def buildKernel(self, X, kernelNames, regions, yVar):
numVarComp = len(regions)
hyp0_kernels = []
kernelsList = []
for r_i, r in enumerate(regions):
regionSize = r.sum()
kernelName = kernelNames[r_i]
#choose kernel
if (kernelName == 'lin'):
kernel = kernels.linearKernel(X[:, r])
elif (kernelName == 'rbf_lin'):
kernel1 = kernels.ScaledKernel(kernels.RBFKernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'poly2_lin'):
kernel1 = kernels.ScaledKernel(kernels.Poly2KernelHomo(kernels.linearKernel(X[:, r])))
hyp0_kernels.append(0.5*np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5*np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'poly3_lin'):
kernel1 = kernels.ScaledKernel(kernels.Poly3KernelHomo(kernels.linearKernel(X[:, r])))
hyp0_kernels.append(0.5*np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5*np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName in ['nn_lin']):
kernel1 = kernels.ScaledKernel(kernels.NNKernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'matern5_lin'):
kernel1 = kernels.ScaledKernel(kernels.Matern5Kernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'matern3_lin'):
kernel1 = kernels.ScaledKernel(kernels.Matern3Kernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'poly2'):
kernel = kernels.linearKernel(X[:, r])
kernel = kernels.Poly2Kernel(kernel)
hyp0_kernels.append(np.log(1.0)) #bias hyp
elif (kernelName == 'poly3'):
kernel = kernels.linearKernel(X[:, r])
kernel = kernels.Poly3Kernel(kernel)
hyp0_kernels.append(np.log(1.0)) #bias hyp
elif (kernelName == 'rbf'):
kernel = kernels.RBFKernel(X[:, r])
hyp0_kernels.append(np.log(1.0)) #ell
elif (kernelName == 'gabor'):
kernel = kernels.GaborKernel(X[:, r])
hyp0_kernels += [np.log(1.0), np.log(1.0)] #ell and p
elif (kernelName == 'nn'):
kernel = kernels.NNKernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'rq'):
kernel = kernels.RQKernel(X[:, r])
hyp0_kernels += [np.log(1.0), np.log(1.0)] #ell and alpha
elif (kernelName == 'matern1'):
kernel = kernels.Matern1Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'matern3'):
kernel = kernels.Matern3Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'matern5'):
kernel = kernels.Matern5Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp0'):
kernel = kernels.PP0Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp1'):
kernel = kernels.PP1Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp2'):
kernel = kernels.PP2Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp3'):
kernel = kernels.PP3Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
else: raise Exception('unknown kernel: ' + kernelName)
#scale kernel
kernel = kernels.ScaledKernel(kernel)
hyp0_kernels.append(0.5*np.log(0.5*yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel)
if (kernelName in ['add']):
combinedKernel = kernels.AdditiveKernel(kernelsList, y.shape[0])
hyp0_kernels = np.concatenate((np.zeros(len(kernelsList)), hyp0_kernels))
else: combinedKernel = kernels.SumKernel(kernelsList)
return combinedKernel, hyp0_kernels
def buildKernel(self, X, kernelNames, regions, yVar):
numVarComp = len(regions)
hyp0_kernels = []
kernelsList = []
for r_i, r in enumerate(regions):
regionSize = r.sum()
kernelName = kernelNames[r_i]
#choose kernel
if (kernelName == 'lin'):
kernel = kernels.linearKernel(X[:, r])
elif (kernelName == 'rbf_lin'):
kernel1 = kernels.ScaledKernel(kernels.RBFKernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'poly2_lin'):
kernel1 = kernels.ScaledKernel(
kernels.Poly2KernelHomo(kernels.linearKernel(X[:, r])))
hyp0_kernels.append(0.5 *
np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5 *
np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'poly3_lin'):
kernel1 = kernels.ScaledKernel(
kernels.Poly3KernelHomo(kernels.linearKernel(X[:, r])))
hyp0_kernels.append(0.5 *
np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(0.5 *
np.log(0.5 / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName in ['nn_lin']):
kernel1 = kernels.ScaledKernel(kernels.NNKernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'matern5_lin'):
