def test(self):
N = 3 # how many points per function
tree = bt.BinaryBranchingTree(0, 10, fDebug=False) # set to true to print debug messages
tree.add(None, 1, 0.5) # single branching point
(fm, fmb) = tree.GetFunctionBranchTensor()
# print fmb
tree.printTree()
print('fm', fm)
# print fmb
t = np.linspace(0.01, 1, 10)
(XForKernel, indicesBranch, Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True)
# GP flow kernel
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
K = KbranchParam.compute_K(Xtrue, Xtrue)
assert KbranchParam.Bv.value == 0.5
samples, L, K = bk.SampleKernel(KbranchParam, XForKernel, D=1, tol=1e-6, retChol=True)
samples2 = bk.SampleKernel(KbranchParam, XForKernel, D=1, tol=1e-6, retChol=False)
# Also try the independent kernel
indKernel = bk.IndKern(gpflow.kernels.RBF(1))
samples3, L, K = bk.SampleKernel(indKernel, XForKernel, D=1, tol=1e-6, retChol=True)
samples4 = KbranchParam.SampleKernel(XForKernel, b=Bvalues)
XAssignments = bk.GetFunctionIndexSample(t) # assign to either branch randomly
XAssignments[XAssignments[:, 0] <= tree.GetBranchValues(), 1] = 1
samples5 = KbranchParam.SampleKernelFromTree(XAssignments, b=tree.GetBranchValues())
def test(self):
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
t = np.linspace(0.01, 1, 60)
(XForKernel, indicesBranch, Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True)
# Specify the kernel and its hyperparameters
# These determine how smooth and variable the branching functions are
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
samples = bk.SampleKernel(KbranchParam, XForKernel)
# Plot the sample
bk.PlotSample(XForKernel, samples, B=Bvalues)
# Fit model
BgridSearch = [0.1, branchingPoint, 1.1]
globalBranchingLabels = XForKernel[:, 1] # use correct labels for tests
# could add a mistake
print('Sparse model')
d = FitBranchingModel.FitModel(BgridSearch, XForKernel[:, 0], samples, globalBranchingLabels,
maxiter=20, priorConfidence=0.80, M=10)
bmode = BgridSearch[np.argmax(d['loglik'])]
assert bmode == branchingPoint, bmode
# Plot model
pred = d['prediction'] # prediction object from GP
_=bplot.plotBranchModel(bmode, XForKernel[:, 0], samples, pred['xtest'], pred['mu'], pred['var'],
d['Phi'], fPlotPhi=True, fColorBar=True, fPlotVar = True)
_=bplot.PlotBGPFit(samples, XForKernel[:, 0], BgridSearch, d)
print('Try dense model')
d = FitBranchingModel.FitModel(BgridSearch, XForKernel[:, 0], samples, globalBranchingLabels,
maxiter=20, priorConfidence=0.80, M=0)
bmode = BgridSearch[np.argmax(d['loglik'])]
assert bmode == branchingPoint, bmode
print('Try sparse model with fixed inducing points')
d = FitBranchingModel.FitModel(BgridSearch, XForKernel[:, 0], samples, globalBranchingLabels,
maxiter=20, priorConfidence=0.80, M=20, fixInducingPoints=True)
bmode = BgridSearch[np.argmax(d['loglik'])]
assert bmode == branchingPoint, bmode
print('Try sparse model with fixed hyperparameters')
d = FitBranchingModel.FitModel(BgridSearch, XForKernel[:, 0], samples, globalBranchingLabels,
maxiter=20, priorConfidence=0.80, M=15,
likvar=1e-3, kerlen=2., kervar=1., fixHyperparameters=True)
