def __init__(self, x, dw, h):
N = x.shape[0]
L = x.shape[1] - 1
B = mckean.bMat(x, dw)
self.b = tf.constant(B, dtype=tf.float32)
self.models = []
self.trainable_weights = []
for j in range(L):
m = tf.keras.Sequential([
tf.keras.layers.Input(1),
tf.keras.layers.Dense(
100, activation=tf.nn.relu), # input shape required
tf.keras.layers.Dense(100, activation=tf.nn.relu),
tf.keras.layers.Dense(1)
])
self.trainable_weights.extend(m.trainable_weights)
self.models.append(m)
u, udW = mckean.genproc_1dim_ex(L, h, N, mckean.a, mckean.b)
self.f = tf.constant(np.mean(
mckean.f(
np.tile(x[:, -1], (N, 1)).transpose(),
np.tile(u[:, -1], (N, 1))), 1),
dtype=tf.float32)
self.loss_fn = VarianceError()
self.pred_y = tf.zeros((N))
def __init__(self, x, dw, h):
# bv = mean(b(X(:,l)*ones(1,N),ones(N,1)*X(:,l)'),2);
# B(:,((l-1)*K+1):(l*K))=A.*(bv.*dW(:,l+1)*ones(1,K));
self.K = 10
N = x.shape[0]
L = x.shape[1] - 1
B = np.zeros((N, L))
for l in range(L):
xm = np.tile(x[:, l], (N, 1))
B[:, l] = np.mean(mckean.b(xm.transpose(), xm), 1) * dw[:, l + 1]
self.b = B
self.b = tf.constant(B, dtype=tf.float32)
u, udW = mckean.genproc_1dim_ex(L, h, N, mckean.a, mckean.b)
self.f = tf.constant(np.mean(
mckean.f(
np.tile(x[:, -1], (N, 1)).transpose(),
np.tile(u[:, -1], (N, 1))), 1),
dtype=tf.float32)
self.alpha = tf.Variable(tf.zeros([self.K]))
base = np.zeros((N, L, self.K))
for l in range(L):
base[:, l, :] = mckean.genPoly(
x[:, l],
self.K) #* np.tile(self.b[:, 5], (self.K, 1)).transpose()
self.tbase = tf.constant(base, dtype=tf.float32)
import mckean
import numpy as np
h = 0.02
L = int(1 / h)
N = 1000
M = 100
# Matlab result: mean=0.4084 std=0.0087
result_mc = np.zeros(M)
for j in range(M):
X, deltaW = mckean.genproc_1dim_ex(L, h, N, mckean.a, mckean.b)
result_mc[j] = np.mean(mckean.f(X[:, -1], X[:, -1]))
print(np.mean(result_mc))
print(np.std(result_mc))
#tf.math.reduce_variance(tf.keras.backend.sum(x*self.b, axis=1)-self.f)
epochs = range(100)
for epoch in epochs:
for i in range(30):
current_loss = model.trainstep(optimizer, tX)
print('Epoch %2d: loss=%2.8f' % (epoch, current_loss))
result_mc = np.zeros(M)
result_mc_cv = np.zeros(M)
result_cv = np.zeros(M)
for j in range(M):
X, deltaW = mckean.genproc_1dim_ex(L, h, N, mckean.a, mckean.b)
tX = tf.constant(X[:, 1:], dtype=tf.float32)
cvF = np.sum(model(tX).numpy() * mckean.bMat(X, deltaW), axis=1)
result_cv[j] = np.mean(cvF)
u, udW = mckean.genproc_1dim_ex(L, h, N, mckean.a, mckean.b)
fT = np.mean(
mckean.f(
np.tile(X[:, -1], (N, 1)).transpose(), np.tile(u[:, -1], (N, 1))),
1)
result_mc[j] = np.mean(fT)
result_mc_cv[j] = np.mean(fT - cvF)
np.savez("data/nncv_f2.npz", result_mc, result_mc_cv)
print('MC: mean=%2.6f std=%2.6f' % (np.mean(result_mc), np.std(result_mc)))
print('MC-CV: mean=%2.6f std=%2.6f' %
(np.mean(result_mc_cv), np.std(result_mc_cv)))
plot.boxplot([result_mc, result_mc_cv])
learning_rate = 0.1
optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)
current_loss = model.loss(model(X))
print('Initial Loss: loss=%2.5f' % current_loss)
epochs = range(100)
for epoch in epochs:
with tf.GradientTape() as t:
t.watch(model.alpha)
current_loss = model.loss(model(X))
dAlpha = t.gradient(current_loss, [model.alpha])
optimizer.apply_gradients(zip(dAlpha, [model.alpha]))
print('Epoch %2d: loss=%2.5f' % (epoch, current_loss))
print(model.alpha)
result_mc = np.zeros(M)
result_mc_cv = np.zeros(M)
result_mc_cv2 = np.zeros(M)
for j in range(M):
X, deltaW = mckean.genproc_1dim_ex(L, h, N, mckean.a, mckean.b)
cvF = np.sum(model(X).numpy() * mckean.bMat(X, deltaW), axis=1)
result_mc[j] = np.mean(mckean.f(X[:, -1], X[:, -1]))
result_mc_cv[j] = np.mean(mckean.f(X[:, -1], X[:, -1]) - cvF)
result_mc_cv2[j] = np.mean(cvF - mckean.f(X[:, -1], X[:, -1]))
print('MC: mean=%2.6f std=%2.6f' % (np.mean(result_mc), np.var(result_mc)))
print('MC-CV: mean=%2.6f std=%2.6f' %
(np.mean(result_mc_cv), np.var(result_mc_cv)))