ThotDjehuty
dd51156174
Each of the eight v2.0 companion notebooks (10_bsde through 17_generative_calibration) now follows the mandatory pedagogical sandwich structure: PRE markdown : theorem / model / pivot equation / what the cell verifies CODE cell : labelled prints + at least one matplotlib figure POST markdown: expected result, graph reading, conclusion Each notebook carries at least one concrete real-world example (heat plate, inverted pendulum, opinion polarization, collective decision, OU drift under Cauchy noise, mixture vs gaussian MMD, etc.) Generator script: scripts/enrich_v2_notebooks.py Doc plots refreshed via scripts/inject_doc_plots.py.
91 lines
2.6 KiB
ReStructuredText
91 lines
2.6 KiB
ReStructuredText
Generative calibration — Gaussian MMD loss
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==========================================
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Maximum-Mean-Discrepancy distance with Gaussian kernel (`mmd_gaussian`). Self-distance is exactly zero; the metric grows monotonically with sample shift.
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.. note:: Companion executed notebook: `17_generative_calibration.ipynb <../../examples/notebooks/17_generative_calibration.ipynb>`_
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17 — MMD calibration loss
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=========================
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.. code-block:: python
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import numpy as np
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import matplotlib.pyplot as plt
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from optimizr import _core as opt
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plt.rcParams['figure.figsize'] = (7, 4)
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plt.rcParams['figure.dpi'] = 110
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.. code-block:: python
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x = np.linspace(0.0, 5.0, 80)
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shifts = np.linspace(0.0, 6.0, 40)
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d = [opt.mmd_gaussian(x.tolist(), (x + s).tolist(), 1.0) for s in shifts]
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print('MMD self =', d[0])
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print('MMD at shift 6.0 =', d[-1])
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.. code-block:: python
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fig, ax = plt.subplots()
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ax.plot(shifts, d, lw=2)
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ax.set_xlabel('translation Δ'); ax.set_ylabel('MMD(P, P + Δ)')
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ax.set_title('Gaussian-kernel MMD vs translation (σ = 1)')
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ax.grid(alpha=0.3); fig.tight_layout(); plt.show()
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.. AUTO-PLOT-BEGIN
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.. image:: ../_static/auto/algorithms__generative_calibration_hooks/block_03_fig_01.png
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:align: center
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:width: 80%
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.. AUTO-PLOT-END
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.. image:: ../_static/v2/generative_calibration_hooks/plot_01.png
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:align: center
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:width: 80%
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Bandwidth dependence
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--------------------
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.. code-block:: python
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fig, ax = plt.subplots()
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for sigma in [0.25, 0.5, 1.0, 2.0]:
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d = [opt.mmd_gaussian(x.tolist(), (x + s).tolist(), sigma) for s in shifts]
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ax.plot(shifts, d, label=f'σ = {sigma:g}')
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ax.set_xlabel('translation Δ'); ax.set_ylabel('MMD'); ax.legend(); ax.grid(alpha=0.3)
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ax.set_title('MMD as a function of kernel bandwidth')
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fig.tight_layout(); plt.show()
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.. AUTO-PLOT-BEGIN
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.. image:: ../_static/auto/algorithms__generative_calibration_hooks/block_04_fig_01.png
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:align: center
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:width: 80%
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.. AUTO-PLOT-END
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.. image:: ../_static/v2/generative_calibration_hooks/plot_02.png
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:align: center
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:width: 80%
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**Verified:** `MMD(x, x) = 0`; metric is strictly monotonic in shift.
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API
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---
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.. code-block:: rust
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pub fn mmd_distance(x: &[f64], y: &[f64], loss: &MmdLoss) -> Result<f64>;
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pub fn calibration_step<S: GenerativeSampler>(sampler: &mut S, target: &[f64], loss: &MmdLoss, lr: f64) -> Result<f64>;
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pub trait GenerativeSampler { fn sample(&self, n: usize, seed: u64) -> Vec<f64>; fn parameters(&self) -> Vec<f64>; fn perturb(&mut self, deltas: &[f64]); }
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pub struct MmdLoss { pub sigma: f64 }
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