# 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.
indKernel = bk.IndKern(gpflow.kernels.RBF(1))
samplesInd = bk.SampleKernel(indKernel, XForKernel)
def test(self):
tree = bt.BinaryBranchingTree(
0, 10, fDebug=False) # set to true to print debug messages
tree.add(None, 1, 0.5) # single branching point
(fm, fmb) = tree.GetFunctionBranchTensor()
# print fmb
tree.printTree()
print("fm", fm)
# print fmb
t = np.linspace(0.01, 1, 10)
(XForKernel, indicesBranch,
Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True)
# GP flow kernel
Bvalues = np.expand_dims(np.asarray(tree.GetBranchValues()), 1)
KbranchParam = bk.BranchKernelParam(
gpflow.kernels.SquaredExponential(), fm, b=Bvalues)
KbranchParam.kern.lengthscales.assign(2)
KbranchParam.kern.variance.assign(1)
_ = KbranchParam.K(Xtrue, Xtrue)
assert KbranchParam.Bv == 0.5
_ = bk.SampleKernel(KbranchParam,
XForKernel,
D=1,
tol=1e-6,
retChol=True)
_ = bk.SampleKernel(KbranchParam,
XForKernel,
D=1,
tol=1e-6,
retChol=False)
# Also try the independent kernel
indKernel = bk.IndKern(gpflow.kernels.SquaredExponential())
_ = bk.SampleKernel(indKernel, XForKernel, D=1, tol=1e-6, retChol=True)
_ = KbranchParam.SampleKernel(XForKernel, b=Bvalues)
XAssignments = bk.GetFunctionIndexSample(
t) # assign to either branch randomly
XAssignments[XAssignments[:, 0] <= tree.GetBranchValues(), 1] = 1
_ = KbranchParam.SampleKernelFromTree(XAssignments,
b=tree.GetBranchValues())
def test(self):
fDebug = True # Enable debugging output - tensorflow print ops
np.set_printoptions(suppress=True, precision=5)
seed = 43
np.random.seed(seed=seed) # easy peasy reproducibeasy
tf.random.set_seed(seed)
# Data generation
N = 20
t = np.linspace(0, 1, N)
print(t)
Y = np.zeros((N, 1))
idx = np.nonzero(t > 0.5)[0]
idxA = idx[::2]
idxB = idx[1::2]
print(idx)
print(idxA)
print(idxB)
Y[idxA, 0] = 2 * t[idxA]
Y[idxB, 0] = -2 * t[idxB]
globalBranchingLabels = np.ones(N)
globalBranchingLabels[4::2] = 2
globalBranchingLabels[5::2] = 3
XExpanded, indices, _ = VBHelperFunctions.GetFunctionIndexListGeneral(
t)
phiInitial, phiPrior = FitBranchingModel.GetInitialConditionsAndPrior(
globalBranchingLabels, 0.51, False)
ptb = np.min([
np.min(t[globalBranchingLabels == 2]),
np.min(t[globalBranchingLabels == 3]),
])
tree = bt.BinaryBranchingTree(0, 1, fDebug=False)
tree.add(None, 1, np.ones((1, 1)) * ptb) # B can be anything here
(fm1, _) = tree.GetFunctionBranchTensor()
# Look at kernels
fDebug = True
Kbranch1 = bk.BranchKernelParam(gpflow.kernels.Matern32(),
fm1,
b=np.ones((1, 1)) * ptb,
fDebug=fDebug)
K1 = Kbranch1.K(XExpanded, XExpanded)
Kbranch2 = bk.BranchKernelParam(gpflow.kernels.Matern32(),
fm1,
b=np.ones((1, 1)) * 0.20,
fDebug=fDebug)
_ = Kbranch2.K(XExpanded, XExpanded)
Kbranch3 = bk.BranchKernelParam(gpflow.kernels.Matern32(),
fm1,
b=np.ones((1, 1)) * 0.22,
fDebug=fDebug)
_ = Kbranch3.K(XExpanded, XExpanded)
# Look at model
kb = (bk.BranchKernelParam(
gpflow.kernels.Matern32(), fm1, b=np.zeros(
(1, 1))) + gpflow.kernels.White())
kb.kernels[1].variance.assign(
1e-6
) # controls the discontinuity magnitude, the gap at the branching point
