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 _predict(self, meanstar, kstar, kstarstar, prob):
self._updateConstants()
self._updateApproximation()
m = self._mean
tnu = self._tnu
K = self._K
Ln = self._Ln
Ssq = self._Ssq
LnSsq = self._LnSsq
LnSsqkstar = dot(LnSsq, kstar)
LnSsqK = self._LnSsqK
mustar = meanstar + dot(kstar.T, tnu) - dot(
LnSsqkstar.T,
dot(LnSsq, m) + dot(LnSsqK, tnu))
if prob is False:
if nom > 0.0:
return +1.0
return -1.0
sig2star = kstarstar - dotd(dot(LnSsqkstar.T, LnSsq),
kstar) + self._sign2
return LH.probit_sigmoid(mustar / NP.sqrt(1.0 + sig2star))
def _xMeanCov(self, xX, xG0, xG1):
'''
Computes the mean and covariance between the latent variables.
You can provide one or n latent variables.
----------------------------------------------------------------------------
Input:
xX : [D] array of fixed effects or
[n*D] array of fixed effects for each latent variable
xG0 : [k0] array of random effects or
[n*k0] array of random effects for each latent variable
xG1 : [k1] array of random effects or
[n*k1] array of random effects for each latent variable
-----------------------------------------------------------------------------
Output:
xmean : [n*D] means of the provided latent variables
xK01 : [N] or [n*N] covariance between provided and prior latent
variables
xkk : float or [n] covariance between provided latent variables
-----------------------------------------------------------------------------
'''
xmean = xX.dot(self._beta)
if xG0 is not None:
xK01 = self._sig02*(xG0.dot(self._G0.T))
else:
if len(xX.shape)==1:
xK01 = NP.zeros(self._N)
else:
xK01 = NP.zeros((xX.shape[0], self._N))
if len(xG0.shape)==1:
xkk = self._sig02 * xG0.dot(xG0) + self._sign2
else:
xkk = self._sig02 * dotd(xG0,xG0.T) + self._sign2
if xG1 is not None:
xK01 += self._sig12*(xG1.dot(self._G1.T))
if len(xG0.shape)==1:
xkk += self._sig12 * xG1.dot(xG1)
else:
xkk += self._sig12 * dotd(xG1,xG1.T)
return (xmean,xK01,xkk)
def _xMeanCov(self, xX, xG0, xG1):
'''
Computes the mean and covariance between the latent variables.
You can provide one or n latent variables.
----------------------------------------------------------------------------
Input:
xX : [D] array of fixed effects or
[n*D] array of fixed effects for each latent variable
xG0 : [k0] array of random effects or
[n*k0] array of random effects for each latent variable
xG1 : [k1] array of random effects or
[n*k1] array of random effects for each latent variable
-----------------------------------------------------------------------------
Output:
xmean : [n*D] means of the provided latent variables
xK01 : [N] or [n*N] covariance between provided and prior latent
variables
xkk : float or [n] covariance between provided latent variables
-----------------------------------------------------------------------------
'''
xmean = xX.dot(self._beta)
if xG0 is not None:
xK01 = self._sig02 * (xG0.dot(self._G0.T))
else:
if len(xX.shape) == 1:
xK01 = NP.zeros(self._N)
else:
xK01 = NP.zeros((xX.shape[0], self._N))
if len(xG0.shape) == 1:
xkk = self._sig02 * xG0.dot(xG0) + self._sign2
else:
xkk = self._sig02 * dotd(xG0, xG0.T) + self._sign2
if xG1 is not None:
xK01 += self._sig12 * (xG1.dot(self._G1.T))
if len(xG0.shape) == 1:
xkk += self._sig12 * xG1.dot(xG1)
else:
xkk += self._sig12 * dotd(xG1, xG1.T)
return (xmean, xK01, xkk)
def _calculateSig2Mu(self, ttau, tnu, mean):
Ssq = NP.sqrt(ttau)
Ln = self._calculateLn(self._K, Ssq)
LnSsq = stl(Ln, NP.diag(Ssq))
V = dot(LnSsq,self._K)
sig2 = self._dKn() - dotd(V.T,V)
mu = mean + dot(self._K,tnu) - dot(V.T,dot(LnSsq,mean)) - dot(V.T,dot(V,tnu))
return (sig2, mu)
def _calculateSig2Mu(self, ttau, tnu, mean):
Ssq = NP.sqrt(ttau)
Ln = self._calculateLn(self._K, Ssq)
LnSsq = stl(Ln, NP.diag(Ssq))
V = dot(LnSsq, self._K)
sig2 = self._dKn() - dotd(V.T, V)
mu = mean + dot(self._K, tnu) - dot(V.T, dot(LnSsq, mean)) - dot(
V.T, dot(V, tnu))
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 _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 _predict(self, meanstar, kstar, kstarstar, prob):
self._updateConstants()
self._updateApproximation()
m = self._mean
tnu = self._tnu
K = self._K
Ln = self._Ln
Ssq = self._Ssq
LnSsq = self._LnSsq
LnSsqkstar = dot(LnSsq, kstar)
LnSsqK = self._LnSsqK
mustar = meanstar + dot(kstar.T,tnu) - dot(LnSsqkstar.T, dot(LnSsq,m) + dot(LnSsqK,tnu))
if prob is False:
if nom > 0.0:
return +1.0
return -1.0
sig2star = kstarstar - dotd(dot(LnSsqkstar.T, LnSsq), kstar) + self._sign2
return LH.probit_sigmoid(mustar/NP.sqrt(1.0 + sig2star))
def _dKn(self):
d = self._sig02 * dotd(self._G0, self._G0.T) + self._sign2
if self._G1 is not None:
d += self._sig12 * dotd(self._G1, self._G1.T)
return d
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 _dKn(self):
d = self._sig02 * dotd(self._G0, self._G0.T) + self._sign2
if self._G1 is not None:
d += self._sig12 * dotd(self._G1, self._G1.T)
return d
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