def _predict(self, meanstar, kstar, kstarstar, prob):
self._updateConstants()
self._updateApproximation()
m = self._mean
tnu = self._tnu
Lk = self._Lk
H = self._H
V = self._V
Ktnu = self._rdotK(tnu)
mKtnu = m + Ktnu
Vkstar = ddot(V, kstar, left=True)
Hkstar = dot(H, kstar)
mustar = meanstar + dot(kstar.T,tnu) - dot(Vkstar.T, mKtnu) + dot(Hkstar.T, dot(H, mKtnu))
if prob is False:
if nom > 0.0:
return +1.0
return -1.0
sig2star = kstarstar - dotd(kstar.T,Vkstar)\
+ dotd(dot(Hkstar.T, H), kstar) + self._sign2
return LH.probit_sigmoid(mustar/NP.sqrt(1.0 + sig2star))
def _predict(self, meanstar, kstar, kstarstar, prob):
self._updateConstants()
self._updateApproximation()
m = self._mean
tnu = self._tnu
Lk = self._Lk
H = self._H
V = self._V
Ktnu = self._rdotK(tnu)
mKtnu = m + Ktnu
Vkstar = ddot(V, kstar, left=True)
Hkstar = dot(H, kstar)
mustar = meanstar + dot(kstar.T, tnu) - dot(Vkstar.T, mKtnu) + dot(
Hkstar.T, dot(H, mKtnu))
if prob is False:
if nom > 0.0:
return +1.0
return -1.0
sig2star = kstarstar - dotd(kstar.T,Vkstar)\
+ dotd(dot(Hkstar.T, H), kstar) + self._sign2
return LH.probit_sigmoid(mustar / NP.sqrt(1.0 + sig2star))
def _updateApproximationEnd(self, ttau, tnu, tau_, nu_):
self._ttau = ttau
self._tnu = tnu
self._tau_ = tau_
self._nu_ = nu_
self._V = self._calculateV(ttau, self._sign2)
self._Lk = self._calculateLk(self._G01, self._V)
self._H = stl(self._Lk, ddot(self._G01.T, self._V, left=False))
def _updateApproximationEnd(self, ttau, tnu, tau_, nu_):
self._ttau = ttau
self._tnu = tnu
self._tau_ = tau_
self._nu_ = nu_
self._V = self._calculateV(ttau, self._sign2)
self._Lk = self._calculateLk(self._G01, self._V)
self._H = stl(self._Lk, ddot(self._G01.T, self._V, left=False))
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 _calculateUAa(self, b, W):
A = 1.0 + W*self._sign2
V = W/A
Lk = self._calculateLk(self._G01, V)
Gtb = dot(self._G01.T, b)
GtV = ddot(self._G01.T, V, left=False)
LtLGtV = stu(Lk.T, stl(Lk, GtV))
LtLGtVG = dot(LtLGtV, self._G01)
bn = self._sign2*b
a = b + dot(dot(GtV.T, LtLGtVG) - GtV.T, Gtb)\
+ dot(GtV.T, dot(LtLGtV, bn)) - V*bn
return a
def _calculateUAa(self, b, W):
A = 1.0 + W * self._sign2
V = W / A
Lk = self._calculateLk(self._G01, V)
Gtb = dot(self._G01.T, b)
GtV = ddot(self._G01.T, V, left=False)
LtLGtV = stu(Lk.T, stl(Lk, GtV))
LtLGtVG = dot(LtLGtV, self._G01)
bn = self._sign2 * b
a = b + dot(dot(GtV.T, LtLGtVG) - GtV.T, Gtb)\
+ dot(GtV.T, dot(LtLGtV, bn)) - V*bn
return a
def _calculateSig2Mu(self, ttau, tnu, mean):
sign2 = self._sign2
V = self._calculateV(ttau, sign2)
G01 = self._G01
Lk = self._calculateLk(G01, V)
G01tV = ddot(G01.T, V, left=False)
H = stl(Lk, G01tV)
HK = self._ldotK(H)
sig2 = self._dKn() - sign2**2*V - dotd(G01, dot(dot(G01tV, G01), G01.T))\
- 2.0*sign2*dotd(G01, G01tV) + dotd(HK.T, HK)
assert NP.all(NP.isfinite(sig2)), 'sig2 should be finite.'
u = self._mean + self._rdotK(tnu)
mu = u - self._rdotK(V*u) + self._rdotK(H.T.dot(H.dot(u)))
assert NP.all(NP.isfinite(mu)), 'mu should be finite.'
return (sig2, mu)
def _calculateSig2Mu(self, ttau, tnu, mean):
sign2 = self._sign2
V = self._calculateV(ttau, sign2)
G01 = self._G01
Lk = self._calculateLk(G01, V)
G01tV = ddot(G01.T, V, left=False)
H = stl(Lk, G01tV)
HK = self._ldotK(H)
sig2 = self._dKn() - sign2**2*V - dotd(G01, dot(dot(G01tV, G01), G01.T))\
- 2.0*sign2*dotd(G01, G01tV) + dotd(HK.T, HK)
assert NP.all(NP.isfinite(sig2)), 'sig2 should be finite.'
u = self._mean + self._rdotK(tnu)
mu = u - self._rdotK(V * u) + self._rdotK(H.T.dot(H.dot(u)))
assert NP.all(NP.isfinite(mu)), 'mu should be finite.'
return (sig2, mu)
def _calculateLk(self, G01, D):
Bk = dot(G01.T, ddot(D, G01, left=True))
Bk[NP.diag_indices_from(Bk)] += 1.0
Lk = cholesky(Bk, lower=True, check_finite=False)
return Lk
def _calculateLn(self, K, D):
Bn = ddot(D, ddot(K, D, left=False), left=True)
Bn[NP.diag_indices_from(Bn)] += 1.0
Ln = cholesky(Bn, lower=True, check_finite=False)
return Ln
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 _calculateLk(self, G01, D):
Bk = dot(G01.T, ddot(D, G01, left=True))
Bk[NP.diag_indices_from(Bk)] += 1.0
Lk = cholesky(Bk, lower=True, check_finite=False)
return Lk
def _calculateLn(self, K, D):
Bn = ddot(D, ddot(K, D, left=False), left=True)
Bn[NP.diag_indices_from(Bn)] += 1.0
Ln = cholesky(Bn, lower=True, check_finite=False)
return Ln
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
