def test_mixture_api():
# Check basic API
p1 = Normal(mu=0.0, sigma=T.constant(1.0))
p2 = Normal(mu=1.0, sigma=2.0)
m = Mixture(components=[p1, p2], weights=[0.25])
assert len(m.components) == 2
assert len(m.weights) == 2
assert len(m.parameters_) == 4
assert len(m.constants_) == 1
assert len(m.observeds_) == 0
assert p1.mu in m.parameters_
assert p1.sigma in m.constants_
assert p2.mu in m.parameters_
assert p2.sigma in m.parameters_
assert m.X == p1.X
assert m.X == p2.X
assert m.ndim == p1.ndim
assert m.ndim == p2.ndim
m = Mixture(components=[p1, p2])
w = m.compute_weights()
assert_array_equal(w, [0.5, 0.5])
y = T.dscalar(name="y")
w1 = T.constant(0.25)
w2 = y * 2
m = Mixture(components=[p1, p2], weights=[w1, w2])
assert y in m.observeds_
# Check errors
assert_raises(ValueError, Mixture,
components=[p1, p1, p1], weights=[1.0])
def test_likelihood_free_mixture():
p1 = Normal(random_state=1)
p2 = Normal(mu=2.0, random_state=1)
h1 = Histogram(bins=50).fit(p1.rvs(10000))
h2 = Histogram(bins=50).fit(p2.rvs(10000))
m1 = Mixture(components=[p1, p2])
m2 = Mixture(components=[h1, h2])
# Check whether pdf, nnlf and cdf have been overriden
assert isinstance(m1.pdf, theano.compile.function_module.Function)
assert isinstance(m1.nnlf, theano.compile.function_module.Function)
assert isinstance(m1.cdf, theano.compile.function_module.Function)
assert isinstance(m2.pdf, types.MethodType)
assert isinstance(m2.nnlf, types.MethodType)
assert isinstance(m2.cdf, types.MethodType)
# Compare pdfs
rng = check_random_state(1)
X = rng.rand(100, 1) * 10 - 5
assert np.mean(np.abs(m1.pdf(X) - m2.pdf(X))) < 0.05
# Test sampling
X = m2.rvs(10)
assert X.shape == (10, 1)
# Check errors
assert_raises(NotImplementedError, m2.fit, X)
def test_mv_mixture():
p1 = MultivariateNormal(mu=np.array([0.0, 0.0]), sigma=np.eye(2))
p2 = MultivariateNormal(mu=np.array([2.0, 2.0]), sigma=0.5 * np.eye(2))
m = Mixture(components=[p1, p2])
assert m.ndim == 2
X = m.rvs(100)
assert X.shape == (100, 2)
assert_raises(ValueError, Mixture, components=[p1, Normal()])
def test_mv_mixture():
p1 = MultivariateNormal(mu=np.array([0.0, 0.0]),
sigma=np.eye(2))
p2 = MultivariateNormal(mu=np.array([2.0, 2.0]),
sigma=0.5 * np.eye(2))
m = Mixture(components=[p1, p2])
assert m.ndim == 2
X = m.rvs(100)
assert X.shape == (100, 2)
assert_raises(ValueError, Mixture, components=[p1, Normal()])
def test_decomposed_ratio_identity():
components = [Normal(mu=0.0), Normal(mu=0.25), Normal(mu=0.5)]
p = Mixture(components=components, weights=[0.45, 0.1, 0.45])
ratio = DecomposedRatio(
ClassifierRatio(CalibratedClassifierCV(base_estimator=ElasticNetCV())))
ratio.fit(numerator=p, denominator=p, n_samples=10000)
reals = np.linspace(-0.5, 1.0, num=100).reshape(-1, 1)
assert ratio.score(reals, p.pdf(reals) / p.pdf(reals)) == 0.0
assert_array_almost_equal(ratio.predict(reals), np.ones(len(reals)))
assert_array_almost_equal(ratio.predict(reals, log=True),
np.zeros(len(reals)))
def test_decomposed_ratio():
components = [Normal(mu=0.0), Normal(mu=0.25), Normal(mu=0.5)]
p0 = Mixture(components=components, weights=[0.45, 0.1, 0.45])
