def test_lengthscale(self):
"""checked calculations by hand, e.g.,
np.exp(-((2.0 - 1.5)**2 / (2.0**2) + (2.5 - 2.0)**2 / (1.5**2)) / 2)
np.exp(-((2.0 - 3.1)**2 / (2.0**2) + (2.5 - 4.2)**2 / (1.5**2)) / 2)
np.exp(-((4.1 - 1.5)**2 / (2.0**2) + (5.0 - 2.0)**2 / (1.5**2)) / 2)
np.exp(-((4.1 - 3.1)**2 / (2.0**2) + (5.0 - 4.2)**2 / (1.5**2)) / 2)
"""
with self.test_session():
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
lengthscale1 = tf.constant(2.0)
lengthscale2 = tf.constant([2.0, 2.0])
lengthscale3 = tf.constant([2.0, 1.5])
self.assertAllClose(rbf(X, X2, lengthscale1).eval(),
[[0.939413, 0.598996], [0.139456, 0.814647]],
atol=1e-5,
rtol=1e-5)
self.assertAllClose(rbf(X, X2, lengthscale2).eval(),
[[0.939413, 0.598996], [0.139456, 0.814647]],
atol=1e-5,
rtol=1e-5)
self.assertAllClose(rbf(X, X2, lengthscale3).eval(),
[[0.916855, 0.452271], [0.058134, 0.765502]],
atol=1e-5,
rtol=1e-5)
def test_x(self):
with self.test_session():
X = tf.constant([[0.0], [0.0]])
X2 = tf.constant([[0.0], [0.0]])
self.assertAllClose(rbf(X).eval(),
[[1.0, 1.0], [1.0, 1.0]])
self.assertAllClose(rbf(X, X2).eval(),
[[1.0, 1.0], [1.0, 1.0]])
def test_x2(self):
with self.test_session():
X = tf.constant([[10.0], [2.0]])
X2 = tf.constant([[2.0], [10.0]])
self.assertAllClose(rbf(X, X2).eval(),
[[1.266417e-14, 1.0], [1.0, 1.266417e-14]])
self.assertAllClose(rbf(X2, X).eval(),
[[1.266417e-14, 1.0], [1.0, 1.266417e-14]])
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
self.assertAllClose(rbf(X, X2).eval(),
[[0.778800, 0.128734],
[0.000378, 0.440431]], atol=1e-5, rtol=1e-5)
def test_rbf_1d(self):
with self.test_session():
x = tf.constant([0.0])
self.assertAllClose(rbf(x).eval(), [1.0])
x = tf.constant([10.0])
y = tf.constant([2.0])
self.assertAllClose(rbf(x, y=y).eval(), [1.26e-14])
x = tf.constant([0.0])
y = tf.constant([1.0])
sigma = tf.constant(10.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma).eval(), [60.6530685])
x = tf.constant([0.0])
y = tf.constant([1.0])
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma, l=l).eval(), [98.01986694])
x = tf.constant([0.0, 1.0])
self.assertAllClose(rbf(x).eval(), [1.0, 0.606530666])
x = tf.constant([10.0, 3.0])
y = tf.constant([2.0, 3.0])
self.assertAllClose(rbf(x, y=y).eval(), [1.266417e-14, 1.0])
x = tf.constant([0.0, 1.0])
y = tf.constant([1.0, 2.0])
sigma = tf.constant(10.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma).eval(), [60.6530685, 60.6530685])
x = tf.constant([0.0, -23.0])
y = tf.constant([1.0, -93.0])
sigma = tf.constant(10.0)
l = tf.constant(50.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma, l=l).eval(), [99.980003, 37.531109])
def test_rbf_2d(self):
with self.test_session():
x = tf.constant([[0.0], [0.0]])
self.assertAllClose(rbf(x).eval(), [[1.0], [1.0]])
x = tf.constant([[10.0], [2.0]])
y = tf.constant([[2.0], [10.0]])
