"""
mergen.criteria.maxpro
======================
Maximum Projection (MaxPro) criterion.
Reference
---------
Joseph, V. R., Gul, E. & Ba, S. (2015). Maximum projection designs
for computer experiments. *Biometrika*, 102(2), 371-380.
"""
from __future__ import annotations
import numpy as np
from .base import BaseCriterion, _EPS
[docs]
class MaxPro(BaseCriterion):
"""
MaxPro criterion with Euclidean squared distance.
Criterion (minimise)::
MaxPro = Σ_{i<j} 1 / prod_v (x_iv - x_jv)²
Notes
-----
Suffers from boundary bias: corner points are treated as maximally
separated even when they are geometrically close under a periodic
metric. Prefer :class:`UMaxPro` for general use.
References
----------
Joseph, V. R., Gul, E. & Ba, S. (2015).
*Biometrika*, 102(2), 371–380.
"""
[docs]
def evaluate(self, X: np.ndarray, space) -> float:
n = len(X)
score = 0.0
for i in range(n - 1):
sq = np.maximum((X[i] - X[i + 1:]) ** 2, _EPS)
score += np.sum(1.0 / np.prod(sq, axis=1))
return max(score, _EPS)
[docs]
def incremental(self, X, i, new_pt, space, current_score):
mask = np.ones(len(X), dtype=bool)
mask[i] = False
others = X[mask]
sq_old = np.maximum((X[i] - others) ** 2, _EPS)
sq_new = np.maximum((new_pt - others) ** 2, _EPS)
old_contrib = np.sum(1.0 / np.prod(sq_old, axis=1))
new_contrib = np.sum(1.0 / np.prod(sq_new, axis=1))
new_score = max(current_score - old_contrib + new_contrib, _EPS)
log_delta = np.log(new_score) - np.log(max(current_score, _EPS))
return float(log_delta), float(new_score)
[docs]
def begin_1d(self, X, i, current_score):
"""Precompute per-pair contributions and per-axis squared distances."""
mask = np.ones(len(X), dtype=bool)
mask[i] = False
others = X[mask]
sq = np.maximum((X[i] - others) ** 2, _EPS)
contribs = 1.0 / np.prod(sq, axis=1)
return {
'X' : X,
'i' : i,
'others' : others,
'sq' : sq,
'contribs': contribs,
'score' : current_score,
'point' : X[i].copy(),
}
[docs]
def try_1d(self, cache, axis, new_value, space):
"""
O(n) rescaling update for MaxPro (Euclidean variant).
See :meth:`UMaxPro.try_1d` for the algebra; the only difference
is that the per-axis squared distance is the plain Euclidean
``(u - v)²`` rather than the periodic minimum form.
"""
others_axis = cache['others'][:, axis]
sq_old_axis = cache['sq'][:, axis]
sq_new_axis = np.maximum((new_value - others_axis) ** 2, _EPS)
new_contribs = cache['contribs'] * (sq_old_axis / sq_new_axis)
old_sum = float(np.sum(cache['contribs']))
new_sum = float(np.sum(new_contribs))
new_score = max(cache['score'] - old_sum + new_sum, _EPS)
log_delta = np.log(new_score) - np.log(max(cache['score'], _EPS))
new_sq = cache['sq'].copy()
new_sq[:, axis] = sq_new_axis
new_point = cache['point'].copy()
new_point[axis] = new_value
new_cache = {
'X' : cache['X'],
'i' : cache['i'],
'others' : cache['others'],
'sq' : new_sq,
'contribs': new_contribs,
'score' : new_score,
'point' : new_point,
}
return float(log_delta), float(new_score), new_cache
