Higgs Uncertainty Inference

Measuring the Higgs signal strength mu (how many signal events appear relative to the Standard Model expectation) is a canonical LHC analysis. The hard part is not the point estimate but the uncertainty: detector effects and modeling assumptions (systematics) shift the event distributions in ways that are only partly known, and an interval that is honest under nominal conditions can silently under-cover once the true nuisance parameters drift from the training distribution.

The physics data derives from the FAIR Universe HiggsML Uncertainty Challenge. The task turns it into a stress test of uncertainty quantification: hidden pseudo-experiments mix a nominal regime with one whose systematic shifts fall outside the documented training configuration, and the two are indistinguishable per experiment by design.

Build a pipeline that estimates mu for each unlabelled pseudo-experiment and reports a calibrated central 68.27% confidence interval, packaged as a self-contained deliverable at /app/higgs_model/ (checkpoint, model.py, predict.py, run_summary.json).

• Inference runs as python /app/higgs_model/predict.py --data-dir … --checkpoint … --output-path … and writes one JSONL row per experiment: {"experiment_id":…,"mu":…,"mu_lo":…,"mu_hi":…} with finite values satisfying mu_lo < mu <= mu_hi.
• Inference must be deterministic, read only its supplied input, and use no external services or hardcoded per-experiment lookups.
• The checkpoint may occupy at most 2.5 GB, and a few hundred experiments must finish within 20 minutes.
• Intervals must remain useful when hidden nuisance parameters differ from the nominal training distribution.

Visible data staged read-only under /data: labeled training events (train/events.parquet with features, labels, weights, and detailed process labels), unlabelled validation experiments, calibration experiments with separate truth in calibration/labels.parquet, plus systematics.json and metadata.json describing the feature columns and documented nuisance model.

• A runnable starter model under /app/higgs_model/ exercising the full contract.
• A pinned CPU scientific Python stack: NumPy, pandas, pyarrow, scikit-learn, SciPy, XGBoost, LightGBM, iminuit, Optuna, PyTorch Lightning, and statsmodels.
• The machine is offline; everything needed is already present.

A root-only verifier runs the submitted model as the unprivileged agent user, without network access, on hidden pseudo-experiments spanning two regimes: known systematics and shifted systematics. Per-regime and pooled metrics are normalized between an event-blind baseline anchor and a reference-solution anchor, then combined as a weighted geometric mean (known 0.3, shifted 0.3, overall 0.4). The per-regime slices blend point RMSE on mu with the mean Winkler interval score; the pooled slice adds a challenge-style quantiles calibration score. The Winkler score punishes every missed interval by its distance, so covering the aggregate while sacrificing individual experiments cannot profit.

• Hard gates zero the reward: pooled empirical coverage more than 0.15 from 68.27% (with a soft penalty beyond 0.05), mean interval width of 1.60 or more on either regime (the trivial-width anchor), or failing to beat the event-blind baseline on any scored term.
• Safeguard probes also zero it: repeated runs must agree within 1e-6, and a response probe that resamples each experiment's events must change at least half the predictions; a lookup table or constant answer fails.
• Contract failures (malformed rows, non-finite values, inverted intervals, an oversized checkpoint, or a timed-out run) also zero the result.