def verify_la_derivatives(self, lik, y, thr=1e-3):
""" Laplace approximation derivatives verification.
"""
try:
h = 1e-5
lp, dlp, d2lp, d3lp = lik.la(y, self.fmu)
lp_h, dlp_h, d2lp_h, _ = lik.la(y, self.fmu + h)
dlpn, d2lpn, d3lpn = (lp_h - lp) / h, (dlp_h - dlp) / h, (d2lp_h -
d2lp) / h
self.assertLessEqual(erelmax(dlp, dlpn), thr)
self.assertLessEqual(erelmax(d2lp, d2lpn), thr)
self.assertLessEqual(erelmax(d3lp, d3lpn), thr)
hyp = lik.get_hyp()
for i in range(len(hyp)):
lp_dh, dlp_dh, d2lp_dh = lik.la(y, self.fmu, i=i)
hyp[i] += h
lik.set_hyp(hyp)
lp_h, dlp_h, d2lp_h, _ = lik.la(y, self.fmu)
hyp[i] -= h
lik.set_hyp(hyp)
lp_dhn, dlp_dhn = (lp_h - lp) / h, (dlp_h - dlp) / h
d2lp_dhn = (d2lp_h - d2lp) / h
self.assertLessEqual(erelmax(lp_dh, lp_dhn), thr)
self.assertLessEqual(erelmax(dlp_dh, dlp_dhn), thr)
self.assertLessEqual(erelmax(d2lp_dh, d2lp_dhn), thr)
except NotImplementedError, err:
print err
def verify_derivatives(self,inf,cov,mean,lik,thr):
""" Compare numerical against analytical derivatives.
"""
n,D,X,y = self.n,self.D,self.X,self.y
post,nlZ,dnlZ = inf(cov,mean,lik,X,y,deriv=True)
h = 1e-5
hyp = cov.get_hyp(); dhyp = np.zeros_like(hyp) # covariance parameters
for i in range(len(hyp)):
hyp[i] += h; cov.set_hyp(hyp)
_,nlZh = inf(cov,mean,lik,X,y)
hyp[i] -= h; cov.set_hyp(hyp)
dhyp[i] = (nlZh-nlZ)/h
self.assertLessEqual(erel(dhyp,dnlZ.cov),thr)
hyp = mean.get_hyp(); dhyp = np.zeros_like(hyp) # mean parameters
for i in range(len(hyp)):
hyp[i] += h; mean.set_hyp(hyp)
_,nlZh = inf(cov,mean,lik,X,y)
hyp[i] -= h; mean.set_hyp(hyp)
dhyp[i] = (nlZh-nlZ)/h
self.assertLessEqual(erel(dhyp,dnlZ.mean),thr)
hyp = lik.get_hyp(); dhyp = np.zeros_like(hyp) # likelihood parameters
for i in range(len(hyp)):
hyp[i] += h; lik.set_hyp(hyp)
_,nlZh = inf(cov,mean,lik,X,y)
hyp[i] -= h; lik.set_hyp(hyp)
dhyp[i] = (nlZh-nlZ)/h
self.assertLessEqual(erel(dhyp,dnlZ.lik),thr)
def verify_ep_derivatives(self,lik,y,thr=1e-3):
""" Expectation propagation derivatives verification.
"""
try:
h = 1e-5
lZ,dlZ,d2lZ = lik.ep(y,self.fmu,self.fs2)
lZ_h,dlZ_h,d2lZ_h = lik.ep(y,self.fmu+h,self.fs2)
dlZn,d2lZn = (lZ_h-lZ)/h,(dlZ_h-dlZ)/h
self.assertLessEqual(erelmax(dlZ,dlZn),thr)
self.assertLessEqual(erelmax(d2lZ,d2lZn),thr)
hyp = lik.get_hyp()
for i in range(len(hyp)):
lZ_dh = lik.ep(y,self.fmu,self.fs2,i=i)
hyp[i] += h; lik.set_hyp(hyp)
lZ_h,_,_ = lik.ep(y,self.fmu,self.fs2)
hyp[i] -= h; lik.set_hyp(hyp)
lZ_dhn = (lZ_h-lZ)/h
self.assertLessEqual(erelmax(lZ_dh,lZ_dhn),thr)
except NotImplementedError,err: print err
except: raise
def verify_ep_derivatives(self, lik, y, thr=1e-3):
""" Expectation propagation derivatives verification.
"""
try:
h = 1e-5
lZ, dlZ, d2lZ = lik.ep(y, self.fmu, self.fs2)
lZ_h, dlZ_h, d2lZ_h = lik.ep(y, self.fmu + h, self.fs2)
dlZn, d2lZn = (lZ_h - lZ) / h, (dlZ_h - dlZ) / h
self.assertLessEqual(erelmax(dlZ, dlZn), thr)
self.assertLessEqual(erelmax(d2lZ, d2lZn), thr)
hyp = lik.get_hyp()
for i in range(len(hyp)):
lZ_dh = lik.ep(y, self.fmu, self.fs2, i=i)
hyp[i] += h
lik.set_hyp(hyp)
lZ_h, _, _ = lik.ep(y, self.fmu, self.fs2)
hyp[i] -= h
lik.set_hyp(hyp)
lZ_dhn = (lZ_h - lZ) / h
self.assertLessEqual(erelmax(lZ_dh, lZ_dhn), thr)
except NotImplementedError, err:
print err
def verify_la_derivatives(self,lik,y,thr=1e-3):
""" Laplace approximation derivatives verification.
"""
try:
h = 1e-5
lp,dlp,d2lp,d3lp = lik.la(y,self.fmu)
lp_h,dlp_h,d2lp_h,_ = lik.la(y,self.fmu+h)
dlpn,d2lpn,d3lpn = (lp_h-lp)/h,(dlp_h-dlp)/h,(d2lp_h-d2lp)/h
self.assertLessEqual(erelmax(dlp,dlpn),thr)
self.assertLessEqual(erelmax(d2lp,d2lpn),thr)
self.assertLessEqual(erelmax(d3lp,d3lpn),thr)
hyp = lik.get_hyp()
for i in range(len(hyp)):
lp_dh,dlp_dh,d2lp_dh = lik.la(y,self.fmu,i=i)
hyp[i] += h; lik.set_hyp(hyp)
lp_h,dlp_h,d2lp_h,_ = lik.la(y,self.fmu)
hyp[i] -= h; lik.set_hyp(hyp)
lp_dhn,dlp_dhn = (lp_h-lp)/h,(dlp_h-dlp)/h
d2lp_dhn = (d2lp_h-d2lp)/h
self.assertLessEqual(erelmax(lp_dh,lp_dhn),thr)
self.assertLessEqual(erelmax(dlp_dh,dlp_dhn),thr)
self.assertLessEqual(erelmax(d2lp_dh,d2lp_dhn),thr)
except NotImplementedError,err: print err
except: raise