Resolution limits for process comparison from event data
Antony R. Lee, Peter Tiňo, Iain B. Styles
cs.DB · cs.LG · stat.ML
Quick verdict
Formalizes why flat event logs cannot certify concurrency: rigorous, computable theory; evaluation fully simulated and partly true by construction.
Summary
This paper establishes a resolution limit for process comparison: any comparison computed only from the stochastic language of a flat event log cannot certify concurrency. The authors model a process as a distribution over labelled partial orders and compare models through charts (a modular block decomposition and the stochastic-language map) under a Bhattacharyya/Fisher-Rao geometry, characterising exactly what each chart conflates: a genuine concurrency and a balanced interleaving of the same steps share one stochastic language (Theorem 4.1, Example 4.1), no trace-observable comparison is a metric (Corollary 4.1), the directly-follows table loses a factorial amount of rank (Theorem 4.3), and an estimability certificate (smallest singular value of the law matrix) flags undecidable comparisons before any data is collected. A dictionary rewrites named measures - fitness, precision, entropic relevance, earth-mover and Jensen-Shannon distances, behavioural profiles - in this form. On a 20-site simulated Synthea clinical fleet, reading timestamps as partial orders recovers all four generating clusters at adjusted Rand index 1.000, whereas flattening with five standard miners reaches at best 0.633; swapping only the geometry drops recovery to 0.615. Limitations: the evaluation is entirely simulated with ground truth fixed by construction (some curves hold by algebra), the impossibility assumes a uniform scheduling law, and the input representation relies on a companion paper still lacking an identifier.
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Assessment at a glance
5
risk flags identified
● high 0
● medium 3
● low 2
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- Every event log's stochastic language is realised equally well by a concurrency-free chain mixture, so no comparison computed from traces alone can certify concurrency (Lemma 4.1, Theorem 4.1, Corollary 4.1).
- The differences no trace-level comparison can register are spanned by explicit linearisation relations with a dimension and membership test, computable before any data is acquired.
- A concurrency reported by a directly-follows-based miner comes from the miner's own rule: every DFG table a model induces is induced also by a model with no concurrency (Section 4.4, Theorem 4.3).
- Where traces conflate concurrency, the distinction is recoverable from timestamps read as partial orders: on a simulated 20-site clinical fleet this recovers all four generating clusters at ARI 1.000 versus 0.633 for the best flattened route.
- The remedy for the conflation is a choice of what is recorded rather than a larger sample, and the estimability certificate (sigma-min of the law matrix) identifies undecidable comparisons before data collection.
Strengths
Computable negative result, not just a warning
Theorem 4.1 gives an explicit basis of ker rT with a dimension and membership test; Corollary 4.1 turns the folklore of 'representational bias' (van der Aalst 2016) into a precise, checkable statement that no trace-observable comparison is a metric on chain-complete spaces.
Decision-first framing with pre-data certificates
The four-stage procedure (Fig 1b) plus Definition 6.1's sigma_min of the law matrix give a verdict (zero = infeasible at any sample size) and a scale (sigma_min = (j!)^(-1/2) for j concurrent activities, a w! sample-size multiplier) computable before any log is opened.
Carefully controlled two-arm experimental design
Practitioner-relevant dictionary of named measures
Unusual honesty and a reproducibility posture
Weaknesses
Fully simulated and partly circular evaluation
Impossibility is conditional on the uniform scheduling law
Dependence on an unavailable companion paper and supplementary material
Small scale and supplied cluster count
Theory-practice gap for computation at scale
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Scope & Claims
The paper addresses a foundational question in process mining: what can a comparison of process models, computed from flat event logs, actually distinguish? The central claim is a resolution limit - every event log's stochastic language is equally well explained by a concurrency-free model (Lemma 4.1, Theorem 4.1), so no trace-level comparison can certify concurrency; the limit is characterised computably before data collection (kernel bases, rank counts, the estimability certificate), and the remedy is richer recording (timestamps, object-centric references) rather than larger samples. Positioned as OR/decision support for healthcare - capacity planning differs for concurrent versus sequential services - but applicable to process comparison generally. The paper introduces no discovery algorithm and no new distance: a deliberate scoping that makes the contribution a lens rather than a tool.
The remaining sections cover Methodology Assessment, Statistical Evidence, Results & Reproducibility, Limitations & Risks, and Verdict & Recommendations.
- All 5 strengths & 5 weaknesses, analyzed in detail
- 5 risk flags with severity, section & reviewer questions
- Methods & statistical evidence assessment
- 5 questions a peer reviewer would ask
- Full six-dimension evaluation report & recommendations
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Frequently asked questions
Why can't process mining detect concurrency from a standard event log?
A standard log flattens each execution into one total sequence. The paper proves that a truly concurrent model and a model that merely chooses between the two orders with balanced probability produce exactly the same trace frequencies, so every trace-based comparison - fitness, precision, entropic relevance, earth-mover distance, directly-follows graphs - scores them identically. Any concurrency a miner reports therefore comes from the algorithm's built-in rules, not from the data itself.
What does the paper recommend instead of collecting more data?
Record more structure: keep timestamps (treating co-timestamped events as unordered), or use object-centric records that fix ordering within an execution. On the simulated 20-site clinical fleet this recovers all four generating site groups at adjusted Rand index 1.000, whereas the best route through flattened logs reaches only 0.633.
Was the evaluation done on real hospital data?
No. The authors screened 59 public or credentialed logs (including BPI Challenges 2012/2013 and the eICU database) and found none combining a known generating model, a site key, and within-execution concurrency. The evaluation therefore uses a Synthea-simulated 20-site fleet with ground truth fixed by construction, plus synthetic mixture experiments.
Is code available for this paper?
Yes - the proc-posets package (GitHub, archived at Zenodo, DOI 10.5281/zenodo.22757993) implements the computational stages. The clinical fleet is generated by the open-source Synthea simulator, with generation parameters in the supplementary material and available from the authors on request.
About this review
This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Proofs of Theorems 4.1-4.4 and Proposition 6.1 are in supplementary material absent from the extracted text; their correctness is taken from the authors' statements.
- Figures 1-4 and the supplementary dictionary and fleet-recovery tables are described textually only; exact curves and table values could not be independently inspected.
- The companion paper Lee et al. (2026b), on which the input representation depends, is listed as 'identifier awaited', so the cospan construction could not be checked.
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