def _rmll_gradient(self,
optSig02=True,
optSig12=True,
optSign2=True,
optBeta=True):
self._updateConstants()
self._updateApproximation()
K0 = self._K0
K1 = self._K1
m = self._mean
ttau = self._ttau
tnu = self._tnu
Ssq = self._Ssq
LnSsq = self._LnSsq
LnSsqK = self._LnSsqK
Smtnu = ttau * m - tnu
b = Smtnu - dot(LnSsq.T, dot(LnSsqK, Smtnu))
ret = []
if optSig02:
r = 0.5 * (dot(b, dot(K0, b)) - trace2(LnSsq.T, dot(LnSsq, K0)))
ret.append(r)
if optSig12:
r = 0.5 * (dot(b, dot(K1, b)) - trace2(LnSsq.T, dot(LnSsq, K1)))
ret.append(r)
if optSign2:
r = 0.5 * (dot(b, b) - trace2(LnSsq.T, LnSsq))
ret.append(r)
if optBeta:
r = -dot(b, self._X)
ret += list(r)
ret = NP.array(ret)
assert NP.all(NP.isfinite(
ret)), 'Not finite regular marginal loglikelihood gradient.'
return ret
def _rmll_gradient(self,
optSig02=True,
optSig12=True,
optSign2=True,
optBeta=True):
self._updateConstants()
self._updateApproximation()
m = self._mean
H = self._H
V = self._V
ttau = self._ttau
tnu = self._tnu
G0 = self._G0
G1 = self._G1
Smtnu = ttau * m - tnu
KSmtnu = self._rdotK(Smtnu)
b = Smtnu - V * KSmtnu + dot(H.T, dot(H, KSmtnu))
ret = []
if optSig02:
r = 0.5*(dot(b, dot(G0, dot(G0.T, b))) - trace2(ddot(V, G0, left=True), G0.T)\
+ trace2(H.T, dot(dot(H, G0), G0.T)))
ret.append(r)
if optSig12:
r = 0.5*(dot(b, dot(G1, dot(G1.T, b))) - trace2(ddot(V, G1, left=True), G1.T)\
+ trace2(H.T, dot(dot(H, G1), G1.T)))
ret.append(r)
if optSign2:
r = 0.5*(dot(b, b) - NP.sum(V)\
+ trace2(H.T, H))
ret.append(r)
if optBeta:
ret += list(-dot(b, self._X))
return NP.array(ret)
def _rmll_gradient(self, optSig02=True, optSig12=True, optSign2=True, optBeta=True):
self._updateConstants()
self._updateApproximation()
m = self._mean
H = self._H
V = self._V
ttau = self._ttau
tnu = self._tnu
G0 = self._G0
G1 = self._G1
Smtnu = ttau*m - tnu
KSmtnu = self._rdotK(Smtnu)
b = Smtnu - V*KSmtnu + dot(H.T, dot(H, KSmtnu))
ret = []
if optSig02:
r = 0.5*(dot(b, dot(G0, dot(G0.T, b))) - trace2(ddot(V, G0, left=True), G0.T)\
+ trace2(H.T, dot(dot(H, G0), G0.T)))
ret.append(r)
if optSig12:
r = 0.5*(dot(b, dot(G1, dot(G1.T, b))) - trace2(ddot(V, G1, left=True), G1.T)\
+ trace2(H.T, dot(dot(H, G1), G1.T)))
ret.append(r)
if optSign2:
r = 0.5*(dot(b, b) - NP.sum(V)\
+ trace2(H.T, H))
ret.append(r)
if optBeta:
ret += list(-dot(b, self._X))
return NP.array(ret)
def _rmll_gradient(self, optSig02=True, optSig12=True, optSign2=True, optBeta=True):
self._updateConstants()
self._updateApproximation()
K0 = self._K0
K1 = self._K1
m = self._mean
ttau = self._ttau
tnu = self._tnu
Ssq = self._Ssq
LnSsq = self._LnSsq
LnSsqK = self._LnSsqK
Smtnu = ttau*m - tnu
b = Smtnu - dot(LnSsq.T, dot(LnSsqK, Smtnu) )
ret = []
if optSig02:
r = 0.5*(dot(b,dot(K0,b)) - trace2(LnSsq.T, dot(LnSsq, K0)))
ret.append(r)
if optSig12:
r = 0.5*(dot(b,dot(K1,b)) - trace2(LnSsq.T, dot(LnSsq, K1)))
ret.append(r)
if optSign2:
r = 0.5*(dot(b,b) - trace2(LnSsq.T, LnSsq))
ret.append(r)
if optBeta:
r = -dot(b, self._X)
ret += list(r)
ret = NP.array(ret)
assert NP.all(NP.isfinite(ret)), 'Not finite regular marginal loglikelihood gradient.'
