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