self.assertAllClose(rbf(x, y=y).eval(), [[1.266417e-14], [1.266417e-14]])
x = tf.constant([[0.0], [10.0]])
y = tf.constant([[1.0], [1.0]])
sigma = tf.constant(10.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma).eval(), [[6.065307e01], [2.576757e-16]])
x = tf.constant([[0.0], [10.0]])
y = tf.constant([[1.0], [1.0]])
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma, l=l).eval(), [[98.019867], [19.789869]])
x = tf.constant([[10.0, 3.0], [10.0, 3.0]])
self.assertAllClose(rbf(x, y=y).eval(), [[2.576757e-18, 1.353353e-01], [2.576757e-18, 1.353353e-01]])
x = tf.constant([[10.0, 3.0], [10.0, 3.0]])
y = tf.constant([[2.0, 3.0], [2.0, 3.0]])
self.assertAllClose(rbf(x, y=y).eval(), [[1.266417e-14, 1.0], [1.266417e-14, 1.0]])
x = tf.constant([[0.0, 1.0], [10.0, -3.0]])
y = tf.constant([[1.0, 2.0], [1.0, 2.0]])
sigma = tf.constant(10.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma).eval(), [[6.065307e01, 6.065307e01], [2.576757e-16, 3.726653e-04]]
)
x = tf.constant([[10.0, 3.0], [10.0, 3.0]])
y = tf.constant([[2.0, 3.0], [2.0, 3.0]])
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma, l=l).eval(), [[27.80373, 100], [27.80373, 100]])
def test_rbf_1d(self):
with self.test_session():
x = tf.constant([0.0])
self.assertAllClose(rbf(x).eval(), [1.0])
x = tf.constant([10.0])
y = tf.constant([2.0])
self.assertAllClose(rbf(x, y=y).eval(), [1.26e-14])
x = tf.constant([0.0])
y = tf.constant([1.0])
sigma = tf.constant(10.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma).eval(), [60.6530685])
x = tf.constant([0.0])
y = tf.constant([1.0])
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma, l=l).eval(), [98.01986694])
x = tf.constant([0.0, 1.0])
self.assertAllClose(rbf(x).eval(), [1.0, 0.606530666])
x = tf.constant([10.0, 3.0])
y = tf.constant([2.0, 3.0])
self.assertAllClose(rbf(x, y=y).eval(), [1.266417e-14, 1.0])
x = tf.constant([0.0, 1.0])
y = tf.constant([1.0, 2.0])
sigma = tf.constant(10.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma).eval(), [60.6530685, 60.6530685])
x = tf.constant([0.0, -23.0])
y = tf.constant([1.0, -93.0])
sigma = tf.constant(10.0)
l = tf.constant(50.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma, l=l).eval(), [99.980003, 37.531109])
def test_x2(self):
with self.test_session():
X = tf.constant([[10.0], [2.0]])
X2 = tf.constant([[2.0], [10.0]])
self.assertAllClose(
rbf(X, X2).eval(), [[1.266417e-14, 1.0], [1.0, 1.266417e-14]])
self.assertAllClose(
rbf(X2, X).eval(), [[1.266417e-14, 1.0], [1.0, 1.266417e-14]])
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
self.assertAllClose(rbf(X, X2).eval(),
[[0.778800, 0.128734], [0.000378, 0.440431]],
atol=1e-5,
rtol=1e-5)
def gaussian_process_classification_example():
ed.set_seed(42)
data, metadata = crabs('~/data')
X_train = data[:100, 3:]
y_train = data[:100, 1]
N = X_train.shape[0] # Number of data points.