return ret
def _rmll_gradient(self, optSig02=True, optSig12=True, optSign2=True, optBeta=True):
self._updateConstants()
self._updateApproximation()
W = self._W
Wsq = self._Wsq
f = self._f
K = self._K
K0 = self._K0
K1 = self._K1
m = self._mean
a = self._a
Ln = self._Ln
X = self._X
LnWsq = stl(Ln, NP.diag(Wsq))
LnWsqK = dot(LnWsq, K)
d = self._dKn()
h = self._likelihood.third_derivative_log(f)
diags = (d - dotd(LnWsqK.T, LnWsqK)) * h
ret = []
if optSig02:
dK0a = dot(K0, a)
dF0 = dK0a - dot(LnWsqK.T, dot(LnWsq, dK0a))
r = dot(a, dF0) - dot(a, dF0) + 0.5*dot(a, dK0a)\
+ 0.5*NP.sum( diags*dF0 )\
- 0.5*trace2( LnWsq.T, dot(LnWsq,K0) )
ret.append(r)
if optSig12:
dK1a = dot(K1, a)
dF1 = dK1a - dot(LnWsqK.T, dot(LnWsq, dK1a))
r = dot(a, dF1) - dot(a, dF1) + 0.5*dot(a, dK1a)\
+ 0.5*NP.sum( diags*dF1 )\
- 0.5*trace2( LnWsq.T, dot(LnWsq,K1) )
ret.append(r)
if optSign2:
dFn = a - dot(LnWsqK.T, dot(LnWsq, a))
r = dot(a, dFn) - dot(a, dFn) + 0.5*dot(a, a)\
+ 0.5*NP.sum( diags*dFn )\
- 0.5*trace2( LnWsq.T, LnWsq )
ret.append(r)
if optBeta:
dFmb = -dot(LnWsqK.T, dot(LnWsq, X))
dFb = dFmb+X
r = dot(a, dFb) - dot(a, dFmb)\
+ 0.5*NP.sum( diags*dFb.T, 1)
ret += list(r)
ret = NP.array(ret)
assert NP.all(NP.isfinite(ret)), 'Not finite regular marginal loglikelihood gradient.'
return ret
def _rmll_gradient(self, optSig02=True, optSig12=True, optSign2=True, optBeta=True):
self._updateConstants()
self._updateApproximation()
(f,a)=(self._f,self._a)
(W,Wsq) = (self._W,self._Wsq)
Lk = self._Lk
m = self._mean
X = self._X
G0 = self._G0
G1 = self._G1
sign2 = self._sign2
G01 = self._G01
#g = self._likelihood.gradient_log(f)
#a==g
h = self._likelihood.third_derivative_log(f)
V = W/self._A
d = self._dKn()
G01tV = ddot(G01.T, V, left=False)
H = stl(Lk, G01tV)
dkH = self._ldotK(H)
diags = (d - sign2**2 * V - dotd(G01, dot(dot(G01tV, G01), G01.T))\
- 2.0*sign2*dotd(G01, G01tV) + dotd(dkH.T, dkH)) * h
ret = []
if optSig02:
dK0a = dot(G0, dot(G0.T, a))
t = V*dK0a - dot(H.T, dot(H, dK0a))
dF0 = dK0a - self._rdotK(t)
LkG01VG0 = dot(H, G0)
VG0 = ddot(V, G0, left=True)
ret0 = dot(a, dF0) - 0.5*dot(a, dK0a) + dot(f-m, t)\
+ 0.5*NP.sum( diags*dF0 )\
+ -0.5*trace2(VG0, G0.T) + 0.5*trace2( LkG01VG0.T, LkG01VG0 )
ret.append(ret0)
if optSig12:
dK1a = dot(G1, dot(G1.T, a))
t = V*dK1a - dot(H.T, dot(H, dK1a))
dF1 = dK1a - self._rdotK(t)
LkG01VG1 = dot(H, G1)
VG1 = ddot(V, G1, left=True)
ret1 = dot(a, dF1)- 0.5*dot(a, dK1a) + dot(f-m, t)\
+ 0.5*NP.sum( diags*dF1 )\
+ -0.5*trace2(VG1, G1.T) + 0.5*trace2( LkG01VG1.T, LkG01VG1 )
ret.append(ret1)
if optSign2:
t = V*a - dot(H.T, dot(H, a))
dFn = a - self._rdotK(t)
retn = dot(a, dFn)- 0.5*dot(a, a) + dot(f-m, t)\
+ 0.5*NP.sum( diags*dFn )\
+ -0.5*NP.sum(V) + 0.5*trace2( H.T, H )
ret.append(retn)
if optBeta:
t = ddot(V, X, left=True) - dot(H.T, dot(H, X))
dFbeta = X - self._rdotK(t)
retbeta = dot(a, dFbeta) + dot(f-m, t)
for i in range(dFbeta.shape[1]):
retbeta[i] += 0.5*NP.sum( diags*dFbeta[:,i] )
ret.extend(retbeta)
ret = NP.array(ret)
assert NP.all(NP.isfinite(ret)), 'Not finite regular marginal loglikelihood gradient.'
