def test_distribution_sphere(n=15,
p=10,
sigma=1.,
nsample=2000,
sample_constraints=False):
# see if we really are sampling from
# correct distribution
# by comparing to an accept-reject sampler
con, y = _generate_constraints()[:2]
accept_reject_sample = []
hit_and_run_sample, W = AC.sample_from_sphere(con,
y,
ndraw=25000,
burnin=10000)
statistic = lambda x: np.fabs(x).max()
family = discrete_family([statistic(s) for s in hit_and_run_sample], W)
radius = np.linalg.norm(y)
count = 0
pvalues = []
while True:
U = np.random.standard_normal(n)
U /= np.linalg.norm(U)
U *= radius
if con(U):
accept_reject_sample.append(U)
count += 1
true_sample = np.array(
[statistic(s) for s in accept_reject_sample])
if (count + 1) % 100 == 0:
pvalues.extend([family.cdf(0, t) for t in true_sample])
print np.mean(pvalues), np.std(pvalues)
if sample_constraints:
con, y = _generate_constraints()[:2]
hit_and_run_sample, W = AC.sample_from_sphere(con,
y,
ndraw=10000,
burnin=10000)
family = discrete_family(
[statistic(s) for s in hit_and_run_sample], W)
radius = np.linalg.norm(y)
accept_reject_sample = []
if count >= nsample:
break
U = np.linspace(0, 1, 101)
plt.plot(U, sm.distributions.ECDF(pvalues)(U))
plt.plot([0, 1], [0, 1])
def test_distribution_sphere(n=15, p=10, sigma=1.,
nsim=2000,
sample_constraints=False,
burnin=10000,
ndraw=10000):
# see if we really are sampling from
# correct distribution
# by comparing to an accept-reject sampler
con, y = _generate_constraints()[:2]
accept_reject_sample = []
hit_and_run_sample, W = AC.sample_from_sphere(con, y,
ndraw=ndraw,
burnin=burnin)
statistic = lambda x: np.fabs(x).max()
family = discrete_family([statistic(s) for s in hit_and_run_sample], W)
radius = np.linalg.norm(y)
count = 0
pvalues = []
while True:
U = np.random.standard_normal(n)
U /= np.linalg.norm(U)
U *= radius
if con(U):
accept_reject_sample.append(U)
count += 1
true_sample = np.array([statistic(s) for s in accept_reject_sample])
if (count + 1) % int(nsim / 10) == 0:
pvalues.extend([family.cdf(0, t) for t in true_sample])
print np.mean(pvalues), np.std(pvalues)
if sample_constraints:
con, y = _generate_constraints()[:2]
hit_and_run_sample, W = AC.sample_from_sphere(con, y,
ndraw=ndraw,
burnin=burnin)
family = discrete_family([statistic(s) for s in hit_and_run_sample], W)
radius = np.linalg.norm(y)
accept_reject_sample = []
if count >= nsim:
break
U = np.linspace(0, 1, 101)
def test_sample_sphere():
p = 10
A = np.identity(10)[:3]
b = 2 * np.ones(3)
mean = -np.ones(p)
noise = np.random.standard_normal(p) * 0.1
noise[-3:] = 0.
initial = noise + mean
eta = np.ones(p)
bound = 5
s1 = AC.sample_truncnorm_white_sphere(A,
b,
initial,
eta,
lambda state: bound + 0.01 * np.random.sample() * np.linalg.norm(state)**2,
burnin=1000,
ndraw=1000,
how_often=5)
con = AC.constraints(A, b)
con.covariance = np.diag([1]*7 + [0]*3)
con.mean[:] = mean
print con(initial)
s2 = AC.sample_from_sphere(con, initial)
return s1, s2
def test_sample_sphere(burnin=1000, ndraw=1000):
p = 10
A = np.identity(10)[:3]
b = 2 * np.ones(3)
mean = -np.ones(p)
noise = np.random.standard_normal(p) * 0.1
noise[-3:] = 0.
initial = noise + mean
eta = np.ones(p)
bound = 5
s1 = AC.sample_truncnorm_white_sphere(A,
b,
initial,
eta,
how_often=20,
burnin=burnin,
ndraw=ndraw)
con = AC.constraints(A, b)
con.covariance = np.diag([1] * 7 + [0] * 3)
con.mean[:] = mean
s2 = AC.sample_from_sphere(con, initial, ndraw=ndraw, burnin=burnin)
return s1, s2
def test_sample_sphere(burnin=1000,
ndraw=1000,
nsim=None):
p = 10
A = np.identity(10)[:3]
b = 2 * np.ones(3)
mean = -np.ones(p)
noise = np.random.standard_normal(p) * 0.1
noise[-3:] = 0.
initial = noise + mean
eta = np.ones(p)
bound = 5
s1 = AC.sample_truncnorm_white_sphere(A,
b,
initial,
eta,
how_often=20,
burnin=burnin,
ndraw=ndraw)
con = AC.constraints(A, b)
con.covariance = np.diag([1]*7 + [0]*3)
con.mean[:] = mean
s2 = AC.sample_from_sphere(con, initial, ndraw=ndraw, burnin=burnin)
return s1, s2
def test_sample_sphere():
p = 10
A = np.identity(10)[:3]
b = 2 * np.ones(3)
mean = -np.ones(p)
noise = np.random.standard_normal(p) * 0.1
noise[-3:] = 0.