p1 = Mixture(components=[components[0]] + [components[2]])
ratio = DecomposedRatio(
ClassifierRatio(CalibratedClassifierCV(base_estimator=ElasticNetCV())))
ratio.fit(numerator=p0, denominator=p1, n_samples=10000)
reals = np.linspace(-0.5, 1.0, num=100).reshape(-1, 1)
assert ratio.score(reals, p0.pdf(reals) / p1.pdf(reals)) > -0.1
assert np.mean(np.abs(np.log(ratio.predict(reals)) -
ratio.predict(reals, log=True))) < 0.01
def test_decomposed_ratio_identity():
components = [Normal(mu=0.0), Normal(mu=0.25), Normal(mu=0.5)]
p = Mixture(components=components, weights=[0.45, 0.1, 0.45])
ratio = DecomposedRatio(
ClassifierRatio(CalibratedClassifierCV(base_estimator=ElasticNetCV())))
ratio.fit(numerator=p, denominator=p, n_samples=10000)
reals = np.linspace(-0.5, 1.0, num=100).reshape(-1, 1)
assert ratio.score(reals, p.pdf(reals) / p.pdf(reals)) == 0.0
assert_array_almost_equal(ratio.predict(reals), np.ones(len(reals)))
assert_array_almost_equal(ratio.predict(reals, log=True),
np.zeros(len(reals)))
def check_mixture_pdf(w0, w1, mu1, sigma1, mu2, sigma2):
rng = check_random_state(1)
p1 = Normal(mu=mu1, sigma=sigma1)
p2 = Normal(mu=mu2, sigma=sigma2)
m = Mixture(components=[p1, p2], weights=[w0, w1])
q1 = st.norm(loc=mu1, scale=sigma1)
q2 = st.norm(loc=mu2, scale=sigma2)
X = rng.rand(50, 1)
assert_array_almost_equal(
m.pdf(X).ravel(),
w0 * q1.pdf(X).ravel() + (w1 if w1 is not None else
(1 - w0)) * q2.pdf(X).ravel())
def check_mixture_pdf(w0, w1, mu1, sigma1, mu2, sigma2):
rng = check_random_state(1)
p1 = Normal(mu=mu1, sigma=sigma1)
p2 = Normal(mu=mu2, sigma=sigma2)
m = Mixture(components=[p1, p2], weights=[w0, w1])
q1 = st.norm(loc=mu1, scale=sigma1)
q2 = st.norm(loc=mu2, scale=sigma2)
X = rng.rand(50, 1)
assert_array_almost_equal(m.pdf(X).ravel(),
w0 * q1.pdf(X).ravel() +
(w1 if w1 is not None
else (1 - w0)) * q2.pdf(X).ravel())
def test_fit():
p1 = Normal(mu=T.constant(0.0), sigma=T.constant(2.0))
p2 = Normal(mu=T.constant(3.0), sigma=T.constant(2.0))
p3 = Exponential(inverse_scale=T.constant(0.5))
g = theano.shared(0.5)
m = Mixture(components=[p1, p2, p3], weights=[g, g*g])
X = np.concatenate([st.norm(loc=0.0, scale=2.0).rvs(300, random_state=0),
st.norm(loc=3.0, scale=2.0).rvs(100, random_state=1),
st.expon(scale=1. / 0.5).rvs(500, random_state=2)])
X = X.reshape(-1, 1)
s0 = m.score(X)
m.fit(X)
assert np.abs(g.eval() - 1. / 3.) < 0.05
assert m.score(X) <= s0
def test_likelihood_free_mixture():
p1 = Normal(random_state=1)
p2 = Normal(mu=2.0, random_state=1)
h1 = Histogram(bins=50).fit(p1.rvs(10000))
h2 = Histogram(bins=50).fit(p2.rvs(10000))
m1 = Mixture(components=[p1, p2])
m2 = Mixture(components=[h1, h2])
# Check whether pdf, nnlf and cdf have been overriden
assert isinstance(m1.pdf, theano.compile.function_module.Function)
assert isinstance(m1.nnlf, theano.compile.function_module.Function)
assert isinstance(m1.cdf, theano.compile.function_module.Function)
assert isinstance(m2.pdf, types.MethodType)
assert isinstance(m2.nnlf, types.MethodType)
assert isinstance(m2.cdf, types.MethodType)
# Compare pdfs
rng = check_random_state(1)
X = rng.rand(100, 1) * 10 - 5
