def sample_conditional(self, index):
if index < 0 or index >= self.dimension:
raise ValueError("Conditional index out of bounds")
# all indices but the current
cond_inds = hstack((arange(0, index), arange(index + 1, self.dimension)))
# print "conditioning on index %d" % index
# print "other indices:", cond_inds
# partition the Gaussian x|y, precompute matrix inversion
mu_x = self.full_target.mu[index]
Sigma_xx = self.full_Sigma[index, index]
mu_y = self.full_target.mu[cond_inds]
Sigma_yy = self.full_Sigma[cond_inds, cond_inds].reshape(len(cond_inds), len(cond_inds))
L_yy = cholesky(Sigma_yy)
Sigma_xy = self.full_Sigma[index, cond_inds]
Sigma_yx = self.full_Sigma[cond_inds, index]
y = self.current_state[cond_inds]
# mu=mu_x+Sigma_xy Sigma_yy^(-1)(y-mu_y)
mu = mu_x + Sigma_xy.dot(MatrixTools.cholesky_solve(L_yy, y - mu_y))
# solve Sigma=Sigma_xx-Sigma_yy^-1 Sigma_yx=Sigma_xy-Sigma_xy L_yy^(-T)_yy^(-1) Sigma_yx
Sigma = Sigma_xx - Sigma_xy.dot(MatrixTools.cholesky_solve(L_yy, Sigma_yx))
# return sample from x|y
conditional_sample = randn() * sqrt(Sigma) + mu
return conditional_sample
def main():
# covariance has stretched Eigenvalues, and rotated basis
Sigma = eye(2)
Sigma[0, 0] = 30
Sigma[1, 1] = 1
theta = -pi / 4
U = MatrixTools.rotation_matrix(theta)
Sigma = U.T.dot(Sigma).dot(U)
gaussian = Gaussian(Sigma=Sigma)
distribution = GaussianFullConditionals(gaussian, [0., 0.])
mcmc_sampler = Gibbs(distribution)
start = zeros(distribution.dimension)
mcmc_params = MCMCParams(start=start, num_iterations=20000)
chain = MCMCChain(mcmc_sampler, mcmc_params)
chain.append_mcmc_output(StatisticsOutput(plot_times=True, lag=100))
chain.append_mcmc_output(
PlottingOutput(distribution=gaussian,
plot_from=1,
colour_by_likelihood=False,
num_samples_plot=0,
lag=100))
chain.run()
def __init__(self,
mu=array([0, 0]),
Sigma=eye(2),
is_cholesky=False,
ell=None):
Distribution.__init__(self, len(Sigma))
assert (len(shape(mu)) == 1)
assert (max(shape(Sigma)) == len(mu))
self.mu = mu
self.ell = ell
if is_cholesky:
self.L = Sigma
if ell == None:
assert (shape(Sigma)[0] == shape(Sigma)[1])
else:
assert (shape(Sigma)[1] == ell)
else:
assert (shape(Sigma)[0] == shape(Sigma)[1])
if ell is not None:
self.L, _, _ = MatrixTools.low_rank_approx(Sigma, ell)
self.L = self.L.T
assert (shape(self.L)[1] == ell)
else:
try:
self.L = cholesky(Sigma)
except LinAlgError:
# some really crude check for PSD (which only corrects for orunding errors
self.L = cholesky(Sigma + eye(len(Sigma)) * 1e-5)
def main():
# covariance has stretched Eigenvalues, and rotated basis
Sigma = eye(2)
Sigma[0, 0] = 30
Sigma[1, 1] = 1
theta = -pi / 4
U = MatrixTools.rotation_matrix(theta)
Sigma = U.T.dot(Sigma).dot(U)
gaussian = Gaussian(Sigma=Sigma)
distribution = GaussianFullConditionals(gaussian, [0., 0.])
