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 _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 _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