return ret
def _rmll_gradient(self,
optSig02=True,
optSig12=True,
optSign2=True,
optBeta=True):
self._updateConstants()
self._updateApproximation()
W = self._W
Wsq = self._Wsq
f = self._f
K = self._K
K0 = self._K0
K1 = self._K1
m = self._mean
a = self._a
Ln = self._Ln
X = self._X
LnWsq = stl(Ln, NP.diag(Wsq))
LnWsqK = dot(LnWsq, K)
d = self._dKn()
h = self._likelihood.third_derivative_log(f)
diags = (d - dotd(LnWsqK.T, LnWsqK)) * h
ret = []
if optSig02:
dK0a = dot(K0, a)
dF0 = dK0a - dot(LnWsqK.T, dot(LnWsq, dK0a))
r = dot(a, dF0) - dot(a, dF0) + 0.5*dot(a, dK0a)\
+ 0.5*NP.sum( diags*dF0 )\
- 0.5*trace2( LnWsq.T, dot(LnWsq,K0) )
ret.append(r)
if optSig12:
dK1a = dot(K1, a)
dF1 = dK1a - dot(LnWsqK.T, dot(LnWsq, dK1a))
r = dot(a, dF1) - dot(a, dF1) + 0.5*dot(a, dK1a)\
+ 0.5*NP.sum( diags*dF1 )\
- 0.5*trace2( LnWsq.T, dot(LnWsq,K1) )
ret.append(r)
if optSign2:
dFn = a - dot(LnWsqK.T, dot(LnWsq, a))
r = dot(a, dFn) - dot(a, dFn) + 0.5*dot(a, a)\
+ 0.5*NP.sum( diags*dFn )\
- 0.5*trace2( LnWsq.T, LnWsq )
ret.append(r)
if optBeta:
dFmb = -dot(LnWsqK.T, dot(LnWsq, X))
dFb = dFmb + X
r = dot(a, dFb) - dot(a, dFmb)\
+ 0.5*NP.sum( diags*dFb.T, 1)
ret += list(r)
ret = NP.array(ret)
assert NP.all(NP.isfinite(
ret)), 'Not finite regular marginal loglikelihood gradient.'
return ret
def _rmll_gradient(self,
optSig02=True,
optSig12=True,
optSign2=True,
optBeta=True):
self._updateConstants()
self._updateApproximation()
(f, a) = (self._f, self._a)
(W, Wsq) = (self._W, self._Wsq)
Lk = self._Lk
m = self._mean
X = self._X
G0 = self._G0
G1 = self._G1
sign2 = self._sign2
G01 = self._G01
#g = self._likelihood.gradient_log(f)
#a==g
h = self._likelihood.third_derivative_log(f)
V = W / self._A
d = self._dKn()
G01tV = ddot(G01.T, V, left=False)
H = stl(Lk, G01tV)
dkH = self._ldotK(H)
diags = (d - sign2**2 * V - dotd(G01, dot(dot(G01tV, G01), G01.T))\
- 2.0*sign2*dotd(G01, G01tV) + dotd(dkH.T, dkH)) * h
ret = []
if optSig02:
dK0a = dot(G0, dot(G0.T, a))
t = V * dK0a - dot(H.T, dot(H, dK0a))
dF0 = dK0a - self._rdotK(t)
LkG01VG0 = dot(H, G0)
VG0 = ddot(V, G0, left=True)
ret0 = dot(a, dF0) - 0.5*dot(a, dK0a) + dot(f-m, t)\
+ 0.5*NP.sum( diags*dF0 )\
+ -0.5*trace2(VG0, G0.T) + 0.5*trace2( LkG01VG0.T, LkG01VG0 )
ret.append(ret0)
if optSig12:
dK1a = dot(G1, dot(G1.T, a))
t = V * dK1a - dot(H.T, dot(H, dK1a))
dF1 = dK1a - self._rdotK(t)
LkG01VG1 = dot(H, G1)
VG1 = ddot(V, G1, left=True)
ret1 = dot(a, dF1)- 0.5*dot(a, dK1a) + dot(f-m, t)\
+ 0.5*NP.sum( diags*dF1 )\
+ -0.5*trace2(VG1, G1.T) + 0.5*trace2( LkG01VG1.T, LkG01VG1 )
ret.append(ret1)
if optSign2:
t = V * a - dot(H.T, dot(H, a))
dFn = a - self._rdotK(t)
retn = dot(a, dFn)- 0.5*dot(a, a) + dot(f-m, t)\
+ 0.5*NP.sum( diags*dFn )\
+ -0.5*NP.sum(V) + 0.5*trace2( H.T, H )
ret.append(retn)
if optBeta:
t = ddot(V, X, left=True) - dot(H.T, dot(H, X))
dFbeta = X - self._rdotK(t)
retbeta = dot(a, dFbeta) + dot(f - m, t)
for i in range(dFbeta.shape[1]):
retbeta[i] += 0.5 * NP.sum(diags * dFbeta[:, i])
ret.extend(retbeta)
ret = NP.array(ret)
assert NP.all(NP.isfinite(
ret)), 'Not finite regular marginal loglikelihood gradient.'
return ret