initial = noise + mean
eta = np.ones(p)
bound = 5
s1 = AC.sample_truncnorm_white_sphere(
A,
b,
initial,
eta,
lambda state: bound + 0.01 * np.random.sample() * np.linalg.norm(state
)**2,
burnin=1000,
ndraw=1000,
how_often=5)
con = AC.constraints(A, b)
con.covariance = np.diag([1] * 7 + [0] * 3)
con.mean[:] = mean
print con(initial)
s2 = AC.sample_from_sphere(con, initial)
return s1, s2
def test_conditional_sampling(n=20, p=25, sigma=20,
ndraw=1000,
burnin=1000,
nsim=None):
"""
goodness of fit samples from
inactive constraints intersect a sphere
this test verifies the sampler is doing what it should
"""
con, y, L, X = _generate_constraints(n=n, p=p, sigma=sigma)
X_E = X[:,L.active]
C_Ei = np.linalg.pinv(X_E.T.dot(X_E))
R_E = lambda z: z - X_E.dot(C_Ei.dot(X_E.T.dot(z)))
X_minus_E = X[:,L.inactive]
RX_minus_E = R_E(X_minus_E)
inactive_bound = L.feature_weights[L.inactive]
active_subgrad = L.feature_weights[L.active] * L.active_signs
irrep_term = X_minus_E.T.dot(X_E.dot(C_Ei.dot(active_subgrad)))
inactive_constraints = AC.constraints(
np.vstack([RX_minus_E.T,
-RX_minus_E.T]),
np.hstack([inactive_bound - irrep_term,
inactive_bound + irrep_term]),
covariance = np.identity(n))
con = inactive_constraints
conditional_con = con.conditional(X_E.T, np.dot(X_E.T, y))
Z, W = AC.sample_from_sphere(conditional_con,
y,
ndraw=ndraw,
burnin=burnin)
T1 = np.dot(X_E.T, Z.T) - np.dot(X_E.T, y)[:,None]
nt.assert_true(np.linalg.norm(T1) < 1.e-7)
T2 = (R_E(Z.T)**2).sum(0) - np.linalg.norm(R_E(y))**2
nt.assert_true(np.linalg.norm(T2) < 1.e-7)
def test_conditional_sampling(n=20,
p=25,
sigma=20,
ndraw=1000,
burnin=1000,
nsim=None):
"""
goodness of fit samples from
inactive constraints intersect a sphere
this test verifies the sampler is doing what it should
"""
con, y, L, X = _generate_constraints(n=n, p=p, sigma=sigma)
X_E = X[:, L.active]
C_Ei = np.linalg.pinv(X_E.T.dot(X_E))
R_E = lambda z: z - X_E.dot(C_Ei.dot(X_E.T.dot(z)))
X_minus_E = X[:, L.inactive]
RX_minus_E = R_E(X_minus_E)
inactive_bound = L.feature_weights[L.inactive]
active_subgrad = L.feature_weights[L.active] * L.active_signs
irrep_term = X_minus_E.T.dot(X_E.dot(C_Ei.dot(active_subgrad)))
inactive_constraints = AC.constraints(
np.vstack([RX_minus_E.T, -RX_minus_E.T]),
np.hstack([inactive_bound - irrep_term, inactive_bound + irrep_term]),
covariance=np.identity(n))
con = inactive_constraints
conditional_con = con.conditional(X_E.T, np.dot(X_E.T, y))
Z, W = AC.sample_from_sphere(conditional_con,
y,
ndraw=ndraw,
burnin=burnin)
T1 = np.dot(X_E.T, Z.T) - np.dot(X_E.T, y)[:, None]
nt.assert_true(np.linalg.norm(T1) < 1.e-7)
T2 = (R_E(Z.T)**2).sum(0) - np.linalg.norm(R_E(y))**2
nt.assert_true(np.linalg.norm(T2) < 1.e-7)
def test_conditional_sampling(n=20, p=25, sigma=20):
"""
goodness of fit samples from
inactive constraints intersect a sphere
this test verifies the sampler is doing what it should
"""
con, y, L = _generate_constraints(n=n, p=p, sigma=sigma)
print L.active.shape
con = L.inactive_constraints
conditional_con = con.conditional(L._X_E.T, np.dot(L._X_E.T, y))
Z, W = AC.sample_from_sphere(conditional_con, y, ndraw=1000, burnin=1000)
T1 = np.dot(L._X_E.T, Z.T) - np.dot(L._X_E.T, y)[:, None]
nt.assert_true(np.linalg.norm(T1) < 1.e-7)
T2 = (np.dot(L.R_E, Z.T)**2).sum(0) - np.linalg.norm(np.dot(L.R_E, y))**2
nt.assert_true(np.linalg.norm(T2) < 1.e-7)
def test_conditional_sampling(n=20, p=25, sigma=20):
"""
goodness of fit samples from
inactive constraints intersect a sphere
this test verifies the sampler is doing what it should
"""
con, y, L = _generate_constraints(n=n, p=p, sigma=sigma)
print L.active.shape
con = L.inactive_constraints
conditional_con = con.conditional(L._X_E.T, np.dot(L._X_E.T, y))
Z, W = AC.sample_from_sphere(conditional_con,
y,
ndraw=1000,
burnin=1000)
T1 = np.dot(L._X_E.T, Z.T) - np.dot(L._X_E.T, y)[:,None]
nt.assert_true(np.linalg.norm(T1) < 1.e-7)
T2 = (np.dot(L.R_E, Z.T)**2).sum(0) - np.linalg.norm(np.dot(L.R_E, y))**2
nt.assert_true(np.linalg.norm(T2) < 1.e-7)
