def test_entropy_bernoulli_bivariate__ci_():
rng = gen_rng(10)
# Generate a bivariate Bernoulli dataset.
PX = [.3, .7]
PY = [[.2, .8], [.6, .4]]
TX = rng.choice([0, 1], p=PX, size=250)
TY = np.zeros(shape=len(TX))
TY[TX == 0] = rng.choice([0, 1], p=PY[0], size=len(TX[TX == 0]))
TY[TX == 1] = rng.choice([0, 1], p=PY[0], size=len(TX[TX == 1]))
T = np.column_stack((TY, TX))
engine = Engine(
T,
cctypes=['categorical', 'categorical'],
distargs=[{
'k': 2
}, {
'k': 2
}],
num_states=64,
rng=rng,
)
engine.transition_lovecat(N=200)
# exact computation
entropy_exact = (-PX[0] * PY[0][0] * np.log(PX[0] * PY[0][0]) -
PX[0] * PY[0][1] * np.log(PX[0] * PY[0][1]) -
PX[1] * PY[1][0] * np.log(PX[1] * PY[1][0]) -
PX[1] * PY[1][1] * np.log(PX[1] * PY[1][1]))
# logpdf computation
logps = engine.logpdf_bulk([-1, -1, -1, -1], [{
0: 0,
1: 0
}, {
0: 0,
1: 1
}, {
0: 1,
1: 0
}, {
0: 1,
1: 1
}])
entropy_logpdf = [-np.sum(np.exp(logp) * logp) for logp in logps]
# mutual_information computation.
entropy_mi = engine.mutual_information([0, 1], [0, 1], N=1000)
# Punt CLT analysis and go for a small tolerance.
assert np.allclose(entropy_exact, entropy_logpdf, atol=.15)
assert np.allclose(entropy_exact, entropy_mi, atol=.15)
assert np.allclose(entropy_logpdf, entropy_mi, atol=.1)
def test_entropy_bernoulli_univariate__ci_():
rng = gen_rng(10)
# Generate a univariate Bernoulli dataset.
T = rng.choice([0,1], p=[.3,.7], size=250).reshape(-1,1)
engine = Engine(T, cctypes=['bernoulli'], rng=rng, num_states=16)
engine.transition(S=15)
# exact computation.
entropy_exact = - (.3*np.log(.3) + .7*np.log(.7))
# logpdf computation.
logps = engine.logpdf_bulk([-1,-1], [{0:0}, {0:1}])
entropy_logpdf = [-np.sum(np.exp(logp)*logp) for logp in logps]
# mutual_information computation.
entropy_mi = engine.mutual_information([0], [0], N=1000)
# Punt CLT analysis and go for 1 dp.
assert np.allclose(entropy_exact, entropy_logpdf, atol=.1)
assert np.allclose(entropy_exact, entropy_mi, atol=.1)
assert np.allclose(entropy_logpdf, entropy_mi, atol=.05)