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Sparse partial-prediction validation

This page records the first known-truth qualification for the 1.1 sparse partial-trajectory prediction tranche. It separates model-based conditional Gaussian prediction from participant-aware split-conformal finite-grid prediction.

The evidence does not claim continuous-domain conformal coverage, latent-function conformal coverage, or propagation of population-estimation uncertainty.

Qualified implementation

The development surface is contained in dedicated modules:

  • eyetrajectoriespy.sparse_partial_prediction
  • eyetrajectoriespy.sparse_partial_conformal

The frozen 1.0 root namespace and fit_sparse_fpca() defaults are unchanged.

Oracle-population conditional prediction

The first qualification component supplies the predictor with known population mean, covariance surface and measurement-error variance. This isolates the conditional-Gaussian calculation from smoothing and population-estimation error.

The simulation uses a three-mode Gaussian functional process, fixed future target grid (0.75, 0.85, 0.95), and native history observations before either cutoff 0.30 or 0.60. Four deterministic scenarios cross:

  • history length: 6 versus 12 observations; and
  • measurement-noise SD: 0.05 versus 0.20.

Each scenario contains 400 independent target curves.

Results

Noise SD Cutoff History n Latent RMSE Mean latent conditional variance Latent standardized-error SD Latent 95% coverage Observed standardized-error SD Observed 95% coverage
0.05 0.30 6 0.2828 0.07568 1.0329 0.9358 1.0372 0.9417
0.05 0.60 12 0.03590 0.001205 1.0344 0.9408 1.0052 0.9458
0.20 0.30 6 0.5837 0.3543 0.9860 0.9500 0.9911 0.9467
0.20 0.60 12 0.1350 0.01763 1.0149 0.9400 1.0168 0.9425

The standardized-error SDs remain close to one and the nominal pointwise 95% intervals show coverage near 0.95 under oracle population truth.

Increasing observed history substantially reduces conditional uncertainty in both noise regimes:

  • low noise: mean latent conditional variance 0.07568 -> 0.001205;
  • higher noise: 0.3543 -> 0.01763.

These are qualification results for the declared simulator, not a universal performance guarantee.

Participant-aware split conformal qualification

The conformal experiment deliberately includes repeated trials.

  • calibration: 60 participants × 2 trials = 120 curves;
  • targets: 180 participants × 2 trials = 360 curves;
  • within-participant latent-score correlation is introduced through shared participant effects;
  • future target grid has three points;
  • alpha = 0.10;
  • calibration unit is participant_id;
  • each participant score is the maximum trial-level nonconformity;
  • each trial-level nonconformity is the maximum standardized absolute future residual across all three target-grid points.

The conformal critical value was 2.32564.

Coverage result

Participant-level simultaneous success requires both target trials and every future target-grid point to lie within their bands.

  • participant-level simultaneous coverage: 0.90556;
  • curve-level simultaneous coverage: 0.95278.

The participant-level result is the claim-matched metric because participant is the declared exchangeability/calibration unit in this repeated-trial design.

Guarded failure evidence

Two failure cases are retained in the qualification artifact:

  1. replacing one required calibration target timestamp 0.85 with 0.86 causes calibration_future_grid_observation_missing rather than interpolation;
  2. deliberate proper-training/calibration curve-ID overlap fails explicitly with ValueError.

Deterministic replay of the conformal scenario passed.

Scope boundaries

The qualification supports the following statements:

  • the base predictor uses the full fitted covariance and native sparse history to produce conditional future means and latent covariance;
  • model-based conditional variances are calibrated under the known Gaussian population used in the oracle simulation;
  • more history reduces conditional uncertainty in the qualified scenarios;
  • participant-aware split conformal calibration can produce finite-grid simultaneous prediction bands for future observed measurements under the declared exchangeability design;
  • repeated trials are not treated as independent calibration units when a group column is supplied;
  • calibration future responses are not interpolated.

It does not support claims of:

  • continuous-domain conformal coverage between target points;
  • conformal coverage for the latent noise-free function;
  • automatic validity under informative missingness or covariate shift;
  • population-estimation uncertainty propagation;
  • universal optimality of the chosen cutoff, grid or simulator;
  • planar/asynchronous prediction; or
  • multilevel functional prediction.

Reproducibility record

The first completed qualification run on the feature branch was:

  • workflow: sparse-partial-prediction-validation;
  • run: 37356266298;
  • artifact: 11365360297;
  • artifact digest: sha256:0418eb4a676e883f1cfb6fb25ed20aed64df9fc52d31d76b2a4976ea7db254fc.

The final merge decision requires a fresh exact-head run after documentation is complete; the record above is retained as the first completed scientific qualification rather than being presented as the eventual final-head release evidence.