def test_two_dimensional_tests_agrees(self):
np.random.seed(43)
me = GaussianQuadraticTest(self.grad_log_normal)
samples = np.random.randn(10,2)
U1,_ = me.get_statisitc_two_dim(10,samples,1)
U2,_ = me.get_statistic_multiple_dim(samples,1)
np.testing.assert_almost_equal(U1,U2)
def test_two_dimensional_tests_agrees(self):
np.random.seed(43)
me = GaussianQuadraticTest(self.grad_log_normal)
samples = np.random.randn(10, 2)
U1, _ = me.get_statisitc_two_dim(10, samples, 1)
U2, _ = me.get_statistic_multiple_dim(samples, 1)
np.testing.assert_almost_equal(U1, U2)
def test_regression_2(self):
np.random.seed(42)
data = np.random.randn(100) * 2.0
me = GaussianQuadraticTest(self.grad_log_normal)
U_stat, _ = me.get_statistic_multiple(data)
pval = me.compute_pvalue(U_stat)
assert pval == 0.0
def test_k_multiple_equals_k_no_dim(self):
N = 10
X = np.random.randn(N,1)
me = GaussianQuadraticTest(self.grad_log_normal)
K1 = me.k_multiple_dim(X)
K2 =me.k_multiple(X[:,0])
np.testing.assert_almost_equal(K1, K2)
def test_two_dimensional_tests_alt(self):
np.random.seed(43)
me = GaussianQuadraticTest(self.grad_log_normal)
samples = np.random.randn(100, 2) + 1
U, _ = me.get_statisitc_two_dim(100, samples, 1)
p = me.compute_pvalue(U)
assert p == 0
def test_regression_2(self):
np.random.seed(42)
data = np.random.randn(100) * 2.0
me = GaussianQuadraticTest(self.grad_log_normal)
U_stat,_ = me.get_statistic_multiple(data)
pval = me.compute_pvalue(U_stat)
assert pval == 0.0
def test_k_multiple_equals_k_no_dim(self):
N = 10
X = np.random.randn(N, 1)
me = GaussianQuadraticTest(self.grad_log_normal)
K1 = me.k_multiple_dim(X)
K2 = me.k_multiple(X[:, 0])
np.testing.assert_almost_equal(K1, K2)
def test_two_dimensional_tests_alt(self):
np.random.seed(43)
me = GaussianQuadraticTest(self.grad_log_normal)
samples = np.random.randn(100,2)+1
U,_ = me.get_statisitc_two_dim(100,samples,1)
p = me.compute_pvalue(U)
assert p == 0
def test_gk_multiple_dim(self):
N = 10
X = np.random.randn(N, 1)
me = GaussianQuadraticTest(self.grad_log_normal)
K = me.k_multiple_dim(X)
gk_alt = me.gk_multiple_dim(X, K, 0)
gk_orig = me.gk_multiple(X[:, 0])
np.testing.assert_almost_equal(gk_alt, gk_orig)
def test_g1k_multiple_dim(self):
N = 10
X = np.random.randn(N,1)
me = GaussianQuadraticTest(self.grad_log_normal)
K = me.k_multiple_dim(X)
g1k_alt = me.g1k_multiple_dim(X,K,0)
g1k_orig = me.g1k_multiple(X[:,0])
np.testing.assert_almost_equal(g1k_alt, g1k_orig)
def test_get_statistic_multiple_equals_get_statistic(self):
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal)
U_matrix_multiple, stat_multiple = me.get_statistic_multiple(X)
U_matrix, stat = me.get_statisitc(N, X)
assert_allclose(stat, stat_multiple)
assert_allclose(U_matrix_multiple, U_matrix)
def test_get_statistic_multiple_equals_get_statistic(self):
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal)
U_matrix_multiple, stat_multiple = me.get_statistic_multiple(X)
U_matrix, stat = me.get_statisitc(N, X)
assert_allclose(stat, stat_multiple)
assert_allclose(U_matrix_multiple, U_matrix)
def test_gk_multiple_equals_gk(self):
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal)
GK = me.gk_multiple(X)
for i in range(N):
for j in range(N):
gk = me.gk(X[i], X[j])
assert_almost_equal(GK[i, j], gk)
def test_gk_multiple_equals_gk(self):
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal)
GK = me.gk_multiple(X)
for i in range(N):
for j in range(N):
gk = me.gk(X[i], X[j])
assert_almost_equal(GK[i, j], gk)
def test_k_multiple_equals_k_no_grad_multiple_given(self):
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal)
K = me.k_multiple(X)
for i in range(N):
for j in range(N):
k = me.k(X[i], X[j])
assert_almost_equal(K[i, j], k)
