Data Science Asked by Jacob Holm on September 28, 2020
I’m trying to sequentially sample from a Gaussian Process prior.
The problem is that the samples eventually converge to zero or diverge to infinity.
I’m using the basic conditionals described e.g. here
Note: the kernel(X,X) function returns the squared exponential kernel with isometric noise.
Here is my code:
n = 32
x_grid = np.linspace(-5,5,n)
x_all = []
y_all = []
for x in x_grid:
x_all = [x] + x_all
X = np.array(x_all).reshape(-1, 1)
# Mean and covariance of the prior
mu = np.zeros((X.shape), np.float)
cov = kernel(X, X)
if len(mu)==1: # first sample is not conditional
y = np.random.randn()*cov + mu
else:
# condition on all previous samples
u1 = mu[0]
u2 = mu[1:]
y2 = np.atleast_2d(np.array(y_all)).T
C11 = cov[:1,:1] # dependent sample
C12 = np.atleast_2d(cov[0,1:])
C21 = np.atleast_2d(cov[1:,0]).T
C22 = np.atleast_2d(cov[1:, 1:])
C22_ = la.inv(C22)
u = u1 + np.dot(C12, np.dot(C22_, (y2 - u2)))
C22_xC21 = np.dot(C22_, C21)
C_minus = np.dot(C12, C22_xC21) # this weirdly becomes larger than C!
C = C11 - C_minus
y = u + np.random.randn()*C
y_all = [y.flatten()[0]] + y_all
Here’s an example with 32 samples, where it collapses:
Here’s an example with 34 samples, where it explodes:
(for this particular kernel, 34 is the number of samples at which (or more) the samples start to diverge.
I’ve gone through this code so many times that I’m going blind – something must be fundamentally wrong with it but I just can’t see it.
1 Asked on April 29, 2021
graphs python semantic segmentation semantic similarity word2vec
1 Asked on April 29, 2021 by pythoner
0 Asked on April 29, 2021 by aslconwnb
autoencoder deep learning keras neural network one hot encoding
0 Asked on April 28, 2021 by gustav1985
0 Asked on April 28, 2021 by talismanic
2 Asked on April 28, 2021
1 Asked on April 28, 2021
data data cleaning data imputation linear regression missing data
1 Asked on April 28, 2021
1 Asked on April 28, 2021 by maeaex1
1 Asked on April 28, 2021
1 Asked on April 28, 2021 by asif17
1 Asked on April 27, 2021 by nsalas
1 Asked on April 27, 2021
2 Asked on April 27, 2021
2 Asked on April 27, 2021 by znoris007
Get help from others!
Recent Questions
Recent Answers
© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP