def test_diag_inv_speed(self):
A = torch.eye(1000) * torch.randn(1000)
s1 = time.time()
torch.inverse(A)
d1 = time.time() - s1
s2 = time.time()
linalg.diag_inv(A)
d2 = time.time() - s2
# According to my tests, d1 is roughly 2 orders of magnitude slower.
self.assertTrue(d1 > d2)
def neg_log_likelihood(self, y, Lambda, Psi_diag):
"""Appendix A (p. 5) in Ghahramani and Hinton (1996).
:param y: (n x p)-dimensional observations.
:param Lambda: Current value for Lambda parameter.
:param Psi_diag: Current value for Psi parameter.
:return: The negative log likelihood of the parameters given y.
"""
assert len(Psi_diag.shape) == 1
k = self.latent_dim
p, n = y.shape
rterm_sum = 0
for yi in y.t():
Ezi = self.E_z_given_y(Lambda, Psi_diag, yi)
Ezzi = self.E_zzT_given_y(Lambda, Psi_diag, yi, k)
Psi_inv = diag(LA.diag_inv(Psi_diag))
A = 1/2. * yi @ Psi_inv @ yi
B = yi @ Psi_inv @ Lambda @ Ezi
C = 1/2. * tr(Lambda.t() @ Psi_inv @ Lambda @ Ezzi)
rterm_sum += A - B + C
logdet = -n/2. * log(det(diag(Psi_diag)))
ll = (logdet - rterm_sum).item()
nll = -ll
return nll
def neg_log_likelihood(self, y, Lambda=None, Psi_diag=None):
"""Appendix A (p. 5) in Ghahramani and Hinton (1996).
:param y: (n x p)-dimensional observations.
:param Lambda: Current value for Lambda parameter.
:param Psi_diag: Current value for Psi parameter.
:return: The negative log likelihood of the parameters given y.
"""
p, n = y.shape
k = self.latent_dim
if Lambda is None and Psi_diag is None:
Lambda, Psi_diag = self.tile_params()
Ez = self.E_z_given_y(Lambda, Psi_diag, y).t()
Ezz = self.E_zzT_given_y(Lambda, Psi_diag, y, k).t()
inv_Psi = diag(LA.diag_inv(Psi_diag))
A = 1/2. * diag(y.t() @ inv_Psi @ y)
B = diag(y.t() @ inv_Psi @ Lambda @ Ez.t())
C = 1/2. * tr(Lambda.t() @ inv_Psi @ Lambda @ Ezz)
rterm_sum = (A - B).sum() + C
logdet = -n/2. * log(det(diag(Psi_diag)))
ll = (logdet - rterm_sum).item()
nll = -ll
return nll
def test_diag_inv_accuracy(self):
A = torch.eye(20) * torch.randn(20)
A_diag = linalg.diag_inv(A)
self.assertTrue(
torch.allclose(A @ A_diag, torch.eye(len(A)), atol=0.01))