D = X_train.shape[1] # Number of features.
print('Number of data points: {}'.format(N))
print('Number of features: {}'.format(D))
#--------------------
# Model.
X = tf.placeholder(tf.float32, [N, D])
f = MultivariateNormalTriL(loc=tf.zeros(N), scale_tril=tf.cholesky(rbf(X)))
y = Bernoulli(logits=f)
#--------------------
# Inference.
# Perform variational inference.
qf = Normal(loc=tf.get_variable('qf/loc', [N]),
scale=tf.nn.softplus(tf.get_variable('qf/scale', [N])))
inference = ed.KLqp({f: qf}, data={X: X_train, y: y_train})
inference.run(n_iter=5000)
def test_rbf_0d(self):
with self.test_session():
x = tf.constant(0.0)
self.assertAllClose(rbf(x).eval(), 1.0)
x = tf.constant(10.0)
y = tf.constant(2.0)
self.assertAllClose(rbf(x, y=y).eval(), 1.26e-14)
x = tf.constant(0.0)
y = tf.constant(1.0)
sigma = tf.constant(10.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma).eval(), 60.6530685)
x = tf.constant(0.0)
y = tf.constant(1.0)
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma, l=l).eval(), 98.01986694)
def main(_):
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(FLAGS.N, FLAGS.V)
# MODEL
x_ph = tf.placeholder(tf.float32, [FLAGS.N, FLAGS.V])
# Form (N, V, V) covariance, one matrix per data point.
K = tf.stack([
rbf(tf.reshape(xn, [FLAGS.V, 1])) + tf.diag([1e-6, 1e-6])
for xn in tf.unstack(x_ph)
])
f = MultivariateNormalTriL(loc=tf.zeros([FLAGS.N, FLAGS.V]),
scale_tril=tf.cholesky(K))
x = Poisson(rate=tf.exp(f))
# INFERENCE
qf = Normal(loc=tf.get_variable("qf/loc", [FLAGS.N, FLAGS.V]),
scale=tf.nn.softplus(
tf.get_variable("qf/scale", [FLAGS.N, FLAGS.V])))
inference = ed.KLqp({f: qf}, data={x: x_data, x_ph: x_data})
inference.run(n_iter=5000)
def converge(n_train):
mse = []
for n in n_train:
training_x = np.linspace(90, 110, n)
training_y = []
for S in training_x:
training_y.append(
HestonVega(S,
K,
T,
r,
sigma,
lmbda,
meanV,
v0,
rho,
'C',
N=nInt))
testing_x = np.linspace(95, 105, n)
testing_y = []
for S in testing_x:
testing_y.append(
HestonVega(S,
K,
T,
r,
sigma,
lmbda,
meanV,
v0,
rho,
'C',
N=nInt))
train32_x = np.array(training_x, dtype='float32').reshape(n, 1)
test32_x = np.array(testing_x, dtype='float32').reshape(n, 1)
Ker = rbf(train32_x).eval()
K_noise = Ker + np.eye(n_train) # *0.1
k_s = rbf(test32_x, train32_x).eval()
L = np.linalg.cholesky(K_noise)
alpha = np.linalg.solve(L.T, np.linalg.solve(L, training_y))
predict_mean = np.dot(k_s, alpha)
mse.append(np.mean((predict_mean - testing_y)**2))
return mse
def test_variance(self):
with self.test_session():
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
variance = tf.constant(1.4)
self.assertAllClose(rbf(X, X2, variance=variance).eval(),
[[1.090321, 0.180228],
[0.000529, 0.616604]], atol=1e-5, rtol=1e-5)
def test_rbf_0d(self):
with self.test_session():
x = tf.constant(0.0)
self.assertAllClose(rbf(x).eval(), 1.0)
x = tf.constant(10.0)
y = tf.constant(2.0)
self.assertAllClose(rbf(x, y=y).eval(), 1.26e-14)
x = tf.constant(0.0)
y = tf.constant(1.0)
sigma = tf.constant(10.0)
self.assertAllClose(rbf(x, y=y, sigma=sigma).eval(), 60.6530685)
x = tf.constant(0.0)