set_trainable(kb.kernels[1].variance, False) # jitter for numerics
# m = assigngp_dense.AssignGP(
# t, XExpanded, Y, kb, indices, np.ones((1, 1)), phiInitial=phiInitial, phiPrior=phiPrior
# )
m = assigngp_dense.AssignGP(
t,
XExpanded,
Y,
kb,
indices,
np.ones((1, 1)),
phiInitial=phiInitial,
phiPrior=phiPrior,
KConst=K1,
fDebug=True,
)
m.UpdateBranchingPoint(np.ones((1, 1)) * ptb, phiInitial.copy())
ptbLL = m.log_posterior_density()
m.UpdateBranchingPoint(np.ones((1, 1)) * 0.20, phiInitial.copy())
eLL = m.log_posterior_density()
m.UpdateBranchingPoint(np.ones((1, 1)) * 0.22, phiInitial.copy())
lll = m.log_posterior_density()
print(eLL, ptbLL, lll)
assert eLL < ptbLL
assert np.allclose(ptbLL, lll)
def runSparseModel(self, M=None, atolPrediction=1e-3, atolLik=1):
fDebug = True # Enable debugging output - tensorflow print ops
np.set_printoptions(precision=4) # precision to print numpy array
seed = 43
np.random.seed(seed=seed) # easy peasy reproducibeasy
tf.set_random_seed(seed)
# Data generation
N = 20
t = np.linspace(0, 1, N)
print(t)
trueB = np.ones((1, 1)) * 0.5
Y = np.zeros((N, 1))
idx = np.nonzero(t > 0.5)[0]
idxA = idx[::2]
idxB = idx[1::2]
print(idx)
print(idxA)
print(idxB)
Y[idxA, 0] = 2 * t[idxA]
Y[idxB, 0] = -2 * t[idxB]
# Create tree structures
tree = bt.BinaryBranchingTree(0, 1, fDebug=False)
tree.add(None, 1, trueB)
(fm, _) = tree.GetFunctionBranchTensor()
XExpanded, indices, _ = VBHelperFunctions.GetFunctionIndexListGeneral(
t)
print('XExpanded', XExpanded.shape)
print('indices', len(indices)) # Create model
Kbranch = bk.BranchKernelParam(
gpflow.kernels.Matern32(1), fm,
b=trueB.copy()) + gpflow.kernels.White(1)
Kbranch.branchkernelparam.kern.variance = 1
Kbranch.white.variance = 1e-6 # controls the discontinuity magnitude, the gap at the branching point
Kbranch.white.variance.set_trainable(False) # jitter for numerics
print('Kbranch matrix', Kbranch.compute_K(XExpanded, XExpanded))
print('Branching K free parameters', Kbranch.branchkernelparam)
print('Branching K branching parameter',
Kbranch.branchkernelparam.Bv.value)
if (M is not None):
ir = np.random.choice(XExpanded.shape[0], M)
ZExpanded = XExpanded[ir, :]
else:
ZExpanded = XExpanded # Test on full data
phiInitial = np.ones((N, 2)) * 0.5 # dont know anything
mV = assigngp_denseSparse.AssignGPSparse(
t,
XExpanded,
Y,
Kbranch,
indices,
Kbranch.branchkernelparam.Bv.value,
ZExpanded,
phiInitial=phiInitial,
fDebug=fDebug)
self.InitParams(mV)
mVFull = assigngp_dense.AssignGP(t,
XExpanded,
Y,
Kbranch,
indices,
Kbranch.branchkernelparam.Bv.value,
fDebug=fDebug,
phiInitial=phiInitial)
self.InitParams(mVFull)
lsparse = mV.compute_log_likelihood()
lfull = mVFull.compute_log_likelihood()
print('Log likelihoods, sparse=%f, full=%f' % (lsparse, lfull))
self.assertTrue(
np.allclose(lsparse, lfull, atol=atolLik),
'Log likelihoods not close, sparse=%f, full=%f' % (lsparse, lfull))
# check models identical
assert np.all(mV.GetPhiExpanded() == mVFull.GetPhiExpanded())
assert mV.likelihood.variance.value == mVFull.likelihood.variance.value
assert mV.kern is mVFull.kern
# Test prediction
Xtest = np.array([[0.6, 2], [0.6, 3]])