assert np.mean(np.abs(m1.pdf(X) - m2.pdf(X))) < 0.05
# Test sampling
X = m2.rvs(10)
assert X.shape == (10, 1)
# Check errors
assert_raises(NotImplementedError, m2.fit, X)
def test_mixture_api():
# Check basic API
p1 = Normal(mu=0.0, sigma=T.constant(1.0))
p2 = Normal(mu=1.0, sigma=2.0)
m = Mixture(components=[p1, p2], weights=[0.25])
assert len(m.components) == 2
assert len(m.weights) == 2
assert len(m.parameters_) == 4
assert len(m.constants_) == 1
assert len(m.observeds_) == 0
assert p1.mu in m.parameters_
assert p1.sigma in m.constants_
assert p2.mu in m.parameters_
assert p2.sigma in m.parameters_
assert m.X == p1.X
assert m.X == p2.X
assert m.ndim == p1.ndim
assert m.ndim == p2.ndim
m = Mixture(components=[p1, p2])
w = m.compute_weights()
assert_array_equal(w, [0.5, 0.5])
y = T.dscalar(name="y")
w1 = T.constant(0.25)
w2 = y * 2
m = Mixture(components=[p1, p2], weights=[w1, w2])
assert y in m.observeds_
# Check errors
assert_raises(ValueError, Mixture, components=[p1, p1, p1], weights=[1.0])
def test_known_density():
components = [Normal(mu=0.0), Normal(mu=0.25), Normal(mu=0.5)]
p0 = Mixture(components=components, weights=[0.45, 0.1, 0.45])
p1 = Mixture(components=[components[0]] + [components[2]])
ratio = KnownDensityRatio(numerator=p0, denominator=p1)
reals = np.linspace(-0.5, 1.0, num=100).reshape(-1, 1)
assert ratio.score(reals, p0.pdf(reals) / p1.pdf(reals)) > -0.01
assert np.mean(np.abs(np.log(ratio.predict(reals)) -
ratio.predict(reals, log=True))) < 0.01
assert ratio.nllr(reals) == -ratio.predict(reals, log=True).sum()
def test_decomposed_ratio():
components = [Normal(mu=0.0), Normal(mu=0.25), Normal(mu=0.5)]
p0 = Mixture(components=components, weights=[0.45, 0.1, 0.45])
p1 = Mixture(components=[components[0]] + [components[2]])
ratio = DecomposedRatio(
ClassifierRatio(CalibratedClassifierCV(base_estimator=ElasticNetCV())))
ratio.fit(numerator=p0, denominator=p1, n_samples=10000)
reals = np.linspace(-0.5, 1.0, num=100).reshape(-1, 1)
assert ratio.score(reals, p0.pdf(reals) / p1.pdf(reals)) > -0.1
assert np.mean(np.abs(np.log(ratio.predict(reals)) -
ratio.predict(reals, log=True))) < 0.01
def test_fit():
p1 = Normal(mu=T.constant(0.0), sigma=T.constant(2.0))
p2 = Normal(mu=T.constant(3.0), sigma=T.constant(2.0))
p3 = Exponential(inverse_scale=T.constant(0.5))
g = theano.shared(0.5)
m = Mixture(components=[p1, p2, p3], weights=[g, g*g])
X = np.concatenate([st.norm(loc=0.0, scale=2.0).rvs(300, random_state=0),
st.norm(loc=3.0, scale=2.0).rvs(100, random_state=1),
st.expon(scale=1. / 0.5).rvs(500, random_state=2)])
X = X.reshape(-1, 1)
s0 = m.score(X)
m.fit(X)
assert np.abs(g.eval() - 1. / 3.) < 0.05
assert m.score(X) >= s0
# Simulator
A = theano.shared(true_theta[0], name="A")
B = theano.shared(true_theta[1], name="B")
R = np.array([[1.31229955, 0.10499961, 0.48310515, -0.3249938, -0.26387927],
[0.10499961, 1.15833058, -0.55865473, 0.25275522, -0.39790775],
[0.48310515, -0.55865473, 2.25874579, -0.52087938, -0.39271231],
[0.3249938, 0.25275522, -0.52087938, 1.4034925, -0.63521059],
[-0.26387927, -0.39790775, -0.39271231, -0.63521059, 1.]])