y = tf.constant(1.0)
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma, l=l).eval(), 98.01986694)
def test_variance(self):
with self.test_session():
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
variance = tf.constant(1.4)
self.assertAllClose(rbf(X, X2, variance=variance).eval(),
[[1.090321, 0.180228], [0.000529, 0.616604]],
atol=1e-5,
rtol=1e-5)
def test_all(self):
with self.test_session():
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
lengthscale = tf.constant([2.0, 1.5])
variance = tf.constant(1.4)
self.assertAllClose(rbf(X, X2, lengthscale, variance).eval(),
[[1.283597, 0.633180],
[0.081387, 1.071704]], atol=1e-5, rtol=1e-5)
def test_all(self):
with self.test_session():
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
lengthscale = tf.constant([2.0, 1.5])
variance = tf.constant(1.4)
self.assertAllClose(rbf(X, X2, lengthscale, variance).eval(),
[[1.283597, 0.633180], [0.081387, 1.071704]],
atol=1e-5,
rtol=1e-5)
def test_lengthscale(self):
"""checked calculations by hand, e.g.,
np.exp(-((2.0 - 1.5)**2 / (2.0**2) + (2.5 - 2.0)**2 / (1.5**2)) / 2)
np.exp(-((2.0 - 3.1)**2 / (2.0**2) + (2.5 - 4.2)**2 / (1.5**2)) / 2)
np.exp(-((4.1 - 1.5)**2 / (2.0**2) + (5.0 - 2.0)**2 / (1.5**2)) / 2)
np.exp(-((4.1 - 3.1)**2 / (2.0**2) + (5.0 - 4.2)**2 / (1.5**2)) / 2)
"""
with self.test_session():
X = tf.constant([[2.0, 2.5], [4.1, 5.0]])
X2 = tf.constant([[1.5, 2.0], [3.1, 4.2]])
lengthscale1 = tf.constant(2.0)
lengthscale2 = tf.constant([2.0, 2.0])
lengthscale3 = tf.constant([2.0, 1.5])
self.assertAllClose(rbf(X, X2, lengthscale1).eval(),
[[0.939413, 0.598996],
[0.139456, 0.814647]], atol=1e-5, rtol=1e-5)
self.assertAllClose(rbf(X, X2, lengthscale2).eval(),
[[0.939413, 0.598996],
[0.139456, 0.814647]], atol=1e-5, rtol=1e-5)
self.assertAllClose(rbf(X, X2, lengthscale3).eval(),
[[0.916855, 0.452271],
[0.058134, 0.765502]], atol=1e-5, rtol=1e-5)
def test_raises(self):
with self.test_session():
X1 = tf.constant([[0.0]])
X2 = tf.constant([[0.0]])
lengthscale = tf.constant(-5.0)
variance = tf.constant(-1.0)
with self.assertRaisesOpError('Condition'):
rbf(X1, X2, variance=variance).eval()
rbf(X1, X2, lengthscale).eval()
rbf(X1, X2, lengthscale, variance).eval()
def test_raises(self):
with self.test_session():
X1 = tf.constant([[0.0]])
X2 = tf.constant([[0.0]])
lengthscale = tf.constant(-5.0)
variance = tf.constant(-1.0)
with self.assertRaisesOpError('Condition'):
rbf(X1, X2, variance=variance).eval()
rbf(X1, X2, lengthscale).eval()
rbf(X1, X2, lengthscale, variance).eval()
def test_rbf_2d(self):
with self.test_session():
x = tf.constant([[0.0], [0.0]])
self.assertAllClose(rbf(x).eval(), [[1.0], [1.0]])
x = tf.constant([[10.0], [2.0]])
y = tf.constant([[2.0], [10.0]])
self.assertAllClose(
rbf(x, y=y).eval(), [[1.266417e-14], [1.266417e-14]])
x = tf.constant([[0.0], [10.0]])
y = tf.constant([[1.0], [1.0]])
sigma = tf.constant(10.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma).eval(),
[[6.065307e+01], [2.576757e-16]])
x = tf.constant([[0.0], [10.0]])
y = tf.constant([[1.0], [1.0]])