mu_f, var_f = mVFull.predict_f(Xtest)
mu_s, var_s = mV.predict_f(Xtest)
print('Sparse model mu=', mu_s, ' variance=', var_s)
print('Full model mu=', mu_f, ' variance=', var_f)
self.assertTrue(
np.allclose(mu_s, mu_f, atol=atolPrediction),
'mu not close sparse=%s - full=%s ' % (str(mu_s), str(mu_f)))
self.assertTrue(
np.allclose(var_s, var_f, atol=atolPrediction),
'var not close sparse=%s - full=%s ' % (str(var_s), str(var_f)))
return lsparse, lfull
def test(self):
np.set_printoptions(suppress=True, precision=5)
seed = 43
np.random.seed(seed=seed) # easy peasy reproducibeasy
tf.set_random_seed(seed)
# Data generation
N = 20
t = np.linspace(0, 1, N)
print(t)
trueB = np.ones((1, 1)) * 0.5
Y = np.zeros((N, 1))
idx = np.nonzero(t > 0.5)[0]
idxA = idx[::2]
idxB = idx[1::2]
print(idx)
print(idxA)
print(idxB)
Y[idxA, 0] = 2 * t[idxA]
Y[idxB, 0] = -2 * t[idxB]
# Create tree structures
tree = bt.BinaryBranchingTree(0, 1, fDebug=False)
tree.add(None, 1, trueB)
assert tree.getRoot().val == trueB
assert tree.getRoot().idB == 1
(fm, _) = tree.GetFunctionBranchTensor()
XExpanded, indices, _ = VBHelperFunctions.GetFunctionIndexListGeneral(
t)
# Create model
Kbranch = bk.BranchKernelParam(
gpflow.kernels.Matern32(1), fm,
b=trueB.copy()) + gpflow.kernels.White(1)
Kbranch.kernels[
1].variance = 1e-6 # controls the discontinuity magnitude, the gap at the branching point
Kbranch.kernels[1].variance.set_trainable(False) # jitter for numerics
# Create model
phiPrior = np.ones((N, 2)) * 0.5 # dont know anything
phiInitial = np.ones((N, 2)) * 0.5 # dont know anything
phiInitial[:, 0] = np.random.rand(N)
phiInitial[:, 1] = 1 - phiInitial[:, 0]
m = assigngp_dense.AssignGP(t,
XExpanded,
Y,
Kbranch,
indices,
Kbranch.kernels[0].Bv.value,
phiPrior=phiPrior,
phiInitial=phiInitial)
InitKernParams(m)
m.likelihood.variance.set_trainable(False)
print('Model before initialisation\n', m,
'\n===========================')
gpflow.train.ScipyOptimizer().minimize(m, maxiter=100)
m.likelihood.variance.set_trainable(True)
gpflow.train.ScipyOptimizer().minimize(m, maxiter=100)
print('Model after initialisation\n', m,
'\n===========================')
ttestl, mul, varl = VBHelperFunctions.predictBranchingModel(m)
_, _, covl = VBHelperFunctions.predictBranchingModel(m, full_cov=True)
for i in range(len(varl)):
assert np.all(covl[i].diagonal().flatten() == varl[i].flatten())
assert len(varl) == 3, 'Must have 3 predictions for 3 functions'
assert np.all(varl[0] > 0), 'neg variances for variance function 0'
assert np.all(varl[1] > 0), 'neg variances for variance function 1'
assert np.all(varl[2] > 0), 'neg variances for variance function 2'
PhiOptimised = m.GetPhi()
print('phiPrior', phiPrior)
print('PhiOptimised', PhiOptimised)
assert np.allclose(
PhiOptimised[idxA, 2],
1), 'PhiOptimised idxA=%s' % str(PhiOptimised[idxA, :])
assert np.allclose(
PhiOptimised[idxB, 1],
1), 'PhiOptimised idxB=%s' % str(PhiOptimised[idxB, :])
# reset model and test informative KL prior
m.UpdateBranchingPoint(Kbranch.kernels[0].Bv.value,
phiInitial) # reset initial phi
InitKernParams(m)