kernel1 = kernels.ScaledKernel(kernels.Matern5Kernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'matern3_lin'):
kernel1 = kernels.ScaledKernel(kernels.Matern3Kernel(X[:, r]))
hyp0_kernels.append(np.log(1.0)) #ell
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel1)
kernel2 = kernels.ScaledKernel(kernels.linearKernel(X[:, r]))
hyp0_kernels.append(
0.5 * np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel2)
continue
elif (kernelName == 'poly2'):
kernel = kernels.linearKernel(X[:, r])
kernel = kernels.Poly2Kernel(kernel)
hyp0_kernels.append(np.log(1.0)) #bias hyp
elif (kernelName == 'poly3'):
kernel = kernels.linearKernel(X[:, r])
kernel = kernels.Poly3Kernel(kernel)
hyp0_kernels.append(np.log(1.0)) #bias hyp
elif (kernelName == 'rbf'):
kernel = kernels.RBFKernel(X[:, r])
hyp0_kernels.append(np.log(1.0)) #ell
elif (kernelName == 'gabor'):
kernel = kernels.GaborKernel(X[:, r])
hyp0_kernels += [np.log(1.0), np.log(1.0)] #ell and p
elif (kernelName == 'nn'):
kernel = kernels.NNKernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'rq'):
kernel = kernels.RQKernel(X[:, r])
hyp0_kernels += [np.log(1.0), np.log(1.0)] #ell and alpha
elif (kernelName == 'matern1'):
kernel = kernels.Matern1Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'matern3'):
kernel = kernels.Matern3Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'matern5'):
kernel = kernels.Matern5Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp0'):
kernel = kernels.PP0Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp1'):
kernel = kernels.PP1Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp2'):
kernel = kernels.PP2Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
elif (kernelName == 'pp3'):
kernel = kernels.PP3Kernel(X[:, r])
hyp0_kernels += [np.log(1.0)] #ell
else:
raise Exception('unknown kernel: ' + kernelName)
#scale kernel
kernel = kernels.ScaledKernel(kernel)
hyp0_kernels.append(0.5 *
np.log(0.5 * yVar / numVarComp)) #scaling hyp
kernelsList.append(kernel)
if (kernelName in ['add']):
combinedKernel = kernels.AdditiveKernel(kernelsList, y.shape[0])
hyp0_kernels = np.concatenate(
(np.zeros(len(kernelsList)), hyp0_kernels))
else:
combinedKernel = kernels.SumKernel(kernelsList)
return combinedKernel, hyp0_kernels
def buildKernelAdapt(self, X, C, y, regions, reml=True, maxiter=100):
#prepare initial values for sig2e and for fixed effects
hyp0_sig2e, hyp0_fixedEffects = self.getInitialHyps(X, C, y)
bestKernelNames = []
kernelsListAll = []
hyp_kernels = []
funcToSolve = self.infExact_scipy
yVar = y.var()
for r_i, r in enumerate(regions):
#if (r_i == 0): kernelsToTry = ['lin']
#else:
# kernelsToTry = ['lin', 'poly2_lin', 'rbf_lin', 'nn_lin']
kernelsToTry = ['lin', 'poly2_lin', 'rbf_lin', 'nn_lin']
if self.verbose:
print
print 'selecting a kernel for region', r_i, 'with', r.sum(), 'SNPs'
#add linear kernel
X_lastRegion = X[:, r]
linKernel = kernels.linearKernel(X_lastRegion)
kernelsListAll.append(kernels.ScaledKernel(linKernel))
kernelsListAll.append(None)
bestFun = np.inf
bestKernelName = None
best_hyp0 = None
bestKernel = None
bestPval = np.inf
#iterate over every possible kernel
for kernelToTry in kernelsToTry:
hyp0 = [0.5*np.log(0.5*yVar)]
if self.verbose: print 'Testing kernel:', kernelToTry
#create the kernel
if (kernelToTry == 'lin'):
kernel = None
df = None
elif (kernelToTry == 'rbf_lin'):
kernel = kernels.RBFKernel(X_lastRegion)
hyp0.append(np.log(1.0)) #ell
df = 2
elif (kernelToTry == 'nn_lin'):
kernel = kernels.NNKernel(X_lastRegion)
hyp0.append(np.log(1.0)) #ell
df = 2
elif (kernelToTry == 'poly2_lin'):
kernel = kernels.Poly2KernelHomo(linKernel)
df = 1
else:
raise Exception('unrecognized kernel name')
if (kernel is not None):
#scale the kernel
kernel = kernels.ScaledKernel(kernel)
hyp0.append(0.5*np.log(0.5*yVar)) #scaling hyp
#add the kernel as the final kernel in the kernels list
kernelsListAll[-1] = kernel
sumKernel = kernels.SumKernel(kernelsListAll)
else:
sumKernel = kernels.SumKernel(kernelsListAll[:-1])
#test log likelihood obtained with this kernel for this region
args = (sumKernel, C, y, reml)
self.optimization_counter=0
