def test_gp():
x = np.linspace(-5,5,10)[:,None] # 10 data points, 1-D
xtest = np.linspace(-6,6,200)[:,None]
y = np.sin(x.flatten()) + np.sqrt(1e-3)*np.random.randn(x.shape[0])
ytest = np.sin(xtest.flatten())
# print 'Inputs'
# print x
# print 'Outputs'
# print y
data = {'inputs':x, 'values':y}
pred = {'inputs':xtest, 'values':ytest}
options = {'likelihood':'GAUSSIAN',
'mcmc-iters':500,
'burn-in':500,
'verbose':False,
'mcmc-diagnostics':True,
'thinning':0,
'priors': {'mean':{'distribution':'Gaussian', 'parameters':{'mu':0.0, 'sigma':1.0}},
'noise':{'distribution':'Lognormal', 'parameters':{'scale':1.0}},
'amp2' :{'distribution':'Lognormal', 'parameters':{'scale':1.0}}
}
}
gp = GP(x.shape[1], **options)
gp.fit(data)
func_m, func_v = gp.predict(pred, full_cov=False, compute_grad=False)
def test_gp():
x = np.linspace(-5,5,10)[:,None] # 10 data points, 1-D
xtest = np.linspace(-6,6,200)[:,None]
y = np.sin(x.flatten()) + np.sqrt(1e-3)*np.random.randn(x.shape[0])
ytest = np.sin(xtest.flatten())
# print 'Inputs'
# print x
# print 'Outputs'
# print y
data = {'inputs':x, 'values':y}
pred = {'inputs':xtest, 'values':ytest}
options = {'likelihood':'GAUSSIAN',
'mcmc-iters':500,
'burn-in':500,
'verbose':False,
'mcmc-diagnostics':True,
'thinning':0,
'priors': {'mean':{'distribution':'Gaussian', 'parameters':{'mu':0.0, 'sigma':1.0}},
'noise':{'distribution':'Lognormal', 'parameters':{'scale':1.0}},
'amp2' :{'distribution':'Lognormal', 'parameters':{'scale':1.0}}
}
}
gp = GP(x.shape[1], **options)
gp.fit(data)
func_m, func_v = gp.predict(pred, full_cov=False, compute_grad=False)
def test_predict():
npr.seed(1)
N = 10
Npend = 3
Ntest = 2
D = 5
gp = GP(D, burnin=5, num_fantasies=7)
pred = npr.rand(Ntest, D)
# Test with 0 points
mu, v = gp.predict(pred)
np.testing.assert_allclose(mu,
0,
rtol=1e-7,
atol=0,
err_msg='',
verbose=True)
np.testing.assert_allclose(v,
1 + 1e-6,
rtol=1e-7,
atol=0,
err_msg='',
verbose=True)
#Test with 1 point
X = np.zeros((1, D))
W = npr.randn(D, 1)
val = X.dot(W).flatten() + np.sqrt(1e-3) * npr.randn()
gp.fit(X, val, fit_hypers=False)
mu, v = gp.predict(pred)
# Points closer to the origin will have less variance
if np.linalg.norm(pred[0] - X) < np.linalg.norm(pred[1] - X):
assert v[0] < v[1]
else:
assert v[0] > v[1]
# Predict at the point itself
mu, v = gp.predict(X)
np.testing.assert_allclose(mu,
val,
rtol=1e-5,
atol=0,
err_msg='',
verbose=True)
# Now let's make sure it doesn't break with more data and pending
inputs = npr.rand(N, D)
vals = inputs.dot(W).flatten() + np.sqrt(1e-3) * npr.randn(N)
pending = npr.rand(Npend, D)
gp.fit(inputs, vals, pending)
mu, v = gp.predict(pred)
# Now let's check the gradients
eps = 1e-5
mu, v, dmu, dv = gp.predict(pred, compute_grad=True)
# The implied loss is np.sum(mu**2) + np.sum(v**2)
dloss = 2 * (dmu * mu[:, np.newaxis, :]).sum(2) + 2 * (
v[:, np.newaxis, np.newaxis] * dv).sum(2)
dloss_est = np.zeros(dloss.shape)
for i in xrange(Ntest):
for j in xrange(D):
pred[i, j] += eps
mu, v = gp.predict(pred)
loss_1 = np.sum(mu**2) + np.sum(v**2)
pred[i, j] -= 2 * eps
mu, v = gp.predict(pred)
loss_2 = np.sum(mu**2) + np.sum(v**2)
pred[i, j] += eps
dloss_est[i, j] = ((loss_1 - loss_2) / (2 * eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-6
def test_predict():
npr.seed(1)
N = 10
Npend = 3
Ntest = 2
D = 5
gp = GP(D, burnin=5, num_fantasies=7)
pred = npr.rand(Ntest,D)
# Test with 0 points
mu, v = gp.predict(pred)
np.testing.assert_allclose(mu, 0, rtol=1e-7, atol=0, err_msg='', verbose=True)
np.testing.assert_allclose(v, 1+1e-6, rtol=1e-7, atol=0, err_msg='', verbose=True)
#Test with 1 point
X = np.zeros((1,D))
W = npr.randn(D,1)
val = X.dot(W).flatten() + np.sqrt(1e-3)*npr.randn()
gp.fit(X, val, fit_hypers=False)
mu, v = gp.predict(pred)
# Points closer to the origin will have less variance
if np.linalg.norm(pred[0] - X) < np.linalg.norm(pred[1] - X):
assert v[0] < v[1]
else:
assert v[0] > v[1]
# Predict at the point itself
mu, v = gp.predict(X)
np.testing.assert_allclose(mu, val, rtol=1e-5, atol=0, err_msg='', verbose=True)
# Now let's make sure it doesn't break with more data and pending
inputs = npr.rand(N,D)
vals = inputs.dot(W).flatten() + np.sqrt(1e-3)*npr.randn(N)
pending = npr.rand(Npend,D)
gp.fit(inputs, vals, pending)
mu, v = gp.predict(pred)
# Now let's check the gradients
eps = 1e-5
mu, v, dmu, dv = gp.predict(pred, compute_grad=True)
# The implied loss is np.sum(mu**2) + np.sum(v**2)
dloss = 2*(dmu*mu[:,np.newaxis,:]).sum(2) + 2*(v[:,np.newaxis,np.newaxis]*dv).sum(2)
dloss_est = np.zeros(dloss.shape)
for i in xrange(Ntest):
for j in xrange(D):
pred[i,j] += eps
mu, v = gp.predict(pred)
loss_1 = np.sum(mu**2) + np.sum(v**2)
pred[i,j] -= 2*eps
mu, v = gp.predict(pred)
loss_2 = np.sum(mu**2) + np.sum(v**2)
pred[i,j] += eps
dloss_est[i,j] = ((loss_1 - loss_2) / (2*eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-6