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TF Cholesky fail on RBF pos-def matrix
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import gpflow as gp | |
import numpy as np | |
import pylab as plt | |
import tensorflow as tf | |
X = np.array([[ 1.16527441e+09], | |
[ 1.16527442e+09], | |
[ 1.16527443e+09], | |
[ 1.16527443e+09], | |
[ 1.16527444e+09], | |
[ 1.16527445e+09], | |
[ 1.16527446e+09], | |
[ 1.16527447e+09], | |
[ 1.16527447e+09], | |
[ 1.16527448e+09], | |
[ 1.16527449e+09], | |
[ 1.16527450e+09], | |
[ 1.16527451e+09], | |
[ 1.16527451e+09], | |
[ 1.16527452e+09], | |
[ 1.16527453e+09], | |
[ 1.16527454e+09], | |
[ 1.16527455e+09], | |
[ 1.16527455e+09], | |
[ 1.16527456e+09], | |
[ 1.16527457e+09], | |
[ 1.16527458e+09], | |
[ 1.16527459e+09], | |
[ 1.16527459e+09], | |
[ 1.16527460e+09], | |
[ 1.16527461e+09], | |
[ 1.16527462e+09], | |
[ 1.16527463e+09], | |
[ 1.16527463e+09], | |
[ 1.16527464e+09], | |
[ 1.16527465e+09], | |
[ 1.16527466e+09], | |
[ 1.16527467e+09], | |
[ 1.16527467e+09], | |
[ 1.16527468e+09], | |
[ 1.16527469e+09], | |
[ 1.16527470e+09], | |
[ 1.16527471e+09], | |
[ 1.16527471e+09], | |
[ 1.16527472e+09], | |
[ 1.16527473e+09], | |
[ 1.16527474e+09], | |
[ 1.16527475e+09], | |
[ 1.16527475e+09], | |
[ 1.16527476e+09], | |
[ 1.16527477e+09], | |
[ 1.16527478e+09], | |
[ 1.16527479e+09], | |
[ 1.16527479e+09], | |
[ 1.16527480e+09], | |
[ 1.16527481e+09], | |
[ 1.16527482e+09], | |
[ 1.16527483e+09], | |
[ 1.16527483e+09], | |
[ 1.16527484e+09], | |
[ 1.16527485e+09], | |
[ 1.16527486e+09], | |
[ 1.16527487e+09], | |
[ 1.16527487e+09], | |
[ 1.16527488e+09], | |
[ 1.16527489e+09], | |
[ 1.16527490e+09], | |
[ 1.16527491e+09], | |
[ 1.16527491e+09], | |
[ 1.16527492e+09], | |
[ 1.16527493e+09], | |
[ 1.16527494e+09], | |
[ 1.16527495e+09], | |
[ 1.16527495e+09], | |
[ 1.16527496e+09], | |
[ 1.16527497e+09], | |
[ 1.16527498e+09], | |
[ 1.16527499e+09], | |
[ 1.16527499e+09], | |
[ 1.16527500e+09], | |
[ 1.16527501e+09], | |
[ 1.16527502e+09], | |
[ 1.16527503e+09], | |
[ 1.16527503e+09], | |
[ 1.16527504e+09], | |
[ 1.16527505e+09], | |
[ 1.16527506e+09], | |
[ 1.16527507e+09], | |
[ 1.16527507e+09], | |
[ 1.16527508e+09], | |
[ 1.16527509e+09], | |
[ 1.16527510e+09], | |
[ 1.16527511e+09], | |
[ 1.16527511e+09], | |
[ 1.16527512e+09], | |
[ 1.16527513e+09], | |
[ 1.16527514e+09], | |
[ 1.16527515e+09], | |
[ 1.16527516e+09], | |
[ 1.16527516e+09], | |
[ 1.16527517e+09], | |
[ 1.16527518e+09], | |
[ 1.16527519e+09], | |
[ 1.16527520e+09], | |
[ 1.16527520e+09], | |
[ 1.16527521e+09], | |
[ 1.16527522e+09], | |
[ 1.16527523e+09], | |
[ 1.16527524e+09], | |
[ 1.16527524e+09], | |
[ 1.16527525e+09], | |
[ 1.16527526e+09], | |
[ 1.16527527e+09], | |
[ 1.16527528e+09], | |
[ 1.16527528e+09], | |
[ 1.16527529e+09], | |
[ 1.16527530e+09], | |
[ 1.16527531e+09], | |
[ 1.16527532e+09], | |
[ 1.16527532e+09], | |
[ 1.16527533e+09], | |
[ 1.16527534e+09], | |
[ 1.16527535e+09], | |
[ 1.16527536e+09], | |
[ 1.16527536e+09]]) | |
Y = np.array([[ 2.46963311], | |
[ 2.81275076], | |
[ 2.69000406], | |
[ 2.58296666], | |
[ 2.31684845], | |
[ 2.18883278], | |
[ 2.25738763], | |
[ 2.39459771], | |
