def alpha_nr(self, maxit=20, init_alpha=[]):
"""
Newton-Raphson procedure for updating the Dirichlet hyperparameter alpha
:param maxit: maximum number of iterations
:param init_alpha: initial guess of alphas
:return: the updated alpha
"""
old_alpha = self.alpha.copy()
try:
M, K = self.gamma_matrix.shape
if not len(init_alpha) > 0:
init_alpha = self.gamma_matrix.mean(axis=0) / K
alpha = init_alpha.copy()
alphap = init_alpha.copy()
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())
# playing here....
z = M * pg(1, alpha.sum())
h = -M * pg(1, alpha)
c = ((grad / h).sum()) / ((1.0 / z) + (1.0 / h).sum())
alpha_change = (grad - c) / h
n_bad = (alpha_change > alpha).sum()
while n_bad > 0:
alpha_change /= 2.0
n_bad = (alpha_change > alpha).sum()
alpha_new = alpha - alpha_change
pos = np.where(alpha_new <= SMALL_NUMBER)[0]
alpha_new[pos] = SMALL_NUMBER
# if (alpha_new < 0).sum() > 0:
# init_alpha /= 10.0
# return self.alpha_nr(maxit=maxit,init_alpha = init_alpha)
diff = np.sum(np.abs(alpha - alpha_new))
alpha = alpha_new
if diff < 1e-6 and it > 1:
return alpha
except:
alpha = old_alpha
return alpha
def alpha_nr(g_term, M, maxit=100, init_alpha=[]):
# with open('./test_g.csv','w') as f:
# for g in g_term:
# f.write("{}\n".format(g))
SMALL_NUMBER = 1e-100
K = len(g_term)
if len(init_alpha) == 0:
init_alpha = np.ones_like(g_term) / K
old_alpha = init_alpha.copy()
# try:
alpha = init_alpha.copy()
# 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())
z = M * pg(1, alpha.sum())
h = -M * pg(1, alpha)
c = ((grad / h).sum()) / ((1.0 / z) + (1.0 / h).sum())
alpha_change = (grad - c) / h
# Check to make sure none of them go negative
n_bad = (alpha_change > alpha).sum()
while n_bad > 0:
alpha_change /= 2.0
n_bad = (alpha_change > alpha).sum()
# alpha_change = np.dot(np.linalg.inv(H),grad)
alpha_new = alpha - alpha_change
pos = np.where(alpha_new <= SMALL_NUMBER)[0]
alpha_new[pos] = SMALL_NUMBER
diff = np.sum(np.abs(alpha - alpha_new))
# print "Alpha: {}, it: {}".format(diff,it)
# print grad.max(),grad.argmax(),alpha[grad.argmax()],alpha_new[grad.argmax()],alpha_change[grad.argmax()],h[grad.argmax()]
alpha = alpha_new
if diff < 1e-6 and it > 10:
return alpha
# except:
# alpha = old_alpha
return alpha
def alpha_nr(self,maxit=20,init_alpha=[]): old_alpha = self.alpha.copy() try: M,K = self.gamma_matrix.shape if not len(init_alpha) > 0: init_alpha = self.gamma_matrix.mean(axis=0)/K alpha = init_alpha.copy() alphap = init_alpha.copy() 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()) # playing here.... z = M*pg(1,alpha.sum()) h = -M*pg(1,alpha) c = ((grad/h).sum())/((1.0/z) + (1.0/h).sum()) alpha_change = (grad - c)/h n_bad = (alpha_change > alpha).sum() while n_bad > 0: alpha_change/=2.0 n_bad = (alpha_change > alpha).sum() alpha_new = alpha - alpha_change pos = np.where(alpha_new <= SMALL_NUMBER)[0] alpha_new[pos] = SMALL_NUMBER # if (alpha_new < 0).sum() > 0: # init_alpha /= 10.0 # return self.alpha_nr(maxit=maxit,init_alpha = init_alpha) diff = np.sum(np.abs(alpha-alpha_new)) alpha = alpha_new if diff < 1e-6 and it > 1: return alpha except: alpha = old_alpha return alpha
def alpha_nr(self,maxit=20,init_alpha=[]):
old_alpha = self.alpha.copy()
try:
M,K = self.gamma_matrix.shape
if not len(init_alpha) > 0:
init_alpha = self.gamma_matrix.mean(axis=0)/K
alpha = init_alpha.copy()
alphap = init_alpha.copy()
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())
# playing here....
z = M*pg(1,alpha.sum())
h = -M*pg(1,alpha)
c = ((grad