ll_flatprior = m.compute_log_likelihood()
phiInfPrior = np.ones((N, 2)) * 0.5 # dont know anything
phiInfPrior[-1, :] = [0.99, 0.01]
# phiInfPrior[-2, :] = [0.01, 0.99]
m.UpdateBranchingPoint(Kbranch.kernels[0].Bv.value,
phiInitial,
prior=phiInfPrior)
ll_betterprior = m.compute_log_likelihood()
assert ll_betterprior > ll_flatprior, '%f <> %f' % (ll_betterprior,
ll_flatprior)
def test(self):
np.set_printoptions(suppress=True, precision=5)
seed = 43
np.random.seed(seed=seed) # easy peasy reproducibeasy
tf.random.set_seed(seed)
# Data generation
N = 20
t = np.linspace(0, 1, N)
print(t)
trueB = np.ones((1, 1)) * 0.5
Y = np.zeros((N, 1))
idx = np.nonzero(t > 0.5)[0]
idxA = idx[::2]
idxB = idx[1::2]
print(idx)
print(idxA)
print(idxB)
Y[idxA, 0] = 2 * t[idxA]
Y[idxB, 0] = -2 * t[idxB]
# Create tree structures
tree = bt.BinaryBranchingTree(0, 1, fDebug=False)
tree.add(None, 1, trueB)
assert tree.getRoot().val == trueB
assert tree.getRoot().idB == 1
(fm, _) = tree.GetFunctionBranchTensor()
XExpanded, indices, _ = VBHelperFunctions.GetFunctionIndexListGeneral(
t)
# Create model
Kbranch = (bk.BranchKernelParam(
gpflow.kernels.Matern32(), fm, b=trueB.copy()) +
gpflow.kernels.White())
Kbranch.kernels[1].variance.assign(
1e-6
) # controls the discontinuity magnitude, the gap at the branching point
gpflow.set_trainable(Kbranch.kernels[1].variance,
False) # jitter for numerics
# Create model
phiPrior = np.ones((N, 2)) * 0.5 # dont know anything
phiInitial = np.ones((N, 2)) * 0.5 # dont know anything
phiInitial[:, 0] = np.random.rand(N)
phiInitial[:, 1] = 1 - phiInitial[:, 0]
m = assigngp_dense.AssignGP(
t,
XExpanded,
Y,
Kbranch,
indices,
Kbranch.kernels[0].Bv,
phiPrior=phiPrior,
phiInitial=phiInitial,
)
InitKernParams(m)
gpflow.set_trainable(m.likelihood.variance, False)
print("Model before initialisation\n", m,
"\n===========================")
opt = gpflow.optimizers.Scipy()
opt.minimize(
m.training_loss,
variables=m.trainable_variables,
options=dict(disp=True, maxiter=100),
)
gpflow.set_trainable(m.likelihood.variance, True)
opt.minimize(
m.training_loss,
variables=m.trainable_variables,
options=dict(disp=True, maxiter=100),
)
print("Model after initialisation\n", m,
"\n===========================")
ttestl, mul, varl = VBHelperFunctions.predictBranchingModel(m)
_, _, covl = VBHelperFunctions.predictBranchingModel(m, full_cov=True)
assert len(varl) == 3, "Must have 3 predictions for 3 functions"
assert np.all(varl[0] > 0), "neg variances for variance function 0"
assert np.all(varl[1] > 0), "neg variances for variance function 1"
assert np.all(varl[2] > 0), "neg variances for variance function 2"
PhiOptimised = m.GetPhi()
print("phiPrior", phiPrior)
print("PhiOptimised", PhiOptimised)
assert np.allclose(
PhiOptimised[idxA, 2],
1), "PhiOptimised idxA=%s" % str(PhiOptimised[idxA, :])
assert np.allclose(
PhiOptimised[idxB, 1],
1), "PhiOptimised idxB=%s" % str(PhiOptimised[idxB, :])
# reset model and test informative KL prior
m.UpdateBranchingPoint(Kbranch.kernels[0].Bv,
phiInitial) # reset initial phi
InitKernParams(m)
ll_flatprior = m.log_posterior_density()
