def test_tuple_map():
"""
Test MAP parameter estimation under the tuple distribution.
"""
from cargo.numpy import tolist_deeply
model = Tuple([(Binomial(estimation_n=1), 2),
(Binomial(estimation_n=1), 1)])
engine = ModelEngine(model)
assert_almost_equal_deep(
tolist_deeply(
engine.map(
([(2, 3), (2, 3)], [(2, 3)]),
[([0, 1], [0])] * 1 + [([1, 0], [1])] * 9,
numpy.ones(10),
), ),
([(10.0 / 13.0, 1), (2.0 / 13.0, 1)], [(10.0 / 13.0, 1)]),
)
assert_almost_equal_deep(
tolist_deeply(
engine.map(
([(2, 3), (2, 3)], [(2, 3)]),
[([0, 1], [0])] * 1 + [([1, 0], [1])] * 9,
[1.00] * 1 + [3.00] * 9,
), ),
([(28.0 / 31.0, 1), (2.0 / 31.0, 1)], [(28.0 / 31.0, 1)]),
)
def test_tuple_map():
"""
Test MAP parameter estimation under the tuple distribution.
"""
from cargo.numpy import tolist_deeply
model = Tuple([(Binomial(estimation_n = 1), 2), (Binomial(estimation_n = 1), 1)])
engine = ModelEngine(model)
assert_almost_equal_deep(
tolist_deeply(
engine.map(
([(2, 3), (2, 3)], [(2, 3)]),
[([0, 1], [0])] * 1 + [([1, 0], [1])] * 9,
numpy.ones(10),
),
),
([(10.0 / 13.0, 1), (2.0 / 13.0, 1)], [(10.0 / 13.0, 1)]),
)
assert_almost_equal_deep(
tolist_deeply(
engine.map(
([(2, 3), (2, 3)], [(2, 3)]),
[([0, 1], [0])] * 1 + [([1, 0], [1])] * 9,
[1.00] * 1 + [3.00] * 9,
),
),
([(28.0 / 31.0, 1), (2.0 / 31.0, 1)], [(28.0 / 31.0, 1)]),
)
def test_tuple_ml():
"""
Test ML parameter estimation under the tuple distribution.
"""
from cargo.numpy import tolist_deeply
model = Tuple([(Binomial(estimation_n=1), 2),
(Binomial(estimation_n=1), 1)])
engine = ModelEngine(model)
assert_almost_equal_deep(
tolist_deeply(
engine.ml(
[([0, 1], [0])] * 2500 + [([1, 0], [1])] * 7500,
numpy.ones(10000),
), ),
([(0.75, 1), (0.25, 1)], [(0.75, 1)]),
)
assert_almost_equal_deep(
tolist_deeply(
engine.ml(
[([0, 1], [0])] * 1000 + [([1, 0], [1])] * 1000,
[1.00] * 1000 + [3.00] * 1000,
), ),
([(0.75, 1), (0.25, 1)], [(0.75, 1)]),
)
def test_tuple_ml():
"""
Test ML parameter estimation under the tuple distribution.
"""
from cargo.numpy import tolist_deeply
model = Tuple([(Binomial(estimation_n = 1), 2), (Binomial(estimation_n = 1), 1)])
engine = ModelEngine(model)
assert_almost_equal_deep(
tolist_deeply(
engine.ml(
[([0, 1], [0])] * 2500 + [([1, 0], [1])] * 7500,
numpy.ones(10000),
),
),
([(0.75, 1), (0.25, 1)], [(0.75, 1)]),
)
assert_almost_equal_deep(
tolist_deeply(
engine.ml(
[([0, 1], [0])] * 1000 + [([1, 0], [1])] * 1000,
[1.00] * 1000 + [3.00] * 1000,
),
),
([(0.75, 1), (0.25, 1)], [(0.75, 1)]),
)
def test_mixed_binomial_ml():
"""
Test max-likelihood estimation under the mixed binomial distribution.
"""
me = ModelEngine(MixedBinomial())
assert_almost_equal_deep(
me.ml(
[[(1, 2), (4, 5)], [(3, 4), (8, 8)]],
numpy.ones((2, 2)),
),
[5.0 / 7.0, 11.0 / 12.0],
)
def test_mixed_binomial_ml():
"""
Test max-likelihood estimation under the mixed binomial distribution.
"""
me = ModelEngine(MixedBinomial())
assert_almost_equal_deep(
me.ml(
[[(1, 2), (4, 5)],
[(3, 4), (8, 8)]],
numpy.ones((2, 2)),
),
[5.0 / 7.0, 11.0 / 12.0],
)
def test_binomial_ll():
"""
Test log-probability computation in the binomial distribution.
"""
me = ModelEngine(Binomial())
assert_almost_equal(me.ll((0.25, 2), 1), -0.98082925)
assert_almost_equal_deep(
me.ll(
[[(0.25, 2), (0.25, 5)], [(0.75, 4), (0.75, 8)]],
[[1, 4], [3, 8]],
),
[[-0.98082925, -4.22342160], [-0.86304622, -2.30145658]],
)
def test_mixed_binomial_ll():
"""
Test log-probability computation in the mixed binomial distribution.