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma, l=l).eval(),
[[98.019867], [19.789869]])
x = tf.constant([[10.0, 3.0], [10.0, 3.0]])
self.assertAllClose(
rbf(x, y=y).eval(),
[[2.576757e-18, 1.353353e-01], [2.576757e-18, 1.353353e-01]])
x = tf.constant([[10.0, 3.0], [10.0, 3.0]])
y = tf.constant([[2.0, 3.0], [2.0, 3.0]])
self.assertAllClose(
rbf(x, y=y).eval(), [[1.266417e-14, 1.0], [1.266417e-14, 1.0]])
x = tf.constant([[0.0, 1.0], [10.0, -3.0]])
y = tf.constant([[1.0, 2.0], [1.0, 2.0]])
sigma = tf.constant(10.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma).eval(),
[[6.065307e+01, 6.065307e+01], [2.576757e-16, 3.726653e-04]])
x = tf.constant([[10.0, 3.0], [10.0, 3.0]])
y = tf.constant([[2.0, 3.0], [2.0, 3.0]])
sigma = tf.constant(10.0)
l = tf.constant(5.0)
self.assertAllClose(
rbf(x, y=y, sigma=sigma, l=l).eval(),
[[27.80373, 100], [27.80373, 100]])
def define_posterior_predictive(X, K, f, sigma_signal, sigma_noise,
lengthscale):
"""
Define the posterior predictive mean and variance.
Parameters
----------
X : tf.placeholder, shape (N, D)
A placeholder for the input data.
K : tf.Tensor, shape (N, N)
The covariance matrix.
f : edward.RandomVariable, shape (N,)
The Gaussian process prior.
sigma_signal : float
The signal variance.
sigma_noise : float
The noise variance.
Returns
-------
x : tf.placeholder, shape (None, D)
A placeholder for the future data.
mu : tf.Tensor, shape (None,)
The mean function.
var : tf.Tensor, shape (None,)
The variance function.
lengthscale : float or array-like
The lengthscale parameter. Can either be a scalar or vector of size D
where D is the number of dimensions of the input space.
"""
N, D = X.shape
x = tf.placeholder(tf.float32, [None, D])
k = rbf(X, x, variance=sigma_signal, lengthscale=lengthscale)
K_inv = tf.matrix_inverse(K)
mu = tf.reduce_sum(tf.matmul(tf.transpose(k), K_inv) * f, axis=1)
c = sigma_signal + sigma_noise
var = c - tf.reduce_sum(
tf.matmul(tf.transpose(k), K_inv) * tf.transpose(k), axis=1)
return x, mu, var
def define_prior(N, D, sigma_noise, sigma_signal, lengthscale):
"""
Define a Gaussian process prior.
Parameters
----------
N : int
The number of observations.
D : int
The number of input dimensions.
sigma_noise : float
The noise variance.
sigma_signal : float
The signal variance.
lengthscale : float or array-like
The lengthscale parameter. Can either be a scalar or vector of size D
where D is the number of dimensions of the input space.
Returns
-------
X : tf.placeholder, shape (N, D)
A placeholder for the input data.
K : tf.Tensor, shape (N, N)
The covariance matrix.
f : edward.RandomVariable, shape (N,)
The Gaussian process prior.
"""
# define model
X = tf.placeholder(tf.float32, [N, D])
K = (rbf(X, variance=sigma_signal, lengthscale=lengthscale) +
np.eye(N) * sigma_noise)
f = MultivariateNormalTriL(loc=tf.zeros(N), scale_tril=tf.cholesky(K))
# check dimensions
assert X.shape == (N, D)
assert K.shape == (N, N)
assert f.shape == (N, )
return X, K, f
def main(_):
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(FLAGS.N, FLAGS.V)
# MODEL
x_ph = tf.placeholder(tf.float32, [FLAGS.N, FLAGS.V])
