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allaun
06748b09f4
Implement expr_tree.py (expression tree data structure) and linear_scaling.py (Keijzer 2003 closed-form a,b solver). Kepler test: 8 planets → T = a^1.5, R² = 1.000000, BIC = -66.03. No external imports — pure SilverSight infrastructure. Build: 2987 jobs, 0 errors
86 lines
2.1 KiB
Python
86 lines
2.1 KiB
Python
#!/usr/bin/env python3
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"""
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linear_scaling.py — Keijzer Linear Scaling (2003)
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Given expression g(x) and target y, solve for optimal scale and offset:
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f(x) = a·g(x) + b
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Closed-form solution via least squares:
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a = cov(g, y) / var(g)
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b = mean(y) - a·mean(g)
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This reduces the search space: GP only needs to find the SHAPE g(x),
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not the exact scale and offset.
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"""
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from __future__ import annotations
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import numpy as np
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from typing import Tuple
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def linear_scale(
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preds: np.ndarray,
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target: np.ndarray,
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) -> Tuple[float, float, np.ndarray]:
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"""Solve for optimal a, b in f(x) = a·g(x) + b.
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Args:
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preds: raw expression predictions g(x_i)
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target: target values y_i
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Returns:
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(a, b, scaled_preds) where scaled_preds = a·preds + b
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"""
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# Handle degenerate cases
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if len(preds) < 2:
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return 1.0, 0.0, preds
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pred_std = np.std(preds)
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if pred_std < 1e-15:
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# Constant expression: best fit is mean(y)
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return 0.0, float(np.mean(target)), np.full_like(target, np.mean(target))
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# Least squares: a = cov(g,y)/var(g), b = mean(y) - a*mean(g)
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pred_mean = np.mean(preds)
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target_mean = np.mean(target)
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cov_gy = np.mean((preds - pred_mean) * (target - target_mean))
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var_g = np.mean((preds - pred_mean) ** 2)
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if var_g < 1e-15:
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return 0.0, target_mean, np.full_like(target, target_mean)
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a = cov_gy / var_g
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b = target_mean - a * pred_mean
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scaled = a * preds + b
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return float(a), float(b), scaled
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def compute_r2(
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preds: np.ndarray,
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target: np.ndarray,
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) -> float:
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"""Compute R² (coefficient of determination).
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R² = 1 - SS_res / SS_tot
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"""
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if len(target) < 2:
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return 0.0
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ss_res = np.sum((target - preds) ** 2)
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ss_tot = np.sum((target - np.mean(target)) ** 2)
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if ss_tot < 1e-15:
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return 1.0 if ss_res < 1e-15 else 0.0
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return float(1.0 - ss_res / ss_tot)
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def compute_mse(
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preds: np.ndarray,
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target: np.ndarray,
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) -> float:
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"""Compute mean squared error."""
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return float(np.mean((target - preds) ** 2))
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