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ChronoEpilogi: Scalable Time Series Selection with Multiple Solutions
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Proposes ChronoEpilogi, a scalable, theoretically sound and complete algorithm for finding all minimal-size optimal predictive subsets (Markov boundaries) of multivariate time series for forecasting a target variable.
Problem
Time-series variable selection for forecasting a target has typically returned a single solution, but multiple minimal-size optimally predictive subsets (Markov boundaries) can exist, and missing them can mislead interpretation and causal analysis.
Approach
Extends forward-backward Markov boundary discovery to time series and adds an equivalence search that identifies informationally equivalent (replaceable) variables, so all Markov boundaries are returned as a cartesian product of equivalence classes under composition and interchangeability assumptions, with a faster forward-equivalent approximation.
Key results
- FE reduces computation time by about 70% versus FBE with only a 0.05 drop in causal f1 on synthetic data; FBE attains causal f1 of 0.99 versus 0.57 for GroupLasso.
- On real datasets FE selects on average under 4% of TS variables (about 96% reduction) with R2 on par with GroupLasso (e.g., Electricity 0.940 vs 0.934).
- Multiple Markov boundaries were found for multiple targets in Electricity (3), Traffic (7), PEMS-BAY (3), and METR-LA (7); Solar yielded a single solution.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use approximate FE instead of FBE (ablation) | ChronoEpilogi · Synthetic MTS | time (s): 375±772 -> 118±178 | Helped |
| use approximate FE instead of FBE (ablation) | ChronoEpilogi · Synthetic MTS | causal f1-score: 0.99± 0.064 -> 0.94± 0.188 | Hurt |
| use ChronoEpilogi-FE instead of GroupLasso | synthetic MTS variable selection · Synthetic MTS | causal f1-score: 0.57± 0.349 -> 0.94± 0.188 | Helped |
| select variables with ChronoEpilogi-FE instead of no selection | forecasting models · Electricity | R2: 0.863 -> 0.940 | Helped |
| select variables with ChronoEpilogi-FE instead of no selection | forecasting models · Solar | R2: 0.968 -> 0.985 | Helped |
| select variables with ChronoEpilogi-FE instead of no selection | forecasting models · Traffic | R2: 0.740 -> 0.783 | Helped |
| select variables with ChronoEpilogi-FE instead of no selection | forecasting models · PEMS-BAY | R2: 0.820 -> 0.860 | Helped |
| select variables with ChronoEpilogi-FE instead of no selection | forecasting models · METR-LA | R2: 0.896 -> 0.886 | Hurt |
| use ChronoEpilogi-FE instead of GroupLasso | real-dataset variable selection · Traffic | R2: 0.797 -> 0.783 | Hurt |
| use ChronoEpilogi-FE instead of GroupLasso | real-dataset variable selection · Electricity | R2: 0.934 -> 0.940 | Helped |
| use ChronoEpilogi-FE instead of GroupLasso | real-dataset variable selection · Solar | R2: 0.984 -> 0.985 | No clear effect |
| use ChronoEpilogi-FE instead of GroupLasso | real-dataset variable selection · PEMS-BAY | R2: 0.867 -> 0.860 | Hurt |
Surprising findings
- Shapley value importance is unstable among variables within the same equivalence class; the top variable's stability is near zero (0.05 for XGB, 0.02 for SVR).
- GroupLasso's performance is more sensitive to hyperparameter tuning than ChronoEpilogi's p-value thresholds.
Limitations
- Soundness and completeness rely on assumptions (composition, interchangeability) and on perfect conditional independence tests; the linear ARDL-based tests may not hold for nonlinear dependencies.
- The FE greedy approximation selects more false positives and lower replaceable-variable F1 than FBE.
- Assumes stationarity, which real datasets with trend or seasonality may violate.
Experimental setup
Datasets: Electricity Solar SF Traffic METR-LA PEMS-BAY Synthetic VAR datasets (270 MTS)
Benchmarks: Electricity Solar SF Traffic METR-LA PEMS-BAY Synthetic VAR datasets
Metrics: causal f1-score R2 RMSE MAPE computation time solution size stability
Baselines: GroupLasso No selection
Builds on: KIAMB TIE* TMFBS GroupLasso ARDL
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