phiInfPrior = np.ones((N, 2)) * 0.5 # dont know anything
phiInfPrior[-1, :] = [0.99, 0.01]
# phiInfPrior[-2, :] = [0.01, 0.99]
m.UpdateBranchingPoint(Kbranch.kernels[0].Bv,
phiInitial,
prior=phiInfPrior)
ll_betterprior = m.log_posterior_density()
assert ll_betterprior > ll_flatprior, "%f <> %f" % (
ll_betterprior,
ll_flatprior,
)
def test(self):
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
t = np.linspace(0.01, 1, 60)
(XForKernel, indicesBranch,
Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True)
# Specify the kernel and its hyperparameters
# These determine how smooth and variable the branching functions are
Bvalues = np.expand_dims(np.asarray(tree.GetBranchValues()), 1)
KbranchParam = bk.BranchKernelParam(
gpflow.kernels.SquaredExponential(), fm, b=Bvalues)
KbranchParam.kern.lengthscales.assign(2.0)
KbranchParam.kern.variance.assign(1.0)
# Sample the kernel
samples = bk.SampleKernel(KbranchParam, XForKernel)
# Plot the sample
bk.PlotSample(XForKernel, samples, B=Bvalues)
# Fit model
BgridSearch = [0.0001, branchingPoint, 1.1]
globalBranchingLabels = XForKernel[:,
1] # use correct labels for tests
# could add a mistake
print("Sparse model")
d = FitBranchingModel.FitModel(
BgridSearch,
XForKernel[:, 0],
samples,
globalBranchingLabels,
maxiter=40,
priorConfidence=0.80,
M=10,
)
bmode = BgridSearch[np.argmax(d["loglik"])]
print("tensorflow version", tf.__version__, "GPflow version",
gpflow.__version__)
print(
"TestSamplingAndPlotting:: Sparse Log likelihood",
d["loglik"],
"BgridSearch",
BgridSearch,
)
assert bmode == branchingPoint, bmode
# Plot model
pred = d["prediction"] # prediction object from GP
_ = bplot.plotBranchModel(
bmode,
XForKernel[:, 0],
samples,
pred["xtest"],
pred["mu"],
pred["var"],
d["Phi"],
fPlotPhi=True,
fColorBar=True,
fPlotVar=True,
)
_ = bplot.PlotBGPFit(samples, XForKernel[:, 0], BgridSearch, d)
d = FitBranchingModel.FitModel(
BgridSearch,
XForKernel[:, 0],
samples,
globalBranchingLabels,
maxiter=40,
priorConfidence=0.80,
M=0,
)
bmode = BgridSearch[np.argmax(d["loglik"])]
print(
"TestSamplingAndPlotting:: Dense Log likelihood",
d["loglik"],
"BgridSearch",
BgridSearch,
)
assert bmode == branchingPoint, bmode
print("Try sparse model with fixed hyperparameters")
d = FitBranchingModel.FitModel(
BgridSearch,
XForKernel[:, 0],
samples,
globalBranchingLabels,
maxiter=20,
priorConfidence=0.80,
M=15,
likvar=1e-3,
kerlen=2.0,
kervar=1.0,
fixHyperparameters=True,
)
# 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.
indKernel = bk.IndKern(gpflow.kernels.SquaredExponential())
_ = bk.SampleKernel(indKernel, XForKernel)
# %% [markdown] # Specify where to evaluate the kernel # %% t = np.linspace(0.01, 1, 10) (XForKernel, indicesBranch, Xtrue) = tree.GetFunctionIndexList(t, fReturnXtrue=True) # %% [markdown] # Specify the kernel and its hyperparameters # These determine how smooth and variable the branching functions are # %% 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 # %% [markdown] # Sample the kernel # %% samples = bk.SampleKernel(KbranchParam, XForKernel) # %% [markdown] # Plot the sample # %% bk.PlotSample(XForKernel, samples)