Branching GP Regression: Sampling from the model

Alexis Boukouvalas, 2017

This notebook shows how to sample from a BGP model



In [1]:

    
import pandas as pd
import numpy as np
import pickle
from matplotlib import pyplot as plt
import gpflow
from BranchedGP import VBHelperFunctions as bplot
from BranchedGP import BranchingTree as bt
from BranchedGP import branch_kernParamGPflow as bk
plt.style.use('ggplot')
%matplotlib inline









    



/Users/mqbssaby/anaconda/lib/python3.6/importlib/_bootstrap.py:205: RuntimeWarning: compiletime version 3.5 of module 'tensorflow.python.framework.fast_tensor_util' does not match runtime version 3.6
  return f(*args, **kwds)

Create the tree

Specify where the branching point is



In [2]:

    
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()

Specify where to evaluate the kernel



In [3]:

    
t = np.linspace(0.01, 1, 10)
(XForKernel, indicesBranch, Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True)

Specify the kernel and its hyperparameters These determine how smooth and variable the branching functions are



In [4]:

    
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

Sample the kernel



In [5]:

    
samples = bk.SampleKernel(KbranchParam, XForKernel)

Plot the sample



In [6]:

    
bk.PlotSample(XForKernel, samples)

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.



In [7]:

    
indKernel = bk.IndKern(gpflow.kernels.RBF(1))
samples = bk.SampleKernel(indKernel, XForKernel)
bk.PlotSample(XForKernel, samples)



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