def get_OracleKernelAdaptiveLangevin_instance(D, target_log_pdf):
step_size = 1.
m = 500
N = 5000
Z = sample_banana(N, D, bananicity, V)
surrogate = KernelExpFiniteGaussian(sigma=10, lmbda=.001, m=m, D=D)
surrogate.fit(Z)
if False:
param_bounds = {'sigma': [-2, 3]}
bo = BayesOptSearch(surrogate, Z, param_bounds)
best_params = bo.optimize()
surrogate.set_parameters_from_dict(best_params)
if False:
sigma = 1. / gamma_median_heuristic(Z)
surrogate.set_parameters_from_dict({'sigma': sigma})
logger.info("kernel exp family uses %s" % surrogate.get_parameters())
if False:
import matplotlib.pyplot as plt
Xs = np.linspace(-30, 30, 50)
Ys = np.linspace(-20, 40, 50)
visualise_fit_2d(surrogate, Z, Xs, Ys)
plt.show()
instance = OracleKernelAdaptiveLangevin(D, target_log_pdf, surrogate, step_size)
return instance
def get_OracleKernelAdaptiveLangevin_instance(D, target_log_pdf):
step_size = 1.
m = 500
N = 5000
Z = sample_banana(N, D, bananicity, V)
surrogate = KernelExpFiniteGaussian(sigma=10, lmbda=.001, m=m, D=D)
surrogate.fit(Z)
if False:
param_bounds = {'sigma': [-2, 3]}
bo = BayesOptSearch(surrogate, Z, param_bounds)
best_params = bo.optimize()
surrogate.set_parameters_from_dict(best_params)
if False:
sigma = 1. / gamma_median_heuristic(Z)
surrogate.set_parameters_from_dict({'sigma': sigma})
logger.info("kernel exp family uses %s" % surrogate.get_parameters())
if False:
import matplotlib.pyplot as plt
Xs = np.linspace(-30, 30, 50)
Ys = np.linspace(-20, 40, 50)
visualise_fit_2d(surrogate, Z, Xs, Ys)
plt.show()
instance = OracleKernelAdaptiveLangevin(D, target_log_pdf, surrogate,
step_size)
return instance
def test_KernelExpFiniteGaussian_fit_equals_update_fit():
sigma = 1.
lmbda = 2.
m = 2
N = 1
D = 2
rng_state = np.random.get_state()
np.random.seed(0)
est_batch = KernelExpFiniteGaussian(sigma, lmbda, m, D)
np.random.seed(0)
est_update = KernelExpFiniteGaussian(sigma, lmbda, m, D)
np.random.set_state(rng_state)
assert_equal(est_batch.b, None)
assert_equal(est_update.b, None)
assert_equal(est_batch.L_C, None)
assert_allclose(est_batch.n, est_update.n)
assert_allclose(est_batch.theta, np.zeros(m))
assert_allclose(est_update.theta, np.zeros(m))
X = np.random.randn(N, D)
est_batch.fit(X)
est_update.update_fit(X)
assert_allclose(est_batch.b, est_update.b)
assert_allclose(est_batch.L_C, est_update.L_C)
assert_allclose(est_batch.n, est_update.n)
assert_allclose(est_batch.theta, est_update.theta)
class KernelExpFiniteGaussianSurrogate(StaticSurrogate):
def __init__(self, ndim, sigma, lmbda, m):
self.surrogate = KernelExpFiniteGaussian(sigma, lmbda, m, D=ndim)
def train(self, samples):
self.surrogate.fit(samples)
def log_pdf_gradient(self, x):
return self.surrogate.grad(x)
def test_KernelExpFiniteGaussian_fit_less_than_m_data_execute():
sigma = 1.
lmbda = 1.
m = 20
N = 10
D = 2
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
X = np.random.randn(N, D)
est.fit(X)
def test_KernelExpFiniteGaussian_fit_exactly_m_data_execute():
sigma = 1.
lmbda = 1.
m = 2
N = m
D = 2
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
X = np.random.randn(N, D)
est.fit(X)
def test_third_order_derivative_tensor_execute():
if not theano_available:
raise SkipTest("Theano not available.")
sigma = 1.
lmbda = 1.