mcmc_sampler = Gibbs(distribution)
start = zeros(distribution.dimension)
mcmc_params = MCMCParams(start=start, num_iterations=20000)
chain = MCMCChain(mcmc_sampler, mcmc_params)
chain.append_mcmc_output(StatisticsOutput(plot_times=True, lag=100))
chain.append_mcmc_output(PlottingOutput(distribution=gaussian, plot_from=1,
colour_by_likelihood=False,
num_samples_plot=0, lag=100))
chain.run()
def main():
# covariance has stretched Eigenvalues, and rotated basis
Sigma1 = eye(2)
Sigma1[0, 0] = 30.0
Sigma1[1, 1] = 1.0
Sigma2 = Sigma1
Sigma2[0, 0] = 20.0
theta = -pi / 4
U = MatrixTools.rotation_matrix(theta)
Sigma1 = U.T.dot(Sigma1).dot(U)
Sigma2 = U.T.dot(Sigma2).dot(U)
gaussian1 = Gaussian(Sigma=Sigma1)
gaussian2 = Gaussian(mu=array([1., 0.]), Sigma=Sigma1)
numTrials=500
vanillap=empty((numTrials,2,2))
blockp=empty((numTrials,2,2))
wildp=empty((numTrials,2,2))
# f = open("/home/dino/git/test_results.dat", "r")
# vanillarej=load(f)
# blockrej=load(f)
# wildrej=load(f)
# f.close()
#
for i in range(numTrials):
print 'trial', i
vanillap[i],blockp[i],wildp[i]=all_tests(gaussian1,gaussian2,n=200)
f = open("/nfs/home2/dino/git/test_results.dat", "w")
vanillarej=sum(vanillap<0.05,0)/numTrials
blockrej=sum(blockp<0.05,0)/numTrials
wildrej=sum(wildp<0.05,0)/numTrials
dump(vanillarej, f)
dump(blockrej, f)
dump(wildrej, f)
f.close()
def main():
# covariance has stretched Eigenvalues, and rotated basis
Sigma1 = eye(2)
Sigma1[0, 0] = 30.0
Sigma1[1, 1] = 1.0
Sigma2 = Sigma1
Sigma2[0, 0] = 20.0
theta = -pi / 4
U = MatrixTools.rotation_matrix(theta)
Sigma1 = U.T.dot(Sigma1).dot(U)
Sigma2 = U.T.dot(Sigma2).dot(U)
gaussian1 = Gaussian(Sigma=Sigma1)
gaussian2 = Gaussian(mu=array([1.0, 0.0]), Sigma=Sigma1)
numTrials = 500
vanillap = empty((numTrials, 2, 2))
blockp = empty((numTrials, 2, 2))
wildp = empty((numTrials, 2, 2))
# f = open("/home/dino/git/test_results.dat", "r")
# vanillarej=load(f)
# blockrej=load(f)
# wildrej=load(f)
# f.close()
#
for i in range(numTrials):
print "trial", i
vanillap[i], blockp[i], wildp[i] = all_tests(gaussian1, gaussian2, n=200)
f = open("/nfs/home2/dino/git/test_results.dat", "w")
vanillarej = sum(vanillap < 0.05, 0) / numTrials
blockrej = sum(blockp < 0.05, 0) / numTrials
wildrej = sum(wildp < 0.05, 0) / numTrials
dump(vanillarej, f)
dump(blockrej, f)
dump(wildrej, f)
f.close()
def main():
numTrials = 500
n=200
Sigma1 = eye(2)
Sigma1[0, 0] = 30.0
Sigma1[1, 1] = 1.0
theta = - pi / 4
U = MatrixTools.rotation_matrix(theta)
Sigma1 = U.T.dot(Sigma1).dot(U)
print Sigma1
gaussian1 = Gaussian(Sigma=Sigma1)
gaussian2 = Gaussian(mu=array([1., 0.]), Sigma=Sigma1)
oracle_samples1 = gaussian1.sample(n=n).samples
oracle_samples2 = gaussian2.sample(n=n).samples
print 'mean1:', mean(oracle_samples1,0)
print 'mean2:', mean(oracle_samples2,0)
plot(oracle_samples1[:,0],oracle_samples1[:,1],'b*')
plot(oracle_samples2[:,0],oracle_samples2[:,1],'r*')
show()
distribution1 = GaussianFullConditionals(gaussian1, list(gaussian1.mu))
distribution2 = GaussianFullConditionals(gaussian2, list(gaussian2.mu))
H0_samples = zeros(numTrials)
HA_samples = zeros(numTrials)
mcmc_sampler1 = Gibbs(distribution1)
mcmc_sampler2 = Gibbs(distribution2)
burnin = 9000
thin = 5
start = zeros(2)
mcmc_params = MCMCParams(start=start, num_iterations=burnin+thin*n, burnin=burnin)
sigma = GaussianKernel.get_sigma_median_heuristic(concatenate((oracle_samples1,oracle_samples2),axis=0))
print 'using bandwidth: ', sigma
kernel = GaussianKernel(sigma=sigma)
for ii in arange(numTrials):
start =time.time()
print 'trial:', ii
oracle_samples1 = gaussian1.sample(n=n).samples
oracle_samples1a = gaussian1.sample(n=n).samples
oracle_samples2 = gaussian2.sample(n=n).samples
