1{
  2  "seed": 1411,
  3  "derivative_bound_check": {
  4    "predicted_max": 0.5873015873015873,
  5    "observed_max": 0.5873012716278044,
  6    "relative_error": 5.374986033014429e-07,
  7    "bound_location": 0.0,
  8    "analytic_numeric_max_gap": 3.1567378289132364e-07
  9  },
 10  "bias_scaling_prediction": {
 11    "predicted_slope": 0.9576460059232068,
 12    "observed_slope": 0.9562668702882926,
 13    "slope_ratio_observed_over_predicted": 0.9985598690681274,
 14    "rows": [
 15      {
 16        "alpha": 0.0,
 17        "predicted_linear_bias": 0.0,
 18        "observed_baseline_b_bias": 0.00013437299130325542,
 19        "joint_train_mse": 9.944095552998701e-05,
 20        "baseline_cross_regime_mse": 0.00010193571553171425,
 21        "joint_cross_regime_mse": 0.00010189734634527286,
 22        "fitted_alpha": 0.0001341819738962893,
 23        "fitted_tau": 0.23011589497233
 24      },
 25      {
 26        "alpha": 0.05,
 27        "predicted_linear_bias": 0.047859601959629336,
 28        "observed_baseline_b_bias": 0.047756090832379305,
 29        "joint_train_mse": 9.580818687379242e-05,
 30        "baseline_cross_regime_mse": 0.00043928052870968753,
 31        "joint_cross_regime_mse": 0.00010018082671487575,
 32        "fitted_alpha": 0.05137334370145234,
 33        "fitted_tau": 0.7992520245044272
 34      },
 35      {
 36        "alpha": 0.1,
 37        "predicted_linear_bias": 0.09554581666349103,
 38        "observed_baseline_b_bias": 0.09560453428039284,
 39        "joint_train_mse": 9.742284768823036e-05,
 40        "baseline_cross_regime_mse": 0.0014248311197335368,
 41        "joint_cross_regime_mse": 9.843910234062992e-05,
 42        "fitted_alpha": 0.09742946903222409,
 43        "fitted_tau": 0.7837634760645263
 44      },
 45      {
 46        "alpha": 0.2,
 47        "predicted_linear_bias": 0.19164426773318896,
 48        "observed_baseline_b_bias": 0.1912787636023856,
 49        "joint_train_mse": 9.918944042284518e-05,
 50        "baseline_cross_regime_mse": 0.005747213710342346,
 51        "joint_cross_regime_mse": 0.00010099567845155088,
 52        "fitted_alpha": 0.2106558905749331,
 53        "fitted_tau": 0.8252081548622062
 54      },
 55      {
 56        "alpha": 0.4,
 57        "predicted_linear_bias": 0.38227219901095233,
 58        "observed_baseline_b_bias": 0.3823734017989071,
 59        "joint_train_mse": 9.843000240422399e-05,
 60        "baseline_cross_regime_mse": 0.02307951568052862,
 61        "joint_cross_regime_mse": 0.00010030937763751038,
 62        "fitted_alpha": 0.3909552665125492,
 63        "fitted_tau": 0.7908966400771289
 64      },
 65      {
 66        "alpha": 0.8,
 67        "predicted_linear_bias": 0.7658530171517917,
 68        "observed_baseline_b_bias": 0.7660247127607649,
 69        "joint_train_mse": 0.00010161823047893185,
 70        "baseline_cross_regime_mse": 0.09097344100691553,
 71        "joint_cross_regime_mse": 9.933993582472864e-05,
 72        "fitted_alpha": 0.7977660621050289,
 73        "fitted_tau": 0.8000909968069085
 74      }
 75    ]
 76  },
 77  "zero_disturbance_prediction": {
 78    "mean_baseline_mse": 9.856082351256858e-05,
 79    "mean_joint_mse": 9.90246763733528e-05,
 80    "joint_over_baseline": 1.0047062599951295,
 81    "rows": [
 82      {
 83        "baseline_mse": 9.32833170934401e-05,
 84        "joint_mse": 9.347766786106346e-05,
 85        "fitted_alpha": -0.0018359754442777662
 86      },
 87      {
 88        "baseline_mse": 0.00010427287559700058,
 89        "joint_mse": 0.00010521555921400823,
 90        "fitted_alpha": 0.0018337445141214646
 91      },
 92      {
 93        "baseline_mse": 9.666887066118742e-05,
 94        "joint_mse": 9.706605944360958e-05,
 95        "fitted_alpha": -0.0009042560167786406
 96      },
 97      {
 98        "baseline_mse": 0.00010147152010286741,
 99        "joint_mse": 0.00010236196998820569,
100        "fitted_alpha": -0.003272748414415243
101      },
102      {
103        "baseline_mse": 9.788786176946618e-05,
104        "joint_mse": 9.834246801682991e-05,
105        "fitted_alpha": 0.0025736185237446737
106      },
107      {
108        "baseline_mse": 9.986842096483505e-05,
109        "joint_mse": 0.00010024066899184692,
110        "fitted_alpha": 0.0011866098219361155
111      },
112      {
113        "baseline_mse": 9.70123687942745e-05,
114        "joint_mse": 9.737927636621525e-05,
115        "fitted_alpha": 0.012784153980822872
116      },
117      {
118        "baseline_mse": 9.802135311747739e-05,
119        "joint_mse": 9.811374110504336e-05,
120        "fitted_alpha": -0.0003468979252745945
121      }
122    ]
123  },
124  "interpretation": "Joint model should recover saturation and improve held-out command-regime error when alpha is nonzero; at alpha=0 no systematic benefit is expected."
125}