# Form (N, V, V) covariance, one matrix per data point.
K = tf.stack([rbf(tf.reshape(xn, [FLAGS.V, 1])) + tf.diag([1e-6, 1e-6])
for xn in tf.unstack(x_ph)])
f = MultivariateNormalTriL(loc=tf.zeros([FLAGS.N, FLAGS.V]),
scale_tril=tf.cholesky(K))
x = Poisson(rate=tf.exp(f))
# INFERENCE
qf = Normal(
loc=tf.get_variable("qf/loc", [FLAGS.N, FLAGS.V]),
scale=tf.nn.softplus(tf.get_variable("qf/scale", [FLAGS.N, FLAGS.V])))
inference = ed.KLqp({f: qf}, data={x: x_data, x_ph: x_data})
inference.run(n_iter=5000)
def test_x(self):
with self.test_session():
X = tf.constant([[0.0], [0.0]])
X2 = tf.constant([[0.0], [0.0]])
self.assertAllClose(rbf(X).eval(), [[1.0, 1.0], [1.0, 1.0]])
self.assertAllClose(rbf(X, X2).eval(), [[1.0, 1.0], [1.0, 1.0]])
from edward.models import Bernoulli, MultivariateNormalTriL, Normal
from edward.util import rbf
ys = df['index'].values
xs = df[['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']].values
N = xs.shape[0]
D = xs.shape[1]
print("Number of data points: {}".format(N))
print("Number of features: {}".format(D))
# In[4]:
X = tf.placeholder(tf.float32, [N, D])
f = MultivariateNormalTriL(loc=tf.zeros(N), scale_tril=tf.cholesky(rbf(X)))
y = Bernoulli(logits=f)
# In[ ]:
qf = Normal(loc=tf.get_variable("qf/loc", [N]),
scale=tf.nn.softplus(tf.get_variable("qf/scale", [N])))
# In[ ]:
inference = ed.KLqp({f: qf}, data={X: xs, y: ys})
inference.run(n_iter=5000)
for n in range(N):
f_n = multivariate_normal.rvs(cov=K, size=1)
for v in range(V):
x[n, v] = poisson.rvs(mu=np.exp(f_n[v]), size=1)
return x
ed.set_seed(42)
N = 308 # number of NBA players
V = 2 # number of shot locations
# DATA
x_data = build_toy_dataset(N, V)
# MODEL
x_ph = tf.placeholder(tf.float32, [N, V]) # inputs to Gaussian Process
# Form (N, V, V) covariance, one matrix per data point.
K = tf.stack([rbf(tf.reshape(xn, [V, 1])) + tf.diag([1e-6, 1e-6])
for xn in tf.unstack(x_ph)])
f = MultivariateNormalTriL(loc=tf.zeros([N, V]), scale_tril=tf.cholesky(K))
x = Poisson(rate=tf.exp(f))
# INFERENCE
qf = Normal(loc=tf.Variable(tf.random_normal([N, V])),
scale=tf.nn.softplus(tf.Variable(tf.random_normal([N, V]))))
inference = ed.KLqp({f: qf}, data={x: x_data, x_ph: x_data})
inference.run(n_iter=5000)
sess = ed.get_session()
training_number = 11 # You can change the number to see training quality with different amount of training dataset
train_x = np.array(np.linspace(90, 110, training_number),
dtype='float32').reshape(training_number, 1)
train_y = []
for S in train_x:
train_y.append(
HestonVega(S, K, T, r, sigma, lmbda, meanV, v0, rho, 'C', N=nInt))
test_x = np.array(np.linspace(90, 110, 200), dtype='float32').reshape(200, 1)
test_y = []
for S in test_x:
test_y.append(
HestonVega(S, K, T, r, sigma, lmbda, meanV, v0, rho, 'C', N=nInt))
Kernel = rbf(train_x).eval()
K_noise = Kernel + np.eye(
training_number
) * 0.01 # without noise, the cov band converge to 0 at the training points