hyp0_all = np.concatenate((hyp0_sig2e, hyp0_fixedEffects, hyp_kernels+hyp0))
optObj = gpUtils.minimize(hyp0_all, funcToSolve, -maxiter, *args)
if (not optObj.success):
print 'Optimization status:', optObj.status
print 'optimization message:', optObj.message
raise Exception('optimization failed')
print 'final LL: %0.5e'%(-optObj.fun)
if (kernelToTry == 'lin'):
linLL = -optObj.fun
pVal = 1.0
else:
llDiff = -optObj.fun - linLL
if (llDiff < 0): pVal = 1.0
else: pVal = 0.5*stats.chi2(df).sf(llDiff)
print 'llDiff: %0.5e'%llDiff, 'pVal:%0.5e'%pVal
if (kernelToTry == 'lin' or (pVal < bestPval and (len(kernelsToTry)==1 or pVal < 0.05/(len(kernelsToTry)-1)))):
bestOptObj = optObj
bestPval = pVal
bestKernelName = kernelToTry
best_hyp0 = hyp0
best_sumKernel = sumKernel
bestKernel = kernel
if (bestKernel is not None): kernelsListAll[-1] = bestKernel
else: kernelsListAll = kernelsListAll[:-1]
hyp_kernels += best_hyp0
bestKernelNames.append(bestKernelName)
if self.verbose: print 'selected kernel:', bestKernelName
if self.verbose:
print 'selected kernels:', bestKernelNames
print
return bestKernelNames
def buildKernelAdapt(self, X, C, y, regions, reml=True, maxiter=100):
#prepare initial values for sig2e and for fixed effects
hyp0_sig2e, hyp0_fixedEffects = self.getInitialHyps(X, C, y)
bestKernelNames = []
kernelsListAll = []
hyp_kernels = []
funcToSolve = self.infExact_scipy
yVar = y.var()
for r_i, r in enumerate(regions):
#if (r_i == 0): kernelsToTry = ['lin']
#else:
# kernelsToTry = ['lin', 'poly2_lin', 'rbf_lin', 'nn_lin']
kernelsToTry = ['lin', 'poly2_lin', 'rbf_lin', 'nn_lin']
if self.verbose:
print
print 'selecting a kernel for region', r_i, 'with', r.sum(
), 'SNPs'
#add linear kernel
X_lastRegion = X[:, r]
linKernel = kernels.linearKernel(X_lastRegion)
kernelsListAll.append(kernels.ScaledKernel(linKernel))
kernelsListAll.append(None)
bestFun = np.inf
bestKernelName = None
best_hyp0 = None
bestKernel = None
bestPval = np.inf
#iterate over every possible kernel
for kernelToTry in kernelsToTry:
hyp0 = [0.5 * np.log(0.5 * yVar)]
if self.verbose: print 'Testing kernel:', kernelToTry
#create the kernel
if (kernelToTry == 'lin'):
kernel = None
df = None
elif (kernelToTry == 'rbf_lin'):
kernel = kernels.RBFKernel(X_lastRegion)
hyp0.append(np.log(1.0)) #ell
df = 2
elif (kernelToTry == 'nn_lin'):
kernel = kernels.NNKernel(X_lastRegion)
hyp0.append(np.log(1.0)) #ell
df = 2
elif (kernelToTry == 'poly2_lin'):
kernel = kernels.Poly2KernelHomo(linKernel)
df = 1
else:
raise Exception('unrecognized kernel name')
if (kernel is not None):
#scale the kernel
kernel = kernels.ScaledKernel(kernel)
hyp0.append(0.5 * np.log(0.5 * yVar)) #scaling hyp
#add the kernel as the final kernel in the kernels list
kernelsListAll[-1] = kernel
sumKernel = kernels.SumKernel(kernelsListAll)
else:
sumKernel = kernels.SumKernel(kernelsListAll[:-1])
#test log likelihood obtained with this kernel for this region
args = (sumKernel, C, y, reml)
self.optimization_counter = 0
hyp0_all = np.concatenate(
(hyp0_sig2e, hyp0_fixedEffects, hyp_kernels + hyp0))
optObj = gpUtils.minimize(hyp0_all, funcToSolve, -maxiter,
*args)
if (not optObj.success):
print 'Optimization status:', optObj.status
print 'optimization message:', optObj.message
raise Exception('optimization failed')
print 'final LL: %0.5e' % (-optObj.fun)
if (kernelToTry == 'lin'):
linLL = -optObj.fun
pVal = 1.0
else:
llDiff = -optObj.fun - linLL
if (llDiff < 0): pVal = 1.0
else: pVal = 0.5 * stats.chi2(df).sf(llDiff)
print 'llDiff: %0.5e' % llDiff, 'pVal:%0.5e' % pVal
if (kernelToTry == 'lin'
or (pVal < bestPval and
(len(kernelsToTry) == 1 or pVal < 0.05 /
(len(kernelsToTry) - 1)))):
bestOptObj = optObj
bestPval = pVal
bestKernelName = kernelToTry
best_hyp0 = hyp0
best_sumKernel = sumKernel
bestKernel = kernel
if (bestKernel is not None): kernelsListAll[-1] = bestKernel
else: kernelsListAll = kernelsListAll[:-1]
hyp_kernels += best_hyp0
bestKernelNames.append(bestKernelName)
if self.verbose: print 'selected kernel:', bestKernelName
if self.verbose:
print 'selected kernels:', bestKernelNames
print
return bestKernelNames
