Eval 03: Lambda Estimation

Validates Lambda estimation Λ(x) = E[ℓ_θθ | X=x] across all three regimes.

Configuration

Parameter	Value
n	5000
Oracle MC	5000 samples
Methods	aggregate, mlp, ridge, rf, lgbm

Results by Regime

Part A: Regime A (RCT) - ComputeLambda

Test	Description	Result
A1	Quadrature vs MC	PASS (0.03% error)
A2	MC convergence rate	PASS (rate=0.43)
A3	Y-independence	PASS (diff=0.00)
A4	Package integration	PASS (0.21% error)

Part A: 4/4 PASS

Part B: Regime B (Linear) - AnalyticLambda

Test	Description	Result
B1	Lambda = E[TT’	X]
B2	theta-independence	PASS (diff=0.00)
B3	Confounded T	PASS (4.6% error)
B4	Package integration	PASS (3.4% error)

Part B: 4/4 PASS

Part C: Regime C (Observational) - EstimateLambda

Method	Corr(λ₁)	Mean Frob	Min Eig	PSD%	Result
aggregate	0.000	0.121	0.041	100%	1/3
mlp	0.997	0.018	0.000	100%	3/3 PASS
ridge	0.508	0.087	0.000	100%	2/3
rf	0.904	0.060	0.000	100%	3/3 PASS
lgbm	0.978	0.033	0.000	100%	3/3 PASS

Best Method: MLP (Corr=0.997, lowest Frobenius error)

Summary

Part	Tests	Result
Part A (RCT)	4	4/4 PASS
Part B (Linear)	4	4/4 PASS
Part C (Observational)	3	3/3 PASS
Total	11	11/11 PASS

Key Findings

• Regime A: ComputeLambda works when treatment is randomized (Y-independent Hessian)

• Regime B: AnalyticLambda = E[TT’|X] is exact for linear models

• Regime C: MLP achieves Corr=0.997 with oracle; aggregate ignores heterogeneity (Corr=0.000)

Run Command

python3 -m evals.eval_03_lambda 2>&1 | tee evals/reports/eval_03_$(date +%Y%m%d_%H%M%S).txt