k_s = rbf(test_x, train_x).eval()
L = np.linalg.cholesky(K_noise)
alpha = np.linalg.solve(L.T, np.linalg.solve(L, train_y))
predict_mean = np.dot(k_s, alpha)
# cov
v = np.linalg.solve(L, k_s.T)
var = rbf(test_x).eval() - np.dot(v.T, v)
# In[608]:
# plot with cov band
data = make_pinwheel(radial_std=0.3,
tangential_std=0.05,
num_classes=5,
num_per_class=30,
rate=0.4)
N = data.shape[0]
D = 2 # number of features
K = 2 # number of latent dimensions
H1 = 2
H2 = 2
# Model: deep/shallow GP (generative model)
X = Normal(loc=tf.zeros([N, K]), scale=tf.ones([N, K]))
Kernal = rbf(X) + tf.eye(N) * 1e-6
cholesky = tf.tile(tf.reshape(tf.cholesky(Kernal), [1, N, N]), [H1, 1, 1])
h1 = MultivariateNormalTriL(loc=tf.zeros([H1, N]), scale_tril=cholesky)
Kernal1 = rbf(tf.transpose(h1)) + tf.eye(N) * 1e-6
cholesky1 = tf.tile(tf.reshape(tf.cholesky(Kernal1), [1, N, N]), [H2, 1, 1])
h2 = MultivariateNormalTriL(loc=tf.zeros([H2, N]), scale_tril=cholesky1)
Kernal2 = rbf(tf.transpose(h2)) + tf.eye(N) * 1e-6
cholesky2 = tf.tile(tf.reshape(tf.cholesky(Kernal2), [1, N, N]), [D, 1, 1])
Y = MultivariateNormalTriL(loc=tf.zeros([D, N]), scale_tril=cholesky2)
# Inference (recongnition model)
qX = Normal(loc=tf.Variable(tf.random_normal([N, K])),
scale=tf.nn.softplus(tf.Variable(tf.random_normal([N, K]))))
# doing this because I don't know how to make the testing work otherwise
# it seems like the test and training data need to have the same N
X_test, y_test = X_test[:-1, :], y_test[:-1]
# unfortunately not sure how to make the linear kernel work at this moment
N, P = X_train.shape
X_tf = tf.placeholder(tf.float32, [N, P])
# latent stochastic function
# ok so here in the loc position is where we can get (x *element-wise* b)
b = Bernoulli(varbvs_prior, dtype=np.float32) # prior from varbvs
gp_mu = tf.reduce_mean(tf.multiply(X_tf, tf.reshape(tf.tile(b, [N]), [N, P])), 1) # mean for prior over GP
f = MultivariateNormalTriL(
loc=gp_mu,
scale_tril=tf.cholesky(rbf(X_tf)) # uses rbf kernel for covariance of GP for now
)
qf = Normal(loc=tf.get_variable("qf/loc", [N]), scale=tf.nn.softplus(tf.get_variable("qf/scale", [N])))
# respose
y_tf = Bernoulli(logits=f)
# inference
infer = ed.KLqp({f: qf}, data={X_tf: X_train, y_tf: y_train})
infer.run(n_samples=3, n_iter=5000)
# criticism
y_post = ed.copy(y_tf, {f: qf})
ed.evaluate('binary_accuracy', data={X_tf: X_test, y_post: y_test})
def test_contraint_raises(self):
with self.test_session():
x = tf.constant(0.0)
y = tf.constant(1.0)
sigma = tf.constant(-1.0)
l = tf.constant(-5.0)
with self.assertRaisesOpError('Condition'):
rbf(x, y=y, sigma=sigma).eval()
rbf(x, y=y, l=l).eval()
rbf(x, y=y, sigma=sigma, l=l).eval()
x = np.inf * tf.constant(1.0)
y = tf.constant(1.0)
sigma = tf.constant(1.0)
l = tf.constant(5.0)
with self.assertRaisesOpError('Inf'):
rbf(x).eval()
rbf(x, y=y).eval()
