def lml_derivative_over_cov(self, dQS):
from numpy_sugar.linalg import cho_solve, ddot, dotd
self._update()
L = self._posterior.L()
Q = self._posterior.cov["QS"][0][0]
ttau = self._site.tau
teta = self._site.eta
diff = teta - ttau * self._posterior.mean
v0 = dot(dQS[0][0], dQS[1] * dot(dQS[0][0].T, diff))
v1 = ttau * dot(Q, cho_solve(L, dot(Q.T, diff)))
dlml = 0.5 * dot(diff, v0)
dlml -= dot(v0, v1)
dlml += 0.5 * dot(v1, dot(dQS[0][0], dQS[1] * dot(dQS[0][0].T, v1)))
dqs = ddot(dQS[1], dQS[0][0].T, left=True)
diag = dotd(dQS[0][0], dqs)
dlml -= 0.5 * sum(ttau * diag)
tmp = cho_solve(L, dot(ddot(Q.T, ttau, left=False), dQS[0][0]))
dlml += 0.5 * sum(ttau * dotd(Q, dot(tmp, dqs)))
return dlml
def compute(self, covariates, X):
A = self._A
L = self._L
Q = self._Q
C = self._C
AMs0 = ddot(A, covariates, left=True)
dens0 = AMs0 - ddot(A, dot(Q, cho_solve(L, dot(Q.T, AMs0))), left=True)
noms0 = dot(self._beta_nom, covariates)
AMs1 = ddot(A, X, left=True)
dens1 = AMs1 - ddot(A, dot(Q, cho_solve(L, dot(Q.T, AMs1))), left=True)
noms1 = dot(self._beta_nom, X)
row00 = sum(covariates * dens0, 0)
row01 = sum(covariates * dens1, 0)
row11 = sum(X * dens1, 0)
betas0 = noms0 * row11
betas0 -= noms1 * row01
betas1 = -noms0 * row01
betas1 += noms1 * row00
denom = row00 * row11
denom -= row01**2
with errstate(divide='ignore', invalid='ignore'):
betas0 /= denom
betas1 /= denom
betas0 = nan_to_num(betas0)
betas1 = nan_to_num(betas1)
ms = dot(covariates, betas0[newaxis, :])
ms += X * betas1
QBiQtCteta = self._QBiQtCteta
teta = self._teta
Am = ddot(A, ms, left=True)
w4 = dot(C * teta, ms)
w4 -= dot(QBiQtCteta, Am)
QBiQtAm = dot(Q, cho_solve(L, dot(Q.T, Am)))
w5 = -sum(Am * ms, 0)
w5 += sum(Am * QBiQtAm, 0)
w5 /= 2
lmls = self._lml_const + w4 + w5
return (lmls, betas1)
def _QBiQtAm(self):
Q = self._Q
L = self._L()
A = self._A()
m = self.m()
return dot(Q, cho_solve(L, dot(Q.T, A * m)))
def _optimal_tbeta_denom(self):
L = self._L()
Q = self._Q
AM = ddot(self._A(), self._tM, left=True)
QBiQtAM = dot(Q, cho_solve(L, dot(Q.T, AM)))
v = dot(self._tM.T, AM) - dot(AM.T, QBiQtAM)
if not is_all_finite(v):
raise ValueError("tbeta_denom should not be %s." % str(v))
return v
def LQt(self):
from numpy_sugar.linalg import cho_solve
if self._LQt_cache is not None:
return self._LQt_cache
L = self.L()
Q = self._cov["QS"][0][0]
self._LQt_cache = cho_solve(L, Q.T)
return self._LQt_cache
def lml(self):
from numpy_sugar.linalg import cho_solve
if self._cache["lml"] is not None:
return self._cache["lml"]
self._update()
L = self._posterior.L()
Q, S = self._posterior.cov["QS"]
Q = Q[0]
ttau = self._site.tau
teta = self._site.eta
ctau = self._cav["tau"]
ceta = self._cav["eta"]
m = self._posterior.mean
TS = ttau + ctau
lml = [
-log(L.diagonal()).sum(),
-0.5 * sum(log(S)),
# lml += 0.5 * sum(log(ttau)),
+0.5 * dot(teta, dot(Q, cho_solve(L, dot(Q.T, teta)))),
-0.5 * dot(teta, teta / TS),
+dot(m, teta) - 0.5 * dot(m, ttau * m),
-0.5 *
dot(m * ttau, dot(Q, cho_solve(L, dot(Q.T, 2 * teta - ttau * m)))),
+sum(self._moments["log_zeroth"]),
+0.5 * sum(log(TS)),
# lml -= 0.5 * sum(log(ttau)),
-0.5 * sum(log(ctau)),
+0.5 * dot(ceta / TS, ttau * ceta / ctau - 2 * teta),
]
lml = fsum(lml)
if not isfinite(lml):
raise ValueError("LML should not be %f." % lml)
self._cache["lml"] = lml
return lml
def lml_derivative_over_mean(self, dm):
from numpy_sugar.linalg import cho_solve
self._update()
L = self._posterior.L()
Q = self._posterior.cov["QS"][0][0]
ttau = self._site.tau
teta = self._site.eta
diff = teta - ttau * self._posterior.mean
dlml = dot(diff, dm)
dlml -= dot(diff, dot(Q, cho_solve(L, dot(Q.T, (ttau * dm.T).T))))
return dlml
def test_cho_solve():
random = RandomState(0)
L = random.randn(2, 2)
b = random.randn(2)
assert_allclose(cho_solve(L, b), [0.82259811, -0.40095633])
def _QBiQtCteta(self):
Q = self._Q
L = self._L()
C = self._C()
teta = self._sitelik_eta
return dot(Q, cho_solve(L, dot(Q.T, C * teta)))
def _BiQt(self):
Q = self._Q
return cho_solve(self._L(), Q.T)
