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gmm.py
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gmm.py
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import argparse
import contextlib
import time
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats
import cupy
@contextlib.contextmanager
def timer(message):
cupy.cuda.Stream.null.synchronize()
start = time.time()
yield
cupy.cuda.Stream.null.synchronize()
end = time.time()
print('%s: %f sec' % (message, end - start))
def estimate_log_prob(X, inv_cov, means):
xp = cupy.get_array_module(X)
n_features = X.shape[1]
log_det = xp.sum(xp.log(inv_cov), axis=1)
precisions = inv_cov ** 2
log_prob = xp.sum((means ** 2 * precisions), 1) - \
2 * xp.dot(X, (means * precisions).T) + xp.dot(X ** 2, precisions.T)
return -0.5 * (n_features * xp.log(2 * np.pi) + log_prob) + log_det
def m_step(X, resp):
xp = cupy.get_array_module(X)
nk = xp.sum(resp, axis=0)
means = xp.dot(resp.T, X) / nk[:, None]
X2 = xp.dot(resp.T, X * X) / nk[:, None]
covariances = X2 - means ** 2
return nk / len(X), means, covariances
def e_step(X, inv_cov, means, weights):
xp = cupy.get_array_module(X)
weighted_log_prob = estimate_log_prob(X, inv_cov, means) + \
xp.log(weights)
log_prob_norm = xp.log(xp.sum(xp.exp(weighted_log_prob), axis=1))
log_resp = weighted_log_prob - log_prob_norm[:, None]
return xp.mean(log_prob_norm), log_resp
def train_gmm(X, max_iter, tol, means, covariances):
xp = cupy.get_array_module(X)
lower_bound = -np.inf
converged = False
weights = xp.array([0.5, 0.5], dtype=np.float32)
inv_cov = 1 / xp.sqrt(covariances)
for n_iter in range(max_iter):
prev_lower_bound = lower_bound
log_prob_norm, log_resp = e_step(X, inv_cov, means, weights)
weights, means, covariances = m_step(X, xp.exp(log_resp))
inv_cov = 1 / xp.sqrt(covariances)
lower_bound = log_prob_norm
change = lower_bound - prev_lower_bound
if abs(change) < tol:
converged = True
break
if not converged:
print('Failed to converge. Increase max-iter or tol.')
return inv_cov, means, weights, covariances
def predict(X, inv_cov, means, weights):
xp = cupy.get_array_module(X)
log_prob = estimate_log_prob(X, inv_cov, means)
return (log_prob + xp.log(weights)).argmax(axis=1)
def calc_acc(X_train, y_train, X_test, y_test, max_iter, tol, means,
covariances):
xp = cupy.get_array_module(X_train)
inv_cov, means, weights, cov = \
train_gmm(X_train, max_iter, tol, means, covariances)
y_train_pred = predict(X_train, inv_cov, means, weights)
train_accuracy = xp.mean(y_train_pred == y_train) * 100
y_test_pred = predict(X_test, inv_cov, means, weights)
test_accuracy = xp.mean(y_test_pred == y_test) * 100
print('train_accuracy : %f' % train_accuracy)
print('test_accuracy : %f' % test_accuracy)
return y_test_pred, means, cov
def draw(X, pred, means, covariances, output):
xp = cupy.get_array_module(X)
for i in range(2):
labels = X[pred == i]
if xp is cupy:
labels = labels.get()
plt.scatter(labels[:, 0], labels[:, 1], c=np.random.rand(1, 3))
if xp is cupy:
means = means.get()
covariances = covariances.get()
plt.scatter(means[:, 0], means[:, 1], s=120, marker='s', facecolors='y',
edgecolors='k')
x = np.linspace(-5, 5, 1000)
y = np.linspace(-5, 5, 1000)
X, Y = np.meshgrid(x, y)
for i in range(2):
dist = stats.multivariate_normal(means[i], covariances[i])
Z = dist.pdf(np.stack([X, Y], axis=-1))
plt.contour(X, Y, Z)
plt.savefig(output)
def run(gpuid, num, dim, max_iter, tol, output):
"""CuPy Gaussian Mixture Model example
Compute GMM parameters, weights, means and covariance matrix, depending on
sampled data. There are two main components, e_step and m_step.
In e_step, compute burden rate, which is expressed `resp`, by latest
weights, means and covariance matrix.
In m_step, compute weights, means and covariance matrix by latest `resp`.
"""
scale = np.ones(dim)
train1 = np.random.normal(1, scale, size=(num, dim)).astype(np.float32)
train2 = np.random.normal(-1, scale, size=(num, dim)).astype(np.float32)
X_train = np.r_[train1, train2]
test1 = np.random.normal(1, scale, size=(100, dim)).astype(np.float32)
test2 = np.random.normal(-1, scale, size=(100, dim)).astype(np.float32)
X_test = np.r_[test1, test2]
y_train = np.r_[np.zeros(num), np.ones(num)].astype(np.int32)
y_test = np.r_[np.zeros(100), np.ones(100)].astype(np.int32)
mean1 = np.random.normal(1, scale, size=dim)
mean2 = np.random.normal(-1, scale, size=dim)
means = np.stack([mean1, mean2])
covariances = np.random.rand(2, dim)
print('Running CPU...')
with timer(' CPU '):
y_test_pred, means, cov = \
calc_acc(X_train, y_train, X_test, y_test, max_iter, tol,
means, covariances)
with cupy.cuda.Device(gpuid):
X_train_gpu = cupy.array(X_train)
y_train_gpu = cupy.array(y_train)
y_test_gpu = cupy.array(y_test)
X_test_gpu = cupy.array(X_test)
means = cupy.array(means)
covariances = cupy.array(covariances)
print('Running GPU...')
with timer(' GPU '):
y_test_pred, means, cov = \
calc_acc(X_train_gpu, y_train_gpu, X_test_gpu, y_test_gpu,
max_iter, tol, means, covariances)
if output is not None:
draw(X_test_gpu, y_test_pred, means, cov, output)
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--gpu-id', '-g', default=0, type=int,
help='ID of GPU.')
parser.add_argument('--num', '-n', default=500000, type=int,
help='number of train data')
parser.add_argument('--dim', '-d', default=2, type=int,
help='dimension of each data')
parser.add_argument('--max-iter', '-m', default=30, type=int,
help='number of iterations')
parser.add_argument('--tol', '-t', default=1e-3, type=float,
help='error tolerance to stop iterations')
parser.add_argument('--output-image', '-o', default=None, type=str,
dest='output', help='output image file name')
args = parser.parse_args()
run(args.gpu_id, args.num, args.dim, args.max_iter, args.tol, args.output)