rbf(x, y=y, sigma=sigma).eval()
rbf(x, y=y, l=l).eval()
rbf(x, y=y, sigma=sigma, l=l).eval()
x = tf.constant(0.0)
y = np.nan * tf.constant(1.0)
sigma = tf.constant(1.0)
l = tf.constant(5.0)
with self.assertRaisesOpError('NaN'):
rbf(x, y=y).eval()
rbf(x, y=y, sigma=sigma).eval()
rbf(x, y=y, l=l).eval()
rbf(x, y=y, sigma=sigma, l=l).eval()
sess = ed.get_session() training_number = 17 idx = np.linspace(0, len(x)-1, training_number, dtype = 'int') x_train = np.array(x[idx], dtype='float32').reshape(training_number, 1) y_train = np.array(y[idx], dtype='float32').reshape(training_number, 1) x_test = np.array(x, dtype='float32').reshape(len(x), 1) y_test = np.array(y, dtype='float32').reshape(len(x), 1) # In[431]: # mean Kernel = rbf(x_train).eval() K_noise = Kernel + np.eye(training_number) * 0.01 # without noise, the cov band converge to 0 at the training points k_s = rbf(x_test, x_train).eval() L = np.linalg.cholesky(K_noise) alpha = np.linalg.solve(L.T, np.linalg.solve(L, y_train)) predict_mean = np.dot(k_s, alpha) # cov v = np.linalg.solve(L, k_s.T) var = rbf(x_test).eval() - np.dot(v.T, v) # In[433]: # plot with cov band
def test_contraint_raises(self):
with self.test_session():
x = tf.constant(0.0)
y = tf.constant(1.0)
sigma = tf.constant(-1.0)
l = tf.constant(-5.0)
with self.assertRaisesOpError("Condition"):
rbf(x, y=y, sigma=sigma).eval()
rbf(x, y=y, l=l).eval()
rbf(x, y=y, sigma=sigma, l=l).eval()
x = np.inf * tf.constant(1.0)
y = tf.constant(1.0)
sigma = tf.constant(1.0)
l = tf.constant(5.0)
with self.assertRaisesOpError("Inf"):
rbf(x).eval()
rbf(x, y=y).eval()
rbf(x, y=y, sigma=sigma).eval()
rbf(x, y=y, l=l).eval()
rbf(x, y=y, sigma=sigma, l=l).eval()
x = tf.constant(0.0)
y = np.nan * tf.constant(1.0)
sigma = tf.constant(1.0)
l = tf.constant(5.0)
with self.assertRaisesOpError("NaN"):
rbf(x, y=y).eval()
rbf(x, y=y, sigma=sigma).eval()
rbf(x, y=y, l=l).eval()
rbf(x, y=y, sigma=sigma, l=l).eval()
X_test, y_test = X_test[:-1, :], y_test[:-1]
# unfortunately not sure how to make the linear kernel work at this moment
N, P = X_train.shape
X_tf = tf.placeholder(tf.float32, [N, P])
# latent stochastic function
# ok so here in the loc position is where we can get (x *element-wise* b)
b = Bernoulli(varbvs_prior, dtype=np.float32) # prior from varbvs
gp_mu = tf.reduce_mean(tf.multiply(X_tf, tf.reshape(tf.tile(b, [N]), [N, P])),
1) # mean for prior over GP
f = MultivariateNormalTriL(
loc=gp_mu,
scale_tril=tf.cholesky(
rbf(X_tf)) # uses rbf kernel for covariance of GP for now
)
qf = Normal(loc=tf.get_variable("qf/loc", [N]),
scale=tf.nn.softplus(tf.get_variable("qf/scale", [N])))
# respose
y_tf = Bernoulli(logits=f)
# inference
infer = ed.KLqp({f: qf}, data={X_tf: X_train, y_tf: y_train})
infer.run(n_samples=3, n_iter=5000)
# criticism
y_post = ed.copy(y_tf, {f: qf})
ed.evaluate('binary_accuracy', data={X_tf: X_test, y_post: y_test})