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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Branching GP Regression
Step1:  Create the tree
Specify where the branching point is
Step2:  Specify where to evaluate the kernel
Step3:  Specify the kernel and its hyperparameters
These determine how smooth and variable the branching functions are
Step4:  Sample the kernel
Step5:  Plot the sample
Step6:  You can rerun the same code as many times as you want and get different sample paths
We can also sample independent functions. This is the assumption in the overlapping mixtures of GPs model (OMGP) discussed in the paper.
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Python Code:
import pickle
import gpflow
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt
from BranchedGP import BranchingTree as bt
from BranchedGP import VBHelperFunctions as bplot
from BranchedGP import branch_kernParamGPflow as bk
plt.style.use("ggplot")
%matplotlib inline
Explanation: Branching GP Regression: Sampling from the model
Alexis Boukouvalas, 2017
This notebook shows how to sample from a BGP model
End of explanation
branchingPoint = 0.5
tree = bt.BinaryBranchingTree(
    0, 10, fDebug=False
)  # set to true to print debug messages
tree.add(None, 1, branchingPoint)  # single branching point
(fm, fmb) = tree.GetFunctionBranchTensor()
Explanation: Create the tree
Specify where the branching point is
End of explanation
t = np.linspace(0.01, 1, 10)
(XForKernel, indicesBranch, Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True)
Explanation: Specify where to evaluate the kernel
End of explanation
Bvalues = np.expand_dims(np.asarray(tree.GetBranchValues()), 1)
KbranchParam = bk.BranchKernelParam(gpflow.kernels.RBF(1), fm, b=Bvalues)
KbranchParam.kern.lengthscales = 2
KbranchParam.kern.variance = 1
Explanation: Specify the kernel and its hyperparameters
These determine how smooth and variable the branching functions are
End of explanation
samples = bk.SampleKernel(KbranchParam, XForKernel)
Explanation: Sample the kernel
End of explanation
bk.PlotSample(XForKernel, samples)
Explanation: Plot the sample
End of explanation
indKernel = bk.IndKern(gpflow.kernels.RBF(1))
samples = bk.SampleKernel(indKernel, XForKernel)
bk.PlotSample(XForKernel, samples)
Explanation: You can rerun the same code as many times as you want and get different sample paths
We can also sample independent functions. This is the assumption in the overlapping mixtures of GPs model (OMGP) discussed in the paper.
End of explanation
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