[ 2.12522259], | |
[ 2.49173322], | |
[ 2.78297639], | |
[ 2.65098281], | |
[ 2.57148568], | |
[ 2.77789879], | |
[ 2.56483398], | |
[ 2.53930404], | |
[ 2.45846044], | |
[ 2.08432404], | |
[ 2.17751587], | |
[ 2.06752078], | |
[ 2.0319239 ], | |
[ 1.89906843], | |
[ 1.96754216], | |
[ 1.69002888], | |
[ 2.14023237], | |
[ 2.14404539], | |
[ 2.13234382], | |
[ 1.82146425], | |
[ 1.79754275], | |
[ 1.87372486], | |
[ 2.21795348], | |
[ 2.2174718 ], | |
[ 2.24379265], | |
[ 2.3705007 ], | |
[ 2.21843136], | |
[ 2.12549238], | |
[ 2.02982958], | |
[ 2.11328605], | |
[ 2.21238481], | |
[ 2.21103339], | |
[ 2.97721817], | |
[ 2.67457913], | |
[ 2.72743356], | |
[ 2.68134139], | |
[ 3.13029503], | |
[ 3.43839799], | |
[ 3.29713706], | |
[ 3.46492849], | |
[ 3.67350701], | |
[ 3.88400577], | |
[ 3.82812032], | |
[ 4.05832468], | |
[ 4.43553132], | |
[ 4.41363113], | |
[ 4.41936664], | |
[ 4.70351457], | |
[ 4.30679838], | |
[ 4.00992616], | |
[ 4.06255067], | |
[ 4.06596992], | |
[ 3.75273823], | |
[ 3.97826996], | |
[ 3.82667734], | |
[ 4.0148188 ], | |
[ 3.8492277 ], | |
[ 4.20674274], | |
[ 4.37250744], | |
[ 4.2806856 ], | |
[ 4.19154178], | |
[ 4.11226701], | |
[ 3.93415102], | |
[ 3.88161289], | |
[ 3.6367137 ], | |
[ 3.51130442], | |
[ 3.58040664], | |
[ 3.38126723], | |
[ 3.48296338], | |
[ 3.37396197], | |
[ 3.1863685 ], | |
[ 3.49161607], | |
[ 2.98974131], | |
[ 3.2761566 ], | |
[ 3.37750468], | |
[ 3.08078927], | |
[ 3.02741803], | |
[ 3.18978172], | |
[ 3.39560613], | |
[ 3.6608262 ], | |
[ 3.39282486], | |
[ 3.26884529], | |
[ 3.31234319], | |
[ 3.43635524], | |
[ 3.38701946], | |
[ 3.2540391 ], | |
[ 3.15468288], | |
[ 3.15481631], | |
[ 3.52582369], | |
[ 2.88244772], | |
[ 3.22489644], | |
[ 3.43033441], | |
[ 3.47408322], | |
[ 3.70102469], | |
[ 3.83587249], | |
[ 3.90001012], | |
[ 4.01125156], | |
[ 3.76123542], | |
[ 3.82831775], | |
[ 4.42422725], | |
[ 4.46235979], | |
[ 4.69925034], | |
[ 5.01875834], | |
[ 5.18805289], | |
[ 5.54333723], | |
[ 5.4755843 ], | |
[ 5.42707204], | |
[ 5.75181478], | |
[ 5.72793423], | |
[ 6.01085997], | |
[ 6.11502704], | |
[ 6.41143633]]) | |
plt.plot(X.flatten(),Y.flatten()) | |
plt.show() | |
K_np = np.exp(-(X - X.T)**2/200.**2/2.) + np.eye(X.shape[0])*0.01 | |
L_np = np.linalg.cholesky(K_np) | |
K_tf = tf.constant(K_np[None,:,:]) | |
L_tf = tf.cholesky(K_tf) | |
sess = tf.Session() | |
L_tf = sess.run(L_tf) | |
assert np.allclose(L_tf, L_np) | |
#The difference of ~1e-14 may be enough to cause divergent behaviour | |
#between numpy and tf | |
with gp.defer_build(): | |
k = gp.kernels.RBF(1,lengthscales=[50]) | |
k.lengthscales.transform = gp.transforms.Logistic(20,500) | |
white = gp.kernels.White(1,variance=0.01) | |
white.variance.set_trainable(False) | |
kern = k + white | |
mean = gp.mean_functions.Linear() | |
m = gp.models.GPR(X, Y, kern=kern, mean_function=mean) | |
m.compile() | |
o = gp.train.ScipyOptimizer(method='BFGS') | |
print(o.minimize(m,maxiter=1000)) | |
print(m) | |
ystar,varstar = m.predict_f(X) | |
plt.plot(X.flatten(),Y.flatten()) | |
plt.plot(X.flatten(),ystar.flatten()) | |
plt.show() |
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