N = 100
D = 2
m = 10
X = np.random.randn(N, D)
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
est.fit(X)
est.third_order_derivative_tensor(X[0])
def test_hessian_execute():
if not theano_available:
raise SkipTest("Theano not available.")
sigma = 1.
lmbda = 1.
N = 100
D = 2
m = 10
X = np.random.randn(N, D)
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
est.fit(X)
est.hessian(X[0])
def get_OracleKernelAdaptiveLangevin_instance(D, target_log_pdf, grad):
step_size = 1.
schedule = one_over_sqrt_t_schedule
acc_star = 0.574
N = 500
m = 500
Z = sample_banana(N=N, D=D, bananicity=0.03, V=100)
surrogate = KernelExpFiniteGaussian(sigma=10, lmbda=1., m=m, D=D)
surrogate.fit(Z)
instance = OracleKernelAdaptiveLangevin(D, target_log_pdf, surrogate, step_size, schedule, acc_star)
return instance
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])
bootsraped_stats = np.empty(num_bootstrap)
for i in range(num_bootstrap):
W = np.sign(np.random.randn(N_test))
WW = np.outer(W, W)
st = np.mean(U_matrix * WW)
bootsraped_stats[i] = N_test * st
p_value = np.mean(bootsraped_stats>stat)
print m, p_value
store_results(result_fname,
D=D,
print "log2_sigmas:", log2_sigmas
print "sigmas:", 2 ** log2_sigmas
Js_mean = np.zeros(res)
Js_var = np.zeros(res)
for i, log2_sigma in enumerate(log2_sigmas):
sigma = 2 ** log2_sigma
surrogate = KernelExpFiniteGaussian(sigma=sigma, lmbda=lmbda, m=m, D=benchmark_samples.shape[1])
vals = surrogate.xvalidate_objective(benchmark_samples)
Js_mean[i] = np.mean(vals)
Js_var[i] = np.var(vals)
print "log2_sigma: %.3f, sigma: %.3f, mean: %.3f, var: %.3f" % (log2_sigma, sigma, Js_mean[i], Js_var[i])
surrogate = KernelExpFiniteGaussian(sigma=sigma, lmbda=lmbda, m=m, D=benchmark_samples.shape[1])
surrogate.fit(benchmark_samples)
fake = empty_class()
def replace_2(x_2d, a, i, j):
a = a.copy()
a[i] = x_2d[0]
a[j] = x_2d[1]
return a
for i in range(benchmark_samples.shape[1]):
for j in range(benchmark_samples.shape[1]):
if i == j:
continue
fake.log_pdf = lambda x_2d: surrogate.log_pdf(replace_2(x_2d, true_mean, i, j))
fake.grad = lambda x_2d: surrogate.grad(replace_2(x_2d, true_mean, i, j))
sigma = 2**log2_sigma
surrogate = KernelExpFiniteGaussian(sigma=sigma,
lmbda=lmbda,
m=m,
D=benchmark_samples.shape[1])
vals = surrogate.xvalidate_objective(benchmark_samples)
Js_mean[i] = np.mean(vals)
Js_var[i] = np.var(vals)
print "log2_sigma: %.3f, sigma: %.3f, mean: %.3f, var: %.3f" % (
log2_sigma, sigma, Js_mean[i], Js_var[i])
surrogate = KernelExpFiniteGaussian(sigma=sigma,
lmbda=lmbda,
m=m,
D=benchmark_samples.shape[1])
surrogate.fit(benchmark_samples)
fake = empty_class()
def replace_2(x_2d, a, i, j):
a = a.copy()
a[i] = x_2d[0]
a[j] = x_2d[1]
return a
for i in range(benchmark_samples.shape[1]):
for j in range(benchmark_samples.shape[1]):
if i == j:
continue
fake.log_pdf = lambda x_2d: surrogate.log_pdf(
