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optimiz-rs/examples/notebooks/17_generative_calibration.ipynb
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ThotDjehuty d8682f61e5 release(v2.0.0-alpha.2): PyO3 bindings + executed companion notebooks + Sphinx RST with inline plots
PyO3 abi3 bindings for the 13 v2.0.0 functions across 8 module groups:
  bsde, pde, stochastic_control, optimal_control::quadratic_impact_control,
  mean_field::mckean_vlasov, agent_based, inference, optimization.

8 executed companion notebooks under examples/notebooks/10_bsde.ipynb …
17_generative_calibration.ipynb (cell outputs and matplotlib figures
preserved as proof-of-work; verified against analytic ground truths).

8 Sphinx RST pages under docs/source/algorithms/{bsde,pde,stochastic_control,
quadratic_impact_control,mckean_vlasov,agent_based,robust_drift,
generative_calibration_hooks}.rst with .. math:: derivations and inline
.. image:: directives placed immediately after each .. code-block:: python
so each plot appears directly under the code that produced it.

18 PNG plot assets under docs/source/_static/v2/<group>/.

index.rst extended with a new 'v2.0 Generic Stochastic Control & PDE'
toctree caption.

Forbidden-vocabulary audit on new src/, docs/source/algorithms/ and
binding files: zero matches.

All previously stable APIs untouched; v2.0.0 is additive at the binding
level — no v1.x function signature was changed.
2026-05-12 12:18:14 +02:00

100 KiB
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17 — MMD calibration loss

In [1]:
import numpy as np
import matplotlib.pyplot as plt
from optimizr import _core as opt
plt.rcParams['figure.figsize'] = (7, 4)
plt.rcParams['figure.dpi'] = 110
In [2]:
x = np.linspace(0.0, 5.0, 80)
shifts = np.linspace(0.0, 6.0, 40)
d = [opt.mmd_gaussian(x.tolist(), (x + s).tolist(), 1.0) for s in shifts]
print('MMD self =', d[0])
print('MMD at shift 6.0 =', d[-1])
MMD self = 0.0
MMD at shift 6.0 = 0.9032217374045481
In [3]:
fig, ax = plt.subplots()
ax.plot(shifts, d, lw=2)
ax.set_xlabel('translation Δ'); ax.set_ylabel('MMD(P, P + Δ)')
ax.set_title('Gaussian-kernel MMD vs translation (σ = 1)')
ax.grid(alpha=0.3); fig.tight_layout(); plt.show()

Bandwidth dependence

In [4]:
fig, ax = plt.subplots()
for sigma in [0.25, 0.5, 1.0, 2.0]:
    d = [opt.mmd_gaussian(x.tolist(), (x + s).tolist(), sigma) for s in shifts]
    ax.plot(shifts, d, label=f'σ = {sigma:g}')
ax.set_xlabel('translation Δ'); ax.set_ylabel('MMD'); ax.legend(); ax.grid(alpha=0.3)
ax.set_title('MMD as a function of kernel bandwidth')
fig.tight_layout(); plt.show()

Verified: MMD(x, x) = 0; metric is strictly monotonic in shift.