p0 = LinearTransform(
Join(components=[
Normal(mu=A, sigma=1),
Normal(mu=B, sigma=3),
Mixture(components=[Normal(mu=-2, sigma=1),
Normal(mu=2, sigma=0.5)]),
Exponential(inverse_scale=3.0),
Exponential(inverse_scale=0.5)
]), R)
def simulator(theta, n_samples, random_state=None):
A.set_value(theta[0])
B.set_value(theta[1])
return p0.rvs(n_samples, random_state=random_state)
X_obs = simulator(true_theta, 20000, random_state=rng)
n_params = len(true_theta)
n_features = X_obs.shape[1]
def test_rvs():
p1 = Normal(mu=0.0, sigma=T.constant(1.0), random_state=0)
p2 = Normal(mu=2.0, sigma=2.0, random_state=0)
m = Mixture(components=[p1, p2], weights=[0.25], random_state=0)
X = m.rvs(2000)
assert (np.mean(X) - (0.25 * p1.mu.eval() + 0.75 * p2.mu.eval())) < 0.1
def generate_samples(with_linear_transformation=False,
add_variation=False,
n_samples=50000,
verbose=True):
"""
Generate 5 independent variables: two Gaussian, mixture of Gaussian, two exponents.
Two Gaussian have different means for original and target distributions.
if with_linear_transformation is True then add linear transformation of generated 5 variables.
if add_variation is True then add random values in variance to obtain gaussian pdf
for orignal and target samples not only with different mean but also with different variance.
:param bool with_linear_transformation: apply or not linear transformation for samples features
:param bool add_variation: make or not different variance for Gaussian distribution for original and target samples.
:param int n_samples: number of generated samples for original/target distributions. For test samples 2*n_samples will be generated
:param bool verbose: print and plot additional info during generation.
:return: train original, train target, exact weights for train original, test original, test target, exact weights for test original
"""
# define linear transformation matrix
R = make_sparse_spd_matrix(5, alpha=0.5, random_state=7)
variation_origin, variation_target = (0, 0)
if add_variation:
r = check_random_state(42)
variation_origin, variation_target = r.uniform() / 3., r.uniform() / 3.
p0 = Join(components=[
Normal(mu=.5, sigma=1 + variation_origin),
Normal(mu=-.5, sigma=3 + variation_origin),
Mixture(components=[Normal(mu=-2, sigma=1),
Normal(mu=2, sigma=0.5)]),
Exponential(inverse_scale=3.0),
Exponential(inverse_scale=0.5)
])
p1 = Join(components=[
Normal(mu=0, sigma=1 + variation_target),
Normal(mu=0, sigma=3 + variation_target),
Mixture(components=[Normal(mu=-2, sigma=1),
Normal(mu=2, sigma=0.5)]),
Exponential(inverse_scale=3.0),
Exponential(inverse_scale=0.5)
])
if with_linear_transformation:
p0 = LinearTransform(p0, R)
p1 = LinearTransform(p1, R)
X0 = p0.rvs(n_samples, random_state=777)
X1 = p1.rvs(n_samples, random_state=777)
exact_weights = numpy.exp(p0.nll(X0) - p1.nll(X0))
exact_weights[numpy.isinf(exact_weights)] = 0.
# generate samples to test reweighting rule (to avoid overfitting)
X0_roc = p0.rvs(2 * n_samples, random_state=777 * 2)
X1_roc = p1.rvs(2 * n_samples, random_state=777 * 2)
# Weighted with true ratios
exact_weights_roc = numpy.exp(p0.nll(X0_roc) - p1.nll(X0_roc))
exact_weights_roc[numpy.isinf(exact_weights_roc)] = 0.
if verbose:
print "Original distribution"
fig = corner.corner(X0,
bins=20,
smooth=0.85,
labels=["X0", "X1", "X2", "X3", "X4"])
plt.show()
print "Target distribution"
fig = corner.corner(X1,
bins=20,
smooth=0.85,
labels=["X0", "X1", "X2", "X3", "X4"])
plt.show()
print "Exact reweighting"
# In this example, we know p0(x) and p1(x) exactly,
#so we can compare the other can compare the approximate reweighting approaches with the exact weights.
draw_distributions(X0, X1, exact_weights)
return X0, X1, exact_weights, X0_roc, X1_roc, exact_weights_roc
def test_rvs():
p1 = Normal(mu=0.0, sigma=T.constant(1.0), random_state=0)
p2 = Normal(mu=2.0, sigma=2.0, random_state=0)
m = Mixture(components=[p1, p2], weights=[0.25], random_state=0)
X = m.rvs(2000)
assert (np.mean(X) - (0.25 * p1.mu.eval() + 0.75 * p2.mu.eval())) < 0.1