def preprocessData(self, ys, u=None, computeMarginal=True):
ys is not None
ys = np.array(ys)
if (ys.ndim == 2):
ys = ys[None]
else:
assert ys.ndim == 3
assert self.J1Emiss.shape[0] == ys.shape[2]
self._T = ys.shape[1]
# This is A.T @ sigInv @ y for each y, summed over each measurement
self.hy = ys.dot(self._hy).sum(axis=0)
# P( y | x ) ~ N( -0.5 * Jy, hy )
self.computeMarginal = computeMarginal
if (computeMarginal):
print('self.Jy', self.Jy)
print('self.hy', self.hy)
partition = np.vectorize(
lambda J, h: Normal.log_partition(nat_params=(-0.5 * J, h)),
signature='(n,n),(n)->()')
self.log_Zy = partition(self.Jy, self.hy)
else:
self.log_Zy = np.zeros(self.hy.shape[0])
if (u is not None):
assert u.shape == (self.T, self.D_latent)
uMask = np.isnan(u)
self.u = (u, uMask, None)
def log_partition( cls, x=None, params=None, nat_params=None, split=False ):
# Compute A( Ѳ ) - log( h( x ) )
assert ( params is None ) ^ ( nat_params is None )
# Need to multiply each partition by the length of each sequence!!!!
A, sigma, C, R, mu0, sigma0 = params if params is not None else cls.natToStandard( *nat_params )
A1, A2 = Regression.log_partition( params=( A, sigma ), split=True )
A3, A4 = Regression.log_partition( params=( C, R ), split=True )
A5, A6, A7 = Normal.log_partition( params=( mu0, sigma0 ), split=True )
if( split == True ):
return A1, A2, A3, A4, A5, A6, A7
return A1 + A2 + A3 + A4 + A5 + A6 + A7
def updateNatParams(self,
z,
n1Trans,
n2Trans,
n3Trans,
n1Emiss,
n2Emiss,
n3Emiss,
n1Init,
n2Init,
u=None,
ys=None,
computeMarginal=True):
self._D_latent = n2Init.shape[0]
self._D_obs = n1Emiss.shape[0]
self.z = z
self.J11s = [-2 * n for n in n1Trans]
self.J12s = [-n.T for n in n3Trans]
self.J22s = [-2 * n for n in n2Trans]
self.log_Zs = [
0.5 * np.linalg.slogdet(np.linalg.inv(J11))[1] for J11 in self.J11s
] if computeMarginal else [0 for _ in self.J11s]
self.J1Emiss = -2 * n1Emiss
self.Jy = -2 * n2Emiss
self._hy = n3Emiss.T
self.J0 = -2 * n1Init
self.h0 = n2Init
self.log_Z0 = Normal.log_partition(
nat_params=(-2 * self.J0, self.h0)) if computeMarginal else 0
if (ys is not None):
self.preprocessData(ys, computeMarginal=computeMarginal)
else:
self._T = None
if (u is not None):
assert u.shape == (self.T, self.D_latent)
uMask = np.isnan(u)
self.u = (u, uMask, None)
else:
uMask = np.zeros(self.T, dtype=bool)
self.u = (None, uMask, self.D_latent)
def updateNatParams(self,
n1Trans,
n2Trans,
n3Trans,
n1Emiss,
n2Emiss,
n3Emiss,
n1Init,
n2Init,
u=None,
ys=None,
computeMarginal=True):
# This doesn't exactly use natural parameters, but uses J = -2 * n1 and h = n2
self._D_latent = n1Trans.shape[0]
self._D_obs = n1Emiss.shape[0]
self.J11 = -2 * n1Trans
self.J12 = -n3Trans.T
self.J22 = -2 * n2Trans
self.log_Z = 0.5 * np.linalg.slogdet(np.linalg.inv(
self.J11))[1] if computeMarginal else 0
self.J1Emiss = -2 * n1Emiss
self.Jy = -2 * n2Emiss
self._hy = n3Emiss.T
self.J0 = -2 * n1Init
self.h0 = n2Init
self.log_Z0 = Normal.log_partition(
nat_params=(-2 * self.J0, self.h0)) if computeMarginal else 0
if (ys is not None):
self.preprocessData(ys, computeMarginal=computeMarginal)
else:
self._T = None
if (u is not None):
assert u.shape == (self.T, self.D_latent)
uMask = np.isnan(u)
self.u = (u, uMask, None)
else:
uMask = np.zeros(self.T, dtype=bool)
self.u = (None, uMask, self.D_latent)
self.fromNatural = True
def emissionProb(self, t, forward=False, ys=None):
# P( y_t | x_t ) as a function of x_t
J = self.Jy
if (ys is None):
h = self.hy[t]
log_Z = self.log_Zy[t]
else:
# A.T @ sigInv @ y
h = np.einsum('ji,mj->i', self._hy, ys[:, t])
log_Z = Normal.log_partition(nat_params=(-0.5 * self.Jy, h))
if (forward):
return J, h, np.array(log_Z)
# Because this is before the integration step
return self.alignOnUpper(J, h, log_Z)
def log_marginalFromAlphaBeta(cls, alpha, beta):
Ja, ha, log_Za = alpha
Jb, hb, log_Zb = beta
return Normal.log_partition(nat_params=(-0.5 * (Ja + Jb),
(ha + hb))) - (log_Za + log_Zb)