Eval 05: Influence Function Assembly

Validates the complete influence function ψ assembly from Theorem 2.

Formula

\[\psi_i = H(\theta_i) - H_\theta(\theta_i) \cdot \Lambda(x_i)^{-1} \cdot \ell_\theta(y_i, t_i, \theta_i)\]

Configuration

Parameter	Value
n	1000
Seed	42
True μ*	0.241

Results

Assembly Comparison

Metric	Package	Oracle
Mean(ψ)	0.241	0.240
Std(ψ)	1.050	0.997

Assembly Quality

Metric	Value	Threshold	Status
Corr(ψ̂, ψ*)	0.995	> 0.9	PASS
Bias	0.001	< 0.1	PASS
RMSE	0.114	< 0.5	PASS

Inference Check

Quantity	Value
True μ*	0.241
Mean(ψ_oracle)	0.240
Mean(ψ_package)	0.241
Oracle bias from true	-0.001
Package bias from true	-0.000

Summary

Test	Result
Corr(ψ̂, ψ*) > 0.9	PASS
|Bias| < 0.1	PASS
RMSE < 0.5	PASS
Overall	PASS

Key Findings

• Package ψ correlates 0.995 with oracle ψ

• Bias is negligible (< 0.01)

• Standard deviation within 5% of oracle

• Assembly correctly combines H, H_θ, Λ⁻¹, and ℓ_θ

Run Command

python3 -m evals.eval_05_psi 2>&1 | tee evals/reports/eval_05_$(date +%Y%m%d_%H%M%S).txt