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_engine_ll_complex_model():
"""
Test log-likelihood computation under a complex model.
"""
from cargo.log import get_logger
get_logger("cargo.llvm.constructs", level = "DEBUG")
# test the model
from cargo.statistics import (
Tuple,
ModelEngine,
MixedBinomial,
FiniteMixture,
)
model = FiniteMixture(Tuple([(MixedBinomial(), 128)]), 8)
engine = ModelEngine(model)
# generate some fake parameters
sample = numpy.empty((), model.sample_dtype )
parameter = numpy.empty((), model.parameter_dtype)
sample["d0"]["n"] = 4
sample["d0"]["k"] = 1
parameter["p"] = 1.0 / 8.0
parameter["c"]["d0"] = 0.5
assert_almost_equal(engine.ll(parameter, sample), -177.445678223)
def test_engine_ll_complex_model():
"""
Test log-likelihood computation under a complex model.
"""
from cargo.log import get_logger
get_logger("cargo.llvm.constructs", level="DEBUG")
# test the model
from cargo.statistics import (
Tuple,
ModelEngine,
MixedBinomial,
FiniteMixture,
)
model = FiniteMixture(Tuple([(MixedBinomial(), 128)]), 8)
engine = ModelEngine(model)
# generate some fake parameters
sample = numpy.empty((), model.sample_dtype)
parameter = numpy.empty((), model.parameter_dtype)
sample["d0"]["n"] = 4
sample["d0"]["k"] = 1
parameter["p"] = 1.0 / 8.0
parameter["c"]["d0"] = 0.5
assert_almost_equal(engine.ll(parameter, sample), -177.445678223)
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_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_delta_given():
"""
Test posterior computation under the trivial delta distribution.
"""
engine = ModelEngine(Delta(float))
assert_equal(engine.given(42.0, [43.0]), 42.0)
def test_delta_given():
"""
Test posterior computation under the trivial delta distribution.
"""
engine = ModelEngine(Delta(float))
assert_equal(engine.given(42.0, [43.0]), 42.0)
def test_delta_ll():
"""
Test likelihood computation under the trivial delta distribution.
"""
engine = ModelEngine(Delta(float))
assert_equal(engine.ll(42.0, 42.1), numpy.finfo(float).min)
assert_equal(engine.ll(42.0, 42.0), 0.0)
def test_delta_ll():
"""
Test likelihood computation under the trivial delta distribution.
"""
engine = ModelEngine(Delta(float))
assert_equal(engine.ll(42.0, 42.1), numpy.finfo(float).min)
assert_equal(engine.ll(42.0, 42.0), 0.0)
def test_finite_mixture_ll():
"""
Test finite-mixture log-likelihood computation.
"""
engine = ModelEngine(FiniteMixture(Delta(float), 2))
p = [[(0.25, 1.0), (0.75, 2.0)]]
assert_almost_equal(engine.ll(p, 1.0 ), numpy.log(0.25))
assert_almost_equal(engine.ll(p, [ 2.0]), numpy.log(0.75))
assert_almost_equal(engine.ll(p, [42.0]), numpy.finfo(float).min)
def test_finite_mixture_given():
"""
Test finite-mixture posterior-parameter computation.
"""
model = FiniteMixture(Delta(float), 2)
engine = ModelEngine(model)
out = engine.given([(0.25, 1.0), (0.75, 2.0)], [2.0])
assert_equal(out["c"].tolist(), [1.0, 2.0])
assert_almost_equal(out["p"][0], 0.0)
assert_almost_equal(out["p"][1], 1.0)
def test_finite_mixture_given_binomials():
"""
Test finite-mixture posterior-parameter computation with binomials.
"""
model = FiniteMixture(MixedBinomial(), 2)
engine = ModelEngine(model)
out = engine.given([(0.25, 0.25), (0.75, 0.75)], [(1, 1), (2, 3)])
assert_equal(out["c"].tolist(), [0.25, 0.75])
assert_almost_equal(out["p"][0], 0.03571429)
assert_almost_equal(out["p"][1], 0.9642857)
def test_finite_mixture_given_enveloped():
"""
Test mixture posterior computation with enveloped arrays.
"""
model = FiniteMixture(Delta(float), 2)
engine = ModelEngine(model)
out = engine.given([(0.25, 1.0), (0.75, 2.0)], [[2.0]] * 3)
for i in xrange(3):
assert_almost_equal(out["p"][i, 0], 0.0)
assert_almost_equal(out["p"][i, 1], 1.0)
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_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_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_finite_mixture_ml():
"""
Test EM estimation of finite mixture distributions.
"""
me = ModelEngine(FiniteMixture(MixedBinomial(), 2))
assert_finite_mixture_ml_ok(me)
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_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_tuple_ll():
"""
Test log-likelihood computation under the tuple distribution.
"""
model = Tuple([(Binomial(), 2), (Binomial(), 1)])
engine = ModelEngine(model)
assert_almost_equal(
engine.ll(
([(0.25, 1), (0.75, 1)], [(0.5, 1)]),
([1, 1], [0]),
),
numpy.log(0.25 * 0.75 * 0.5),
)
assert_almost_equal(
engine.ll(
([(0.25, 1), (0.75, 1)], [(0.5, 1)]),
([0, 1], [0]),
),
numpy.log(0.75 * 0.75 * 0.5),
)
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_tuple_ll():
"""
Test log-likelihood computation under the tuple distribution.
"""
model = Tuple([(Binomial(), 2), (Binomial(), 1)])
engine = ModelEngine(model)
assert_almost_equal(
engine.ll(
([(0.25, 1), (0.75, 1)], [(0.5, 1)]),
([1, 1], [0]),
),
numpy.log(0.25 * 0.75 * 0.5),
)
assert_almost_equal(
engine.ll(
([(0.25, 1), (0.75, 1)], [(0.5, 1)]),
([0, 1], [0]),
),
numpy.log(0.75 * 0.75 * 0.5),
)
