Skip to content

Alternative method to calculate Hessian's inverse (Blei et al. 2003). #8

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
perdaug wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Alternative method to calculate Hessian's inverse (Blei et al. 2003). #8

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
18 changes: 17 additions & 1 deletion code/lda.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -475,7 +475,10 @@ def alpha_nr(self,maxit=20,init_alpha=[]):
g_term = (psi(self.gamma_matrix) - psi(self.gamma_matrix.sum(axis=1))[:,None]).sum(axis=0)
for it in range(maxit):
grad = M *(psi(alpha.sum()) - psi(alpha)) + g_term
H = -M*np.diag(pg(1,alpha)) + M*pg(1,alpha.sum())
h = -M * pg(1,alpha)
z = M*pg(1,alpha.sum())
H = np.diag(h) + z
H_inverse = self.hessian_inverse(h, z)
alpha_new = alpha - np.dot(np.linalg.inv(H),grad)
if (alpha_new < 0).sum() > 0:
init_alpha /= 10.0
Expand All @@ -487,6 +490,19 @@ def alpha_nr(self,maxit=20,init_alpha=[]):
return alpha
return alpha

def hessian_inverse(self, h, z):
"""
Hessian inversion for optimising the LDA implementation (Blei 2003).
"""
z_inverse = 1 / z
diag_h_inverse = np.diag(1 / h)

# Matrix inversion lemma (Minka 2000).
H_inverse = diag_h_inverse - \
((diag_h_inverse * diag_h_inverse) / \
(z_inverse + diag_h_inverse))
return H_inverse

# TODO: tidy up and comment this function
def e_step(self):
temp_beta = np.zeros((self.K,self.n_words))
Expand Down