def test_k_multiple_equals_k_no_grad_multiple_given(self):
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal)
K = me.k_multiple(X)
for i in range(N):
for j in range(N):
k = me.k(X[i], X[j])
assert_almost_equal(K[i, j], k)
def compare_against_mmd_test():
data = loadmat("../data/02-solar.mat")
X = data["X"]
y = data["y"]
X_train, y_train, X_test, y_test, N, N_test = prepare_dataset(X, y)
kernel = RBF(input_dim=1, variance=0.608, lengthscale=0.207)
m = GPRegression(X_train, y_train, kernel, noise_var=0.283)
m.optimize()
pred_mean, pred_std = m.predict(X_test)
s = GaussianQuadraticTest(None)
gradients = compute_gp_regression_gradients(y_test, pred_mean, pred_std)
U_matrix, stat = s.get_statistic_multiple_custom_gradient(y_test[:, 0], gradients[:, 0])
num_test_samples = 10000
null_samples = bootstrap_null(U_matrix, num_bootstrap=num_test_samples)
# null_samples = sample_null_simulated_gp(s, pred_mean, pred_std, num_test_samples)
p_value_ours = 1.0 - np.mean(null_samples <= stat)
y_rep = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
y_rep = np.atleast_2d(y_rep).T
A = np.hstack((X_test, y_test))
B = np.hstack((X_test, y_rep))
feats_p = RealFeatures(A.T)
feats_q = RealFeatures(B.T)
width = 1
kernel = GaussianKernel(10, width)
mmd = QuadraticTimeMMD()
mmd.set_kernel(kernel)
mmd.set_p(feats_p)
mmd.set_q(feats_q)
mmd_stat = mmd.compute_statistic()
# sample from null
num_null_samples = 10000
mmd_null_samples = np.zeros(num_null_samples)
for i in range(num_null_samples):
# fix y_rep from above, and change the other one (that would replace y_test)
y_rep2 = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
y_rep2 = np.atleast_2d(y_rep2).T
A = np.hstack((X_test, y_rep2))
feats_p = RealFeatures(A.T)
width = 1
kernel = GaussianKernel(10, width)
mmd = QuadraticTimeMMD()
mmd.set_kernel(kernel)
mmd.set_p(feats_p)
mmd.set_q(feats_q)
mmd_null_samples[i] = mmd.compute_statistic()
p_value_mmd = 1.0 - np.mean(mmd_null_samples <= mmd_stat)
return p_value_ours, p_value_mmd
def test_k_multiple_equals_k_grad_multiple_given(self):
def fun(self, X):
return -X
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal, grad_log_prob_multiple=fun)
K = me.k_multiple(X)
for i in range(N):
for j in range(N):
k = me.k(X[i], X[j])
assert_almost_equal(K[i, j], k)
def test_k_multiple_equals_k_grad_multiple_given(self):
def fun(self, X):
return -X
N = 10
X = np.random.randn(N)
me = GaussianQuadraticTest(self.grad_log_normal,
grad_log_prob_multiple=fun)
K = me.k_multiple(X)
for i in range(N):
for j in range(N):
k = me.k(X[i], X[j])
assert_almost_equal(K[i, j], k)
def test_corr(self):
np.random.seed(43)
sigma = np.array([[1, 0.5], [0.5, 1]])
def grad_log_correleted(x):
sigmaInv = np.linalg.inv(sigma)
return -np.dot(sigmaInv.T + sigmaInv, x) / 2.0
me = GaussianQuadraticTest(grad_log_correleted)
qm = QuadraticMultiple(me)
X = np.random.multivariate_normal([0, 0], sigma, 200)
reject, p_val = qm.is_from_null(0.05, X, 0.1)
np.testing.assert_almost_equal([0.465, 0.465], p_val)
def run_simulation(sample_size, bootstrap_size=600, average_over=400):
for d in [2, 5, 10, 15, 20, 25]:
samples = []
for i in range(bootstrap_size):
samples.append(baringhaus_stat(np.random.randn(sample_size,
d)))
samples = np.array(samples)
pvals_brainghaus = []
pvals_stein = []
pvals_imq = []
for i in range(average_over):
X = np.random.randn(sample_size, d)
X[:, 0] += np.random.rand(sample_size)
# baringhaus p value
T = baringhaus_stat(X)
pval = float(len(samples[samples > T])) / bootstrap_size
pvals_brainghaus.append(pval)
# gaussian p value
me = GaussianQuadraticTest(grad_log_normal)
qm = QuadraticMultiple2(me)
p = qm.is_from_null(0.1, np.copy(X), 0.5)
pvals_stein.append(p)
