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"paper": "GJblFvJcMb",
"claim": 5,
"arxiv": "2504.19043",
"source_scope": "Section 3.2 (average case) and Section 3.4 (adversarial case)",
"design": {
"K": [
5,
10,
20
],
"n": [
500,
1500,
3500,
10000
],
"n_reps": 50,
"coef": "N(0,1)",
"interactions_scaled_to_main_R2": 0.7,
"noise_var": 0.1,
"binary_factors": true,
"true_pi": "Proposition 1 closed-form"
},
"average_case": [
{
"K": 5,
"sweep": [
{
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"n": 500,
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"rmse_median": 0.006441473842272505,
"bias2_median": 1.925756012859587e-07,
"var_median": 4.0604308635783115e-05,
"variance_dominates": true,
"coverage_pi": 0.9480000000000001,
"rmse_Q": 0.041286964330342096,
"lam": 1.6711055759427953
},
{
"K": 5,
"n": 1500,
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"bias2_median": 4.397210394640941e-08,
"var_median": 1.528652881425369e-05,
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"coverage_pi": 0.968,
"rmse_Q": 0.02456763127249781,
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},
{
"K": 5,
"n": 3500,
"rmse_mean": 0.0023278446035150196,
"rmse_median": 0.0023115791005000963,
"bias2_median": 6.485479860845058e-08,
"var_median": 5.278543139260377e-06,
"variance_dominates": true,
"coverage_pi": 0.952,
"rmse_Q": 0.01693910751191979,
"lam": 1.6711055759427953
},
{
"K": 5,
"n": 10000,
"rmse_mean": 0.00155414240696854,
"rmse_median": 0.0015758935848253172,
"bias2_median": 1.870114581873225e-08,
"var_median": 2.3437304364133936e-06,
"variance_dominates": true,
"coverage_pi": 0.924,
"rmse_Q": 0.010912603985334978,
"lam": 1.6711055759427953
}
],
"rmse_decreases": true,
"variance_dominates_at_maxn": true,
"coverage_pi_at_maxn": 0.924
},
{
"K": 10,
"sweep": [
{
"K": 10,
"n": 500,
"rmse_mean": 0.007013917440829284,
"rmse_median": 0.006713439826552316,
"bias2_median": 1.245846044718415e-06,
"var_median": 4.321492669620198e-05,
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"coverage_pi": 0.938,
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"lam": 1.8314563277706923
},
{
"K": 10,
"n": 1500,
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"bias2_median": 2.1797935534346663e-07,
"var_median": 1.3950627130498467e-05,
"variance_dominates": true,
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},
{
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"bias2_median": 3.448669052052663e-08,
"var_median": 5.359381818842434e-06,
"variance_dominates": true,
"coverage_pi": 0.958,
"rmse_Q": 0.013969799106910681,
"lam": 1.8314563277706923
},
{
"K": 10,
"n": 10000,
"rmse_mean": 0.0013963923026081933,
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"var_median": 1.745040906126524e-06,
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}
],
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},
{
"K": 20,
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"bias2_median": 9.107464676598005e-07,
"var_median": 0.00014098233892214615,
"variance_dominates": true,
"coverage_pi": 0.9460000000000001,
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"lam": 2.0007786273454538
},
{
"K": 20,
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"bias2_median": 3.770463942592464e-07,
"var_median": 2.737060116436915e-05,
"variance_dominates": true,
"coverage_pi": 0.9440000000000002,
"rmse_Q": 0.10284634701539644,
"lam": 2.0007786273454538
},
{
"K": 20,
"n": 3500,
"rmse_mean": 0.003423300986658493,
"rmse_median": 0.003327497302306002,
"bias2_median": 9.342114747453597e-08,
"var_median": 1.0773183248827142e-05,
"variance_dominates": true,
"coverage_pi": 0.9480000000000002,
"rmse_Q": 0.0700078953986648,
"lam": 2.0007786273454538
},
{
"K": 20,
"n": 10000,
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"rmse_median": 0.0019239108847675613,
"bias2_median": 7.217569374034592e-09,
"var_median": 3.699654089227817e-06,
"variance_dominates": true,
"coverage_pi": 0.9530000000000001,
"rmse_Q": 0.03621903868478622,
"lam": 2.0007786273454538
}
],
"rmse_decreases": true,
"variance_dominates_at_maxn": true,
"coverage_pi_at_maxn": 0.9530000000000001
}
],
"adversarial": {
"sweep": [
{
"n": 1000,
"p_R": 0.5,
"value_true": 0.4776537203230401,
"value_hat_mean": 0.4701726775365815,
"coverage_value": 1.0,
"coverage_strategy": null,
"piA_true_support": 2
},
{
"n": 5000,
"p_R": 0.5,
"value_true": 0.536778094188713,
"value_hat_mean": 0.5345057696807607,
"coverage_value": 0.96,
"coverage_strategy": null,
"piA_true_support": 2
},
{
"n": 10000,
"p_R": 0.5,
"value_true": 0.5659109787090211,
"value_hat_mean": 0.5653511755528775,
"coverage_value": 0.98,
"coverage_strategy": null,
"piA_true_support": 3
}
],
"coverage_pattern_n5000_approaches_nominal": true,
"note": "single gender factor, two-party zero-sum game (paper's tractability choice)"
},
"claim5_passed": true
} |