def gaussian():
u = g.Var(shape=(2, ))
half_sigma = g.Low(shape=(2, 2))
sigma = half_sigma @ half_sigma.T
var = [u, half_sigma]
x = g.Inp(name='x', shape=(2, ))
neg_log_pdf = 1 / 2 * g.log(
g.det(sigma)) + 1 / 2 * (x - u) @ g.inv(sigma) @ (x - u).T
log_like = g.trmean(neg_log_pdf)
data = np.random.multivariate_normal(mean=np.array([3, -3]),
cov=np.array([[5, -2], [-2, 2]]),
size=(1000, ),
check_valid='warn')
print('real param')
print(np.array([3, -3]))
print(np.array([[5, -2], [-2, 2]]))
inp_dict = {'x': data}
lr = 0.1
for i in range(600):
ret = log_like.forward(inp_dict)
if (i + 1) % 100 == 0:
print(ret)
print(u.val)
sigma = half_sigma.val @ half_sigma.val.T
print(sigma)
log_like.update()
for v in var:
v.apply_gradient(lr)
return
import numpy as np
import grad as g
x = g.Inp(name='x', shape=(None, 28 * 28))
w1 = g.Var(name='w1', shape=(28 * 28, 300))
w2 = g.Var(name='w2', shape=(300, 100))
w3 = g.Var(name='w3', shape=(100, 10))
var = [w1, w2, w3]
logits = g.relu(g.relu(x @ w1) @ w2) @ w3
loss = g.softmax(logits)
iterations = 100
batch_size = 64
train_x = np.load('/Users/gyc/Machine Learning/data/mnist/train_images.npy')
train_labels = np.load(
'/Users/gyc/Machine Learning/data/mnist/train_labels.npy')
test_x = np.load('/Users/gyc/Machine Learning/data/mnist/test_images.npy')
test_labels = np.load('/Users/gyc/Machine Learning/data/mnist/test_labels.npy')
train_size = train_x.shape[0]
train_x = train_x.reshape(train_size, -1) / 255
test_size = test_x.shape[0]
test_x = test_x.reshape(test_size, -1) / 255
lr = 0.01 / batch_size
for _ in range(iterations):
idx = np.arange(train_size)
var.grad = 0
new_log_prob = log_prob.forward(inp_dict)
log_prob.update()
r -= e / 2 * var.grad
var.grad = 0
acc_prob = min(
1,
np.exp(new_log_prob - 1 / 2 * r @ r - old_log_prob +
1 / 2 * r0 @ r0))
if np.random.uniform() > acc_prob:
var.val = old_val
sample_array[m] = var.forward()
return sample_array
if __name__ == '__main__':
u = g.Var(shape=(2, ))
x_sigma = np.array([[2, 3], [3, 5]])
x = g.Inp(name='x', shape=(2, ))
data = np.random.multivariate_normal(mean=np.array([-3, -5]),
cov=x_sigma,
size=(1000, ))
log_prob = 1 / 2 * u @ u.T + g.tr(
1 / 2 * (x - u) @ np.linalg.inv(x_sigma) @ (x - u).T)
inp_dict = {'x': data}
L = 100
M = 100
e = 1e-3
sample_array = sample(log_prob, u, L, M, e, inp_dict)
print(np.mean(sample_array, axis=0))
def full_gauss(s, n=1): mu = g.Var((n,)) half_sigma = g.Low(shape=(n,n)) v = s@half_sigma.T+mu sigma = half_sigma@half_sigma.T return v, mu, half_sigma
def mean_gauss(s, n=1): mu = g.Var((n,)) log_sigma = g.Var((n,)) half_sigma = g.exp(log_sigma) v = s*half_sigma+mu return v, mu, log_sigma
def one_gauss(): mu = g.Var(()) sigma = g.Var(()) return mu, sigma