# IMQ p value
me2 = MultiquadricQuadraticTest(grad_log_normal, beta=-0.5)
qm2 = QuadraticMultiple2(me2)
p2 = qm2.is_from_null(0.1, np.copy(X), 0.5)
pvals_imq.append(p2)
print('d :', d)
pvals_brainghaus = np.array(pvals_brainghaus)
print(
'baringhaus :',
float(len(pvals_brainghaus[pvals_brainghaus < 0.1])) /
average_over)
pvals_stein = np.array(pvals_stein)
print('Stein :',
float(len(pvals_stein[pvals_stein < 0.1])) / average_over)
pvals_imq = np.array(pvals_imq)
print('IMQ :',
float(len(pvals_imq[pvals_imq < 0.1])) / average_over)
m.optimize()
res = 100
pred_mean, pred_std = m.predict(X_test)
plt.plot(X_test, pred_mean, 'b-')
plt.plot(X_test, pred_mean + 2 * pred_std, 'b--')
plt.plot(X_test, pred_mean - 2 * pred_std, 'b--')
plt.plot(X_train, y_train, 'b.', markersize=3)
plt.plot(X_test, y_test, 'r.', markersize=5)
plt.grid(True)
plt.xlabel(r"$X$")
plt.ylabel(r"$y$")
plt.savefig("gp_regression_data_fit.eps", bbox_inches='tight')
plt.show()
s = GaussianQuadraticTest(None)
gradients = compute_gp_regression_gradients(y_test, pred_mean, pred_std)
U_matrix, stat = s.get_statistic_multiple_custom_gradient(y_test[:, 0], gradients[:, 0])
num_test_samples = 10000
null_samples = bootstrap_null(U_matrix, num_bootstrap=num_test_samples)
sns.distplot(null_samples, kde=False, norm_hist=True)
plt.plot([stat, stat], [0, .012], 'black')
plt.legend([r"$V_n$ test", r"Bootstrapped $B_n$"])
plt.xlabel(r"$V_n$")
plt.ylabel(r"Frequency")
plt.savefig("gp_regression_bootstrap_hist.eps", bbox_inches='tight')
plt.show()
arr = []
me = GaussianSteinTest(grad_log_pob, 1)
for time in times_we_look_at:
chain_at_time = samples[:, time]
# print(time)
# pval = me.compute_pvalue(chain_at_time)
# arr.append(pval)
def grad_log_pob(t):
a = np.sum(manual_grad(t[0], t[1], X), axis=0) + grad_log_prior(t)
return a
P_CHANGE = 0.1
me = GaussianQuadraticTest(grad_log_pob)
qm = QuadraticMultiple(me)
reject, p = qm.is_from_null(0.05, chain_at_time, 0.1)
print(reject)
# import matplotlib.pyplot as plt
#
# print(arr)
#
# plt.plot(arr)
#
# plt.show()
dfs = range(1, 4, 2)
mc_reps = 100
res = np.empty((0, 2))
block = N / np.log(N)
p_change = 1.0 / block
print(p_change)
for df in dfs:
for mc in range(mc_reps):
print(mc)
X = almost_t_student(10 * N, df, 0.01)
X = X[::10]
me = GaussianQuadraticTest(grad_log_normal)
U_stat, _ = me.get_statistic_multiple(X)
pval = me.compute_pvalues_for_processes(U_stat, p_change)
res = np.vstack((res, np.array([df, pval])))
for mc in range(mc_reps):
X = almost_t_student(10 * N, 100, 0.01)
X = X[::10]
me = GaussianQuadraticTest(grad_log_normal)
U_stat, _ = me.get_statistic_multiple(X)
pval = me.compute_pvalues_for_processes(U_stat, p_change)
res = np.vstack((res, np.array([np.Inf, pval])))
np.save('results.npy', res)
arr = np.empty((0, 2))
arr2 = np.empty((0, 2))
for c in [1.0, 1.3, 2.0, 3.0]:
print('c', c)
log_normal = logg(c)
for i in range(23):
print(i)
x = metropolis_hastings(log_normal,
chain_size=500,
thinning=15,
x_prev=np.random.randn(2))
me = GaussianQuadraticTest(grad_log_dens)
qm = QuadraticMultiple(me)
qm2 = QuadraticMultiple2(me)
accept_null, p_val = qm.is_from_null(0.05, x, 0.1)
p_val2 = qm2.is_from_null(0.05, x, 0.1)
print(p_val2)
arr = np.vstack((arr, np.array([c, min(p_val)])))
arr2 = np.vstack((arr2, np.array([c, p_val2])))
df = DataFrame(arr)
pr = seaborn.boxplot(x=0, y=1, data=df)
seaborn.plt.show()
df = DataFrame(arr2)
pr = seaborn.boxplot(x=0, y=1, data=df)
import numpy as np
from stat_test.quadratic_time import GaussianQuadraticTest
from tools.tools import store_results
if __name__ == '__main__':
D = 1
N_test = 500
N_fit = 50000
ms_fit = np.array([1, 2, 5, 10, 25, 50, 75, 100, 250, 500, 1000, 2000, 5000])
sigma = 1
lmbda = 0.01