# chain1 = MCMCChain(mcmc_sampler1, mcmc_params)
# chain1.run()
# gibbs_samples1 = chain1.get_samples_after_burnin()
# gibbs_samples1 = gibbs_samples1[thin*arange(n)]
#
# chain1a = MCMCChain(mcmc_sampler1, mcmc_params)
# chain1a.run()
# gibbs_samples1a = chain1a.get_samples_after_burnin()
# gibbs_samples1a = gibbs_samples1a[thin*arange(n)]
#
# chain2 = MCMCChain(mcmc_sampler2, mcmc_params)
# chain2.run()
# gibbs_samples2 = chain2.get_samples_after_burnin()
# gibbs_samples2 = gibbs_samples2[thin*arange(n)]
# H0_samples[ii]=kernel.estimateMMD(gibbs_samples1,gibbs_samples1a)
# HA_samples[ii]=kernel.estimateMMD(gibbs_samples1,gibbs_samples2)
#
H0_samples[ii]=kernel.estimateMMD(oracle_samples1,oracle_samples1a)
HA_samples[ii]=kernel.estimateMMD(oracle_samples1,oracle_samples2)
end=time.time()
print 'time elapsed: ', end-start
f = open("/home/dino/git/mmdIIDTrueSamples.dat", "w")
dump(H0_samples, f)
dump(HA_samples, f)
dump(gaussian1, f)
dump(gaussian2, f)
f.close()
return None
def main():
numTrials = 500
n = 200
Sigma1 = eye(2)
Sigma1[0, 0] = 30.0
Sigma1[1, 1] = 1.0
theta = -pi / 4
U = MatrixTools.rotation_matrix(theta)
Sigma1 = U.T.dot(Sigma1).dot(U)
print Sigma1
gaussian1 = Gaussian(Sigma=Sigma1)
gaussian2 = Gaussian(mu=array([1., 0.]), Sigma=Sigma1)
oracle_samples1 = gaussian1.sample(n=n).samples
oracle_samples2 = gaussian2.sample(n=n).samples
print 'mean1:', mean(oracle_samples1, 0)
print 'mean2:', mean(oracle_samples2, 0)
plot(oracle_samples1[:, 0], oracle_samples1[:, 1], 'b*')
plot(oracle_samples2[:, 0], oracle_samples2[:, 1], 'r*')
show()
distribution1 = GaussianFullConditionals(gaussian1, list(gaussian1.mu))
distribution2 = GaussianFullConditionals(gaussian2, list(gaussian2.mu))
H0_samples = zeros(numTrials)
HA_samples = zeros(numTrials)
mcmc_sampler1 = Gibbs(distribution1)
mcmc_sampler2 = Gibbs(distribution2)
burnin = 9000
thin = 5
start = zeros(2)
mcmc_params = MCMCParams(start=start,
num_iterations=burnin + thin * n,
burnin=burnin)
sigma = GaussianKernel.get_sigma_median_heuristic(
concatenate((oracle_samples1, oracle_samples2), axis=0))
print 'using bandwidth: ', sigma
kernel = GaussianKernel(sigma=sigma)
for ii in arange(numTrials):
start = time.time()
print 'trial:', ii
oracle_samples1 = gaussian1.sample(n=n).samples
oracle_samples1a = gaussian1.sample(n=n).samples
oracle_samples2 = gaussian2.sample(n=n).samples
# chain1 = MCMCChain(mcmc_sampler1, mcmc_params)
# chain1.run()
# gibbs_samples1 = chain1.get_samples_after_burnin()
# gibbs_samples1 = gibbs_samples1[thin*arange(n)]
#
# chain1a = MCMCChain(mcmc_sampler1, mcmc_params)
# chain1a.run()
# gibbs_samples1a = chain1a.get_samples_after_burnin()
# gibbs_samples1a = gibbs_samples1a[thin*arange(n)]
#
# chain2 = MCMCChain(mcmc_sampler2, mcmc_params)
# chain2.run()
# gibbs_samples2 = chain2.get_samples_after_burnin()
# gibbs_samples2 = gibbs_samples2[thin*arange(n)]
# H0_samples[ii]=kernel.estimateMMD(gibbs_samples1,gibbs_samples1a)
# HA_samples[ii]=kernel.estimateMMD(gibbs_samples1,gibbs_samples2)
#
H0_samples[ii] = kernel.estimateMMD(oracle_samples1, oracle_samples1a)
HA_samples[ii] = kernel.estimateMMD(oracle_samples1, oracle_samples2)
end = time.time()
print 'time elapsed: ', end - start
f = open("/home/dino/git/mmdIIDTrueSamples.dat", "w")
dump(H0_samples, f)
dump(HA_samples, f)
dump(gaussian1, f)
dump(gaussian2, f)
f.close()
return None
def __init__(self, mu=array([0, 0]), Sigma=eye(2), is_cholesky=False, ell=None):
Distribution.__init__(self, len(Sigma))
assert(len(shape(mu)) == 1)
assert(max(shape(Sigma)) == len(mu))
self.mu = mu
self.ell = ell
if is_cholesky:
self.L = Sigma
if ell == None:
assert(shape(Sigma)[0] == shape(Sigma)[1])
else:
assert(shape(Sigma)[1] == ell)
else:
assert(shape(Sigma)[0] == shape(Sigma)[1])
if ell is not None:
self.L, _, _ = MatrixTools.low_rank_approx(Sigma, ell)
self.L = self.L.T
assert(shape(self.L)[1] == ell)
else:
try:
self.L = cholesky(Sigma)
except LinAlgError:
# some really crude check for PSD (which only corrects for orunding errors
self.L = cholesky(Sigma+eye(len(Sigma))*1e-5)