Shapley computation is exponential in the window size, and existing estimators discard the massive overlap between consecutive windows. We show that for SUM, COUNT, AVG, and population/sample variance, exact predicate-level Shapley values admit closed forms in three additively maintained summaries per predicate (count, sum, and sum of squares), with coefficients that depend only on two running harmonic numbers. Attribution therefore reduces to $O(1)$ summary updates per slide for registered predicates, with no coalition enumeration. Overlapping and compositional predicates are answered exactly via atomic refinement of Boolean signatures. We further characterize the phenomenon: every moment-polynomial aggregate admits such a form, while MAX, MIN, and quantiles provably do not at any fixed moment order. Experiments match brute-force Shapley values to floating-point precision on over $10{,}000$ windows, sustain $\approx\!2\,μ$s per slide up to $N=10^6$ ($3{,}200\times$ faster than per-window recomputation of the same formulas), and explain a nighttime fare spike on 2.9M NYC taxi trips at $\approx\!1.8$M summary updates per second.

Explore related subjects

cs.DB

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Pouya Khani, Ira Assent. 2026-08-24. Closed-Form Predicate-Level Shapley Attribution for Sliding-Window Aggregates. https://arxiv.org/abs/2608.23087

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Functional Pilot for Certified Freshness-Aware Semantic--Spatial Range Retrieval

Geographic applications need every object inside a radius that satisfies a semantic threshold, yet embedding indexes return approximate top-ranked lists and may omit qualifying records silently. We present FRESH-GEORANGE, a semantic- spatial range design that separates source-watermark freshness from optional record age. Geographic cells and semantic mi- croblocks provide admissible pruning bounds; a graph proposes verification order but supplies no correctness evidence. Exact mode scans every nonprunable block and the delta overlay. Certified mode may stop early and reports a deterministic query- specific recall lower bound from verified answers and unresolved records. A reproducible CPU pilot uses 2,500 real OpenFlights airport records, a 2,000-record base, and 740 simulated insert, delete, and text-revision events; it evaluates 180 unique queries over five seeds. Exact mode achieved 100.00% set recall on every query. The 95-percent mode achieved 99.91% empirical mean recall with a 99.41% reported mean certificate and no observed bound violation. However, its 7.24 ms median latency was 5.85 times the 1.24 ms spatial-first exact baseline, and full-history delta replay became slower than rebuilding at larger batches. The prototype therefore validates the completeness mechanism, not performance superiority or production freshness. Submission- scale evaluation requires real map diffs, official recent baselines, and truly incremental versioned maintenance.

cs.DB↗

arXiv2026

AkasicMEM: Governed Enterprise Memory for Agents

Agent memory enables enterprise agents to retain knowledge acquired during work and reuse it across tasks and agents, turning execution experience into persistent organizational knowledge. Realizing this potential requires both source--memory integration, through which enterprise sources and accumulated memory can be utilized together, and memory governance, through which shared memory remains subject to organizational policies throughout its lifecycle. These requirements interact when information from enterprise sources persists in memory. As this information is repeatedly derived and reused under changing principals and policies, source restrictions may be bypassed, resulting in information leakage. Preventing such leakage requires authorization continuity, under which source restrictions remain effective throughout source-to-memory and memory-to-memory derivation and reuse. Existing approaches address these concerns individually, but do not treat source--memory integration, memory governance, and authorization continuity as combined core design targets across the memory lifecycle. We define Governed Enterprise Memory as agent memory designed around this combined scope and present AkasicMEM as its realization. AkasicMEM realizes authorization continuity through transitive lineage, policy composition during memory formation, and policy re-evaluation during retrieval. It is built on GraphAI's AkasicDB, a unified vector--graph--relational database whose storage and execution substrate enables the underlying operations of these mechanisms to be jointly optimized and executed.

cs.DB↗

arXiv2026

VectorMaton: Efficient Vector Search with Pattern Constraints via an Enhanced Suffix Automaton

Approximate nearest neighbor search (ANNS) has become a cornerstone in modern vector database systems. Given a query vector, ANNS retrieves the closest vectors from a set of base vectors. In real-world applications, vectors are often accompanied by additional information, such as sequences or structured attributes, motivating the need for fine-grained vector search with constraints on this auxiliary data. Existing methods support attribute-based filtering or range-based filtering on categorical and numerical attributes, but they do not support pattern predicates over sequence attributes. In relational databases, predicates such as LIKE and CONTAINS are fundamental operators for filtering records based on substring patterns. As vector databases increasingly adopt SQL-style query interfaces, enabling pattern predicates over sequence attributes (e.g., texts and biological sequences) alongside vector similarity search becomes essential. In this paper, we formulate a novel problem: given a set of vectors each associated with a sequence, retrieve the nearest vectors whose sequences contain a given query pattern. To address this challenge, we propose VectorMaton, an automaton-based index that integrates pattern filtering with efficient vector search, while maintaining an index size comparable to the dataset size. Extensive experiments on real-world datasets demonstrate that VectorMaton consistently outperforms all baselines, achieving up to 10x higher query throughput at the same accuracy and up to 18x reduction in index size.

cs.DB↗