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Discovering Sequential Patterns with Predictable Inter-event Delays
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Proposes HOPPER, an MDL-based greedy miner that discovers serial episodes whose inter-event delays are modeled by discrete probability distributions (Uniform, Gaussian, Geometric, Poisson).
Problem
Existing sequential pattern set miners based on serial episodes penalize all gaps equally, biasing against long inter-event delays and failing to capture regularity in delays.
Approach
Model each pattern's inter-event delays explicitly with discrete delay distributions and select pattern sets via MDL, so that patterns with predictable (even long) delays compress data well; a greedy pattern-growth search with optimistic gain estimates and delay-aware alignment makes this tractable.
Key results
- On synthetic data with normal delays, HOPPER keeps a high F1 score with mean inter-event delays up to 180, while SQS and SKOPUS deteriorate quickly.
- On the Holidays dataset HOPPER finds a single pattern that recovers all fixed and lunar-calendar holidays, whereas competitors find only fragments.
- On Radio data HOPPER discovers patterns up to 7 events long, versus at most 4 for SQS and 2 for most competitors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Model inter-event delays with probability distributions (HOPPER vs. SQS) | HOPPER · Holidays | average expected pattern distance: 393 vs 19.2 | Helped |
| Model inter-event delays with probability distributions (HOPPER vs. SQS) | HOPPER · Radio | average expected pattern distance: 48 vs 5.8 | Helped |
| Model inter-event delays with probability distributions (HOPPER vs. SQS) | HOPPER · Samba | average expected pattern distance: 110 vs 2.7 | Helped |
Surprising findings
- SKOPUS remains consistent under increasing delay variance, attributed to it ignoring distances between events.
- PPM yields an order of magnitude more patterns, most of which are singletons.
Limitations
- Search space is much larger than in order-only pattern miners, raising susceptibility to noise in principle.
- Only models delays between consecutive events; rule-like dependencies between non-adjacent events are not captured.
- Greedy heuristic provides no optimality guarantee for the MDL objective.
Experimental setup
Datasets: Holidays Radio playlist Lifelog Samba commits Bach Chorales (UCI) Rolling Mill production log Ice skating muscle activations Gutenberg / Romeo and Juliet / A Room with a View / The Great Gatsby text
Benchmarks: synthetic planted-pattern recovery (F1) real-world event sequence datasets (Holidays, Radio, Lifelog, Samba, Chorales, Rolling, Skating, text)
Metrics: F1 score with edit-distance-weighted partial credit number of patterns expected first-to-last event distance number of delay distributions
Baselines: SQS SQUISH SKOPUS ISM PPM
Builds on: SQS SQUISH OMEN Skopus Periodic pattern MDL (Galbrun et al.)
Closest papers by meaning
- SEQRET: Mining Rule Sets from Event Sequences (AAAI 2026 · similarity 0.87)
- Causal Discovery from Event Sequences by Local Cause-Effect Attribution (NeurIPS 2024 · similarity 0.82)
- Towards Understanding Evolving Patterns in Sequential Data (NeurIPS 2024 · similarity 0.82)
- How Patterns Dictate Learnability in Sequential Data (NeurIPS 2025 · similarity 0.82)
- Conformal Anomaly Detection in Event Sequences (ICML 2025 · similarity 0.81)
- Long Range Propagation on Continuous-Time Dynamic Graphs (ICML 2024 · similarity 0.81)
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