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.
112 lines
3.1 KiB
ReStructuredText
112 lines
3.1 KiB
ReStructuredText
Inference — Huber-IRLS drift estimator
|
||
======================================
|
||
|
||
Robust drift estimator (`robust_drift`) for $x_{k+1} = x_k + (a + b x_k) Δt + σ ε_k$ via Huber IRLS — resists 5 % heavy-tailed innovations.
|
||
|
||
.. note:: Companion executed notebook: `16_robust_drift.ipynb <../../examples/notebooks/16_robust_drift.ipynb>`_
|
||
|
||
16 — Robust drift estimation
|
||
============================
|
||
|
||
.. code-block:: python
|
||
|
||
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
|
||
|
||
Synthetic stationary process with 5 % outliers
|
||
----------------------------------------------
|
||
|
||
.. code-block:: python
|
||
|
||
rng = np.random.default_rng(7)
|
||
true_a, true_b = 1.0, -0.5
|
||
dt, n = 0.01, 5000
|
||
x = [0.0]
|
||
for k in range(n):
|
||
if k % 20 == 0:
|
||
eps = rng.uniform(-2.0, 2.0)
|
||
else:
|
||
eps = rng.uniform(-0.1, 0.1)
|
||
x.append(x[-1] + (true_a + true_b * x[-1]) * dt + eps * np.sqrt(dt))
|
||
x = np.array(x)
|
||
print('observation length =', len(x))
|
||
|
||
.. code-block:: python
|
||
|
||
fig, ax = plt.subplots()
|
||
ax.plot(x, lw=0.6)
|
||
ax.axhline(true_a / -true_b, color='red', ls='--', label='OU level a/(-b) = 2')
|
||
ax.set_xlabel('k'); ax.set_ylabel('x_k'); ax.legend(); ax.grid(alpha=0.3)
|
||
ax.set_title('Synthetic series with heavy-tailed innovations')
|
||
fig.tight_layout(); plt.show()
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
.. AUTO-PLOT-BEGIN
|
||
.. image:: ../_static/auto/algorithms__robust_drift/block_03_fig_01.png
|
||
:align: center
|
||
:width: 80%
|
||
|
||
.. AUTO-PLOT-END
|
||
.. image:: ../_static/v2/robust_drift/plot_01.png
|
||
:align: center
|
||
:width: 80%
|
||
|
||
.. code-block:: python
|
||
|
||
res = opt.robust_drift(x.tolist(), dt=dt)
|
||
print(f'a (true 1.0) -> {res["a"]:.4f}')
|
||
print(f'b (true -0.5) -> {res["b"]:.4f}')
|
||
print('IRLS iterations =', res['iterations'])
|
||
|
||
.. code-block:: python
|
||
|
||
# Compare against a naïve OLS that is broken by outliers.
|
||
y = (x[1:] - x[:-1]) / dt
|
||
X = np.vstack([np.ones_like(x[:-1]), x[:-1]]).T
|
||
ols_ab, *_ = np.linalg.lstsq(X, y, rcond=None)
|
||
print('OLS a, b =', ols_ab)
|
||
fig, ax = plt.subplots()
|
||
labels = ['true', 'OLS', 'robust']
|
||
vals_a = [true_a, ols_ab[0], res['a']]
|
||
vals_b = [true_b, ols_ab[1], res['b']]
|
||
ax.bar(np.arange(3) - 0.2, vals_a, width=0.4, label='a')
|
||
ax.bar(np.arange(3) + 0.2, vals_b, width=0.4, label='b')
|
||
ax.set_xticks(range(3)); ax.set_xticklabels(labels)
|
||
ax.legend(); ax.grid(alpha=0.3); ax.set_title('Robust vs OLS drift estimate')
|
||
fig.tight_layout(); plt.show()
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
.. AUTO-PLOT-BEGIN
|
||
.. image:: ../_static/auto/algorithms__robust_drift/block_05_fig_01.png
|
||
:align: center
|
||
:width: 80%
|
||
|
||
.. AUTO-PLOT-END
|
||
.. image:: ../_static/v2/robust_drift/plot_02.png
|
||
:align: center
|
||
:width: 80%
|
||
|
||
**Verified:** Huber IRLS recovers `(a, b)` within `0.2` even with 5 % heavy outliers.
|
||
|
||
API
|
||
---
|
||
|
||
.. code-block:: rust
|
||
|
||
pub fn estimate_robust_drift(observations: &[f64], cfg: &RobustDriftConfig) -> Result<RobustDriftResult>;
|
||
pub struct RobustDriftConfig { pub dt: f64, pub huber_delta: f64, pub max_iterations: usize, pub tolerance: f64 }
|
||
pub struct RobustDriftResult { pub a: f64, pub b: f64, pub iterations: usize }
|