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Sparse Nonlinear Interaction Recovery

  • Task ID: math.sparse_nonlinear_interaction_recovery
  • Domain: math
  • Subdomain: statistical_learning
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: sparse_nonlinear_model, additive_model, pairwise_interactions, support_recovery, feature_selection, robust_regression, non_gaussian_noise, high_coherence_dictionary, nuisance_adjustment, environment_effects, uncertainty_ranking

Runtime and requirements

  • Estimated time: 240-480 minutes
  • Python: >=3.11
  • Packages: numpy
  • GPU required: no
  • Network required: no

Public input and output contract

Inputs

  • design_matrix.npy (data): Standardized observed feature matrix X with shape (n_samples, n_features).
  • observations.npy (data): Response vector generated by sparse nonlinear main effects, sparse pairwise interactions, nuisance effects, and heavy-tailed noise.
  • nuisance_covariates.npy (data): Observed low-dimensional nuisance covariates for drift/batch adjustment.
  • environment_id.npy (data): Observed integer environment/regime id for each sample.
  • group_structure.json (data): Feature group partition.

Outputs

  • beta_hat.csv (data): Recovered signed nonlinear feature effects with per-feature support indicator.
  • hyperparams.json (data): Method metadata, selected tuning values, and convergence diagnostics.
  • diagnostic_trace.csv (data): Diagnostic objective trace; not matched to a reference trajectory.
  • lambda_cv_trace.csv (data): Per-candidate/per-fold validation losses for tuning selection.
  • beta_hat.npy (data): Recovered signed nonlinear additive effect vector in feature-index order.
  • support_indicator.npy (data): Binary feature support vector.
  • support_score.npy (data): Continuous feature support confidence scores in [0, 1].
  • interaction_score.npy (data): Symmetric pairwise interaction confidence matrix in [0, 1] with zero diagonal.
  • interaction_weight.npy (data): Symmetric signed pairwise interaction weight matrix with zero diagonal.
  • hyperparam_vector.npy (data): Vector [sparsity_fraction, interaction_density].
  • objective_trace.npy (data): Finite diagnostic trajectory padded to fixed length.
  • objective_increments.npy (data): Differences of objective_trace between consecutive diagnostic entries.
  • rmse_score.npy (data): Training RMSE for the fitted nonlinear signal against the nuisance-adjusted response.
  • moment_vector.npy (data): Vector [rmse_score, iterations, selected_lambda_cv, lambda_hat].
  • objective_decrease_count.npy (data): Reported diagnostic count for objective decreases; format-only artifact.

Public repository files

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Provenance

This task is included in the current seed42 benchmark set at dataset revision f11a199f71fb4b854ac43a1bf548d5df519141a9.

This page is generated only from files tracked in the public ASI-Bench repository at commit c9c1ba960854. Submission bundles, run logs, private scoring configuration, and private reference answers are not read by this page generator.