How to fit a multiple observations to single Gaussian Process

Question

I am trying to fit multiple observations to a single Gaussian Process.

I try to fit the data of two observations (Y) like this:

import numpy as np
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, ConstantKernel as C


# Example data

# Input data X 
X = np.array([[1.0], [2.0], [3.0], [4.0], [5.0]])

# Output data Y 
Y = np.array([[1.5, 2.5], [2.5, 3.5], [3.5, 4.5], [4.5, 5.5], [5.5, 6.5]])
kernel = C(1.0, (1e-4, 1e1)) * RBF(1.0, (1e-4, 1e1))
gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=10)

# Fitting the model
gp.fit(X, Y)

mean_prediction, cov_prediction = gp.predict(X, return_cov=True)

I am getting two array of mean_prediction and two cov_prediction matrices. But I want a single mean and covariance matrix of same dimension as the observations corresponding to single fitted GP. How can I implement that?

enu · Accepted Answer · 2024-11-14 21:34:27Z

0

If you fit them the following way you should get only one posterior mean, I think in theory you should also get two means but they are indentical so the model will give you just once:

# Input data X 
X = np.array([[1.0], [2.0], [3.0], [4.0], [5.0],[1.0], [2.0], [3.0], [4.0], [5.0]])

# Output data Y 
Y = np.array([[1.5], [2.5], [2.5], [3.5], [3.5], [4.5], [4.5], [5.5], [5.5], [6.5]])
kernel = C(1.0, (1e-4, 1e1)) * RBF(1.0, (1e-4, 1e1))
gp = GaussianProcessRegressor(kernel=kernel, n_restarts_optimizer=10)

# Fitting the model
gp.fit(X, Y)

mean_prediction, cov_prediction = gp.predict([[1.0], [2.0], [3.0], [4.0], [5.0]], return_cov=True)

answered Nov 14, 2024 at 21:34

enu

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