grad = lambda x: est.grad(np.array([x]))[0]
s = GaussianQuadraticTest(grad)
num_bootstrap = 200
result_fname = os.path.splitext(os.path.basename(__file__))[0] + ".txt"
num_repetitions = 150
for _ in range(num_repetitions):
for m in ms_fit:
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
X_test = np.random.randn(N_test, D)
X = np.random.randn(N_fit, D)
est.fit(X)
U_matrix, stat = s.get_statistic_multiple(X_test[:,0])
from pandas import DataFrame
import seaborn
from stat_test.quadratic_time import GaussianQuadraticTest
__author__ = 'kcx'
import numpy as np
def grad_log_normal(x):
return -x
np.random.seed(42)
me = GaussianQuadraticTest(grad_log_normal)
res = np.empty((0, 2))
for i in range(50):
data = np.random.randn(75)
_, s1 = me.get_statisitc(len(data), data)
res = np.vstack((res, np.array([75, s1])))
for i in range(50):
data = np.random.randn(100)
_, s1 = me.get_statisitc(len(data), data)
res = np.vstack((res, np.array([100, s1])))
for i in range(50):
data = np.random.randn(150)
_, s1 = me.get_statisitc(len(data), data)
from pandas import DataFrame
import seaborn
from stat_test.quadratic_time import GaussianQuadraticTest
__author__ = 'kcx'
import numpy as np
def grad_log_normal(x):
return -x
np.random.seed(42)
me = GaussianQuadraticTest(grad_log_normal)
res = np.empty((0,2))
for i in range(50):
data = np.random.randn(75)
_,s1 = me.get_statisitc(len(data),data)
res = np.vstack((res,np.array([75, s1])))
for i in range(50):
data = np.random.randn(100)
_,s1 = me.get_statisitc(len(data),data)
res = np.vstack((res,np.array([100, s1])))
# estimate size of thinning
def get_thinning(X, nlags=50):
autocorrelation = acf(X, nlags=nlags, fft=True)
thinning = np.argmin(np.abs(autocorrelation - 0.95)) + 1
return thinning, autocorrelation
#
# X = gen(TEST_CHAIN_SIZE, np.Inf)
# thinning, autocorr = get_thinning(X)
# print('thinning for AR normal simulation ', thinning, autocorr[thinning])
thinning = 1
tester = GaussianQuadraticTest(grad_log_normal)
def get_pval(X, tester, p_change):
U_stat, _ = tester.get_statistic_multiple(X)
return tester.compute_pvalues_for_processes(U_stat, p_change)
def get_pair(sample_size, df, thinning, tester, p_change):
X = gen(sample_size, df, thinning)
pval = get_pval(X, tester, p_change)
return [df, pval]
P_CHANGE = 0.1
results = []
dfs = range(1, 4, 2)
mc_reps = 100
res = np.empty((0,2))
block = N/np.log(N)
p_change = 1.0/block
print(p_change)
for df in dfs:
for mc in range(mc_reps):
print(mc)
X = almost_t_student(10*N,df,0.01)
X = X[::10]
me = GaussianQuadraticTest(grad_log_normal)
U_stat,_ = me.get_statistic_multiple(X)
pval = me.compute_pvalues_for_processes(U_stat,p_change)
res = np.vstack((res,np.array([df, pval])))
for mc in range(mc_reps):
X = almost_t_student(10*N,100,0.01)
X = X[::10]
me = GaussianQuadraticTest(grad_log_normal)
U_stat,_ = me.get_statistic_multiple(X)
pval = me.compute_pvalues_for_processes(U_stat,p_change)
res = np.vstack((res,np.array([np.Inf, pval])))
np.save('results.npy',res)
import numpy as np
from stat_test.quadratic_time import GaussianQuadraticTest
from tools.tools import store_results
if __name__ == '__main__':
D = 1
N_test = 500
N_fit = 50000
ms_fit = np.array(
[1, 2, 5, 10, 25, 50, 75, 100, 250, 500, 1000, 2000, 5000])
sigma = 1
lmbda = 0.01
grad = lambda x: est.grad(np.array([x]))[0]
s = GaussianQuadraticTest(grad)
num_bootstrap = 200
result_fname = os.path.splitext(os.path.basename(__file__))[0] + ".txt"
num_repetitions = 150
for _ in range(num_repetitions):
for m in ms_fit:
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
X_test = np.random.randn(N_test, D)
X = np.random.randn(N_fit, D)
est.fit(X)
U_matrix, stat = s.get_statistic_multiple(X_test[:, 0])