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1398681 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | """Paired sketch: unbiasedness and CRN variance reduction (Prop. 1)."""
import numpy as np
import pytest
from spectra_rsi import SyntheticWorld, SpectraConfig
from spectra_rsi.sketch import design_matrix, paired_sketch
@pytest.fixture
def world():
return SyntheticWorld(n_slices=100, n_experts=4, rank_per_expert=2, seed=3)
def test_paired_sketch_unbiased(world):
rng = np.random.default_rng(0)
cand = world.make_candidate("single_gain", experts=[1], scale=0.5, rng=rng)
A = design_matrix(20, world.n, 0.2, world.sigma, rng)
true = A @ world.true_delta(cand)
reps = 40
est = np.zeros((reps, 20))
for r in range(reps):
y, _, _ = paired_sketch(world, cand, A, world.sigma, 150, rng)
est[r] = y
bias = np.abs(est.mean(axis=0) - true)
se = est.std(axis=0) / np.sqrt(reps)
# bias within 4 standard errors on at least 95% of rows
assert np.mean(bias < 4 * se + 1e-3) > 0.9
def test_crn_variance_reduction():
"""Common random numbers must shrink paired-difference variance."""
w_crn = SyntheticWorld(100, 4, 2, seed=5, cnr_rho=0.9)
w_ind = SyntheticWorld(100, 4, 2, seed=5, cnr_rho=0.0)
rng = np.random.default_rng(1)
cand_c = w_crn.make_candidate("single_gain", experts=[0], rng=rng)
cand_i = w_ind.make_candidate("single_gain", experts=[0],
rng=np.random.default_rng(1))
var_crn = np.var(w_crn.paired_scores(cand_c, 3, 5000))
var_ind = np.var(w_ind.paired_scores(cand_i, 3, 5000))
assert var_crn < 0.5 * var_ind
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