def test_mom():
"""Test the whether spectral can recover from simple mixture of 3 identical"""
model = MixtureModel.generate(2, 3, dirichlet_scale = 0.9)
_, _, M, _ = model["k"], model["d"], model["M"], model["w"]
N = 1e5
xs = model.sample(N)
moments = model.exact_moments(model.observed_monomials(3))
moments_ = model.empirical_moments(xs, model.observed_monomials(3))
print "moment diff", dict_diff(moments, moments_)
w_true, params = solve_mixture_model(model, moments)
w_data, params_ = solve_mixture_model(model, moments_)
w_true, params = fix_parameters(M, params, w_true)
w_data, params_ = fix_parameters(M, params_, w_data)
print "true", M
print "with exact moments", params
print "error with exact moments", norm(M - params)/norm(M)
print "with empirical moments", params_
print "error with empirical moments", norm(M - params_)/norm(M)
assert norm(M - params)/norm(M) < 1e-10
assert norm(M - params_)/norm(M) < 1e-1
def test_mixture_em():
model = MixtureModel(k = 2, d = 3, M = array([[0.7, 0.3],[0.2, 0.3],[0.1, 0.4]]), w = array([0.6,0.4]))
k, d, M, w = model["k"], model["d"], model["M"], model["w"]
N = 1e5
xs = model.sample(N)
lhood, _, (params, w_true) = MixtureModelEM(k, d).run(xs, params=(M, w))
w_true, params = fix_parameters(M, params, w_true)
lhood_, _, (params_, w_guess) = MixtureModelEM(k, d).run(xs)
w_data, params_ = fix_parameters(M, params_, w_guess)
print "true", M
print "true lhood", model.llikelihood(xs)
print "with em*", params
print "em lhood*", lhood
print "em lhood*", model.using(M = params, w = w_true).llikelihood(xs)
print "error with em*", norm(M - params)/norm(M)
print "with em", params_
print "em lhood", lhood_
print "em lhood", model.using(M = params_, w = w_guess).llikelihood(xs)
print "error with em", norm(M - params_)/norm(M)
assert norm(M - params)/norm(M) < 1e-1
assert norm(M - params_)/norm(M) < 1e-1
def test_mom():
"""Test the whether spectral can recover from simple mixture of 3 identical"""
model = MixtureModel.generate(2, 3, dirichlet_scale=0.9)
_, _, M, _ = model["k"], model["d"], model["M"], model["w"]
N = 1e5
xs = model.sample(N)
moments = model.exact_moments(model.observed_monomials(3))
moments_ = model.empirical_moments(xs, model.observed_monomials(3))
print "moment diff", dict_diff(moments, moments_)
w_true, params = solve_mixture_model(model, moments)
w_data, params_ = solve_mixture_model(model, moments_)
w_true, params = fix_parameters(M, params, w_true)
w_data, params_ = fix_parameters(M, params_, w_data)
print "true", M
print "with exact moments", params
print "error with exact moments", norm(M - params) / norm(M)
print "with empirical moments", params_
print "error with empirical moments", norm(M - params_) / norm(M)
assert norm(M - params) / norm(M) < 1e-10
assert norm(M - params_) / norm(M) < 1e-1
def make_table(model, data, methods):
tbl = []
tbl.append(["Method","Parameter error", "Likelihood"])
tbl.append(["True", 0., model.llikelihood(data)])
print "true", model["M"]
for name, method in methods:
w, params = method(model, data)
w, params = fix_parameters(model["M"], params, w)
print name, params
lhood = model.using(M=params, w=w).llikelihood(data)
tbl.append([name, column_rerr(model["M"], params), lhood])
return tbl