replace_2(x_2d, true_mean, i, j))
fake.grad = lambda x_2d: surrogate.grad(
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])
bootsraped_stats = np.empty(num_bootstrap)
for i in range(num_bootstrap):
W = np.sign(np.random.randn(N_test))
WW = np.outer(W, W)
st = np.mean(U_matrix * WW)
bootsraped_stats[i] = N_test * st
p_value = np.mean(bootsraped_stats > stat)
print m, p_value
store_results(result_fname,
D=D,
log_pdf,
accepted,
log_pdf_density=surrogate,
step_sizes=step_sizes)
plt.suptitle("KMC lite %s, acceptance rate: %.2f" % \
(surrogate.__class__.__name__, np.mean(accepted)))
# now initialise KMC finite with the samples from the surrogate, and run for more
# learn parameters before starting
thinned = samples[np.random.permutation(len(samples))[:N]]
surrogate2 = KernelExpFiniteGaussian(sigma=2, lmbda=0.001, D=D, m=N)
surrogate2.set_parameters_from_dict(
BayesOptSearch(surrogate2, thinned, {
'sigma': [-3, 3]
}).optimize(3))
surrogate2.fit(thinned)
# now use conservative schedule, or None at all if confident in oracle samples
schedule2 = lambda t: 0.01 if t < 3000 else 0.
kmc2 = KMC(surrogate2, target, momentum, kmc.num_steps_min,
kmc.num_steps_max, kmc.step_size[0], kmc.step_size[1],
schedule2, acc_star)
# run MCMC
samples2, proposals2, accepted2, acc_prob2, log_pdf2, times2, step_sizes = mini_mcmc(
kmc2, start, num_iter, D)
visualise_trace(samples2,
log_pdf2,
accepted2,
log_pdf_density=surrogate2,
step_sizes=step_sizes)
# set to around 5000-10000 iterations to have KMC lite explored all of the support
start = np.zeros(D)
start[1] = -3
num_iter = 500
# run MCMC
samples, proposals, accepted, acc_prob, log_pdf, times, step_sizes = mini_mcmc(kmc, start, num_iter, D)
visualise_trace(samples, log_pdf, accepted, log_pdf_density=surrogate, step_sizes=step_sizes)
plt.suptitle("KMC lite %s, acceptance rate: %.2f" % \
(surrogate.__class__.__name__, np.mean(accepted)))
# now initialise KMC finite with the samples from the surrogate, and run for more
# learn parameters before starting
thinned = samples[np.random.permutation(len(samples))[:N]]
surrogate2 = KernelExpFiniteGaussian(sigma=2, lmbda=0.001, D=D, m=N)
surrogate2.set_parameters_from_dict(BayesOptSearch(surrogate2, thinned, {'sigma': [-3,3]}).optimize(3))
surrogate2.fit(thinned)
# now use conservative schedule, or None at all if confident in oracle samples
schedule2 = lambda t: 0.01 if t < 3000 else 0.
kmc2 = KMC(surrogate2, target,
momentum, kmc.num_steps_min, kmc.num_steps_max, kmc.step_size[0], kmc.step_size[1],
schedule2, acc_star)
# run MCMC
samples2, proposals2, accepted2, acc_prob2, log_pdf2, times2, step_sizes = mini_mcmc(kmc2, start, num_iter, D)
visualise_trace(samples2, log_pdf2, accepted2, log_pdf_density=surrogate2, step_sizes=step_sizes)
plt.suptitle("KMC finite, %s, acceptance rate: %.2f" % \
(surrogate.__class__.__name__, np.mean(accepted2)))
plt.show()
