Эксперимент: Conditional-copula probabilistic head (#560)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a two-dimensional copula MVP with exact non-Gaussian lognormal/Gamma marginals and Gaussian-copula dependence. The conditional-density derivative matched finite differences with relative error 6.5e-11; PITs were near Uniform(0,1), rank measures matched analytic predictions within 0.003, and observed NLL gains tracked the predicted -0.5 log(1-rho^2) scaling. At rho=0.8, the copula improved NLL from 2.9782 to 2.4657, so the dependence-separation mechanism manifested clearly.", "metrics": { "baseline": "Independent marginal NLL 2.9782 at rho=0.8; no dependence gain at rho=0.", "idea": "Copula NLL 2.4657 at rho=0.8, observed gain 0.5125 nats versus predicted 0.5108; fitted rho 0.8009. PIT means were approximately 0.5, variances approximately 0.0833, and KS statistics were 0.0033-0.0061." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 copula_experiment.py", "files": [ "copula_experiment.py", "results.json", "results.txt" ], "limitations": "This is a controlled 2D MVP rather than a learned neural conditional spline head: marginals are known analytically, dependence is a constant Gaussian copula rather than context-conditioned or asymmetric/tail-flexible, and no VAE, trajectory model, calibration-region, CRPS, energy-score, or equal-parameter-count neural comparison was tested." }