"""
me = ModelEngine(MixedBinomial())
assert_almost_equal(me.ll(0.25, (1, 2)), -0.98082925)
assert_almost_equal_deep(
me.ll(
[[0.25], [0.75]],
[[(1, 2), (4, 5)], [(3, 4), (8, 8)]],
),
[[-0.98082925, -4.22342160], [-0.86304622, -2.30145658]],
)
def test_binomial_ml():
"""
Test max-likelihood estimation under the binomial distribution.
"""
me = ModelEngine(Binomial(estimation_n=2))
assert_almost_equal_deep(
me.ml(
[[1, 2],
[2, 0]],
numpy.ones((2, 2)),
) \
.tolist(),
[(0.75, 2), (0.50, 2)],
)
def test_binomial_ml():
"""
Test max-likelihood estimation under the binomial distribution.
"""
me = ModelEngine(Binomial(estimation_n = 2))
assert_almost_equal_deep(
me.ml(
[[1, 2],
[2, 0]],
numpy.ones((2, 2)),
) \
.tolist(),
[(0.75, 2), (0.50, 2)],
)
def test_binomial_ll():
"""
Test log-probability computation in the binomial distribution.
"""
me = ModelEngine(Binomial())
assert_almost_equal(me.ll((0.25, 2), 1), -0.98082925)
assert_almost_equal_deep(
me.ll(
[[(0.25, 2), (0.25, 5)],
[(0.75, 4), (0.75, 8)]],
[[1, 4],
[3, 8]],
),
[[-0.98082925, -4.22342160],
[-0.86304622, -2.30145658]],
)
def test_mixed_binomial_ll():
"""
Test log-probability computation in the mixed binomial distribution.
"""
me = ModelEngine(MixedBinomial())
assert_almost_equal(me.ll(0.25, (1, 2)), -0.98082925)
assert_almost_equal_deep(
me.ll(
[[0.25],
[0.75]],
[[(1, 2), (4, 5)],
[(3, 4), (8, 8)]],
),
[[-0.98082925, -4.22342160],
[-0.86304622, -2.30145658]],
)
def assert_finite_mixture_ml_ok(me):
"""
Verify EM estimation of finite mixture distributions.
"""
from cargo.testing import assert_almost_equal_deep
(e,) = \
me.ml(
[[(7, 8)] * 100 + [(1, 8)] * 200],
ones((1, 300)),
)
assert_almost_equal_deep(
e[numpy.argsort(e["p"])].tolist(),
[(1.0 / 3.0, 7.0 / 8.0),
(2.0 / 3.0, 1.0 / 8.0)],
places = 4,
)
def test_finite_mixture_map():
"""
Test EM estimation of MAP finite mixture parameters.
"""
engine = ModelEngine(FiniteMixture(MixedBinomial(), 2))
(e,) = \
engine.map(
[[(1, 1)] * 2],
[[(7, 8)] * 100 + [(1, 8)] * 200],
ones((1, 300)),
)
assert_almost_equal_deep(
e[numpy.argsort(e["p"])].tolist(),
[(1.0 / 3.0, 7.0 / 8.0),
(2.0 / 3.0, 1.0 / 8.0)],
places = 4,
)
def test_mixed_binomial_map():
"""
Test MAP estimation under the mixed binomial distribution.
"""
me = ModelEngine(MixedBinomial())
assert_almost_equal_deep(
me.map(
[(1 , 1 ),
(0.25, 0.75),
(2 , 3 )],
[[(1, 2), (2, 2)],
[(1, 2), (2, 2)],
[(1, 2), (2, 2)]],
numpy.ones((3, 2)),
) \
.tolist(),
[0.75, 0.75, 4.0 / 7.0],
)
def test_mixed_binomial_map():
"""
Test MAP estimation under the mixed binomial distribution.
"""
me = ModelEngine(MixedBinomial())
assert_almost_equal_deep(
me.map(
[(1 , 1 ),
(0.25, 0.75),
(2 , 3 )],
[[(1, 2), (2, 2)],
[(1, 2), (2, 2)],
[(1, 2), (2, 2)]],
numpy.ones((3, 2)),
) \
.tolist(),
[0.75, 0.75, 4.0 / 7.0],
)
def test_binomial_map():
"""
Test MAP estimation under the binomial distribution.
"""
me = ModelEngine(Binomial(estimation_n=2))
assert_almost_equal_deep(
me.map(
[(1 , 1 ),
(0.25, 0.75),
(2 , 3 )],
[[1, 2],
[1, 2],
[1, 2]],
numpy.ones((3, 2)),
) \
.tolist(),
[(0.75 , 2),
(0.75 , 2),
(4.0 / 7.0, 2)],
)
def test_binomial_map():
"""
Test MAP estimation under the binomial distribution.
"""
me = ModelEngine(Binomial(estimation_n = 2))
assert_almost_equal_deep(
me.map(
[(1 , 1 ),
(0.25, 0.75),
(2 , 3 )],
[[1, 2],
[1, 2],
[1, 2]],
numpy.ones((3, 2)),
) \
.tolist(),
[(0.75 , 2),
(0.75 , 2),
(4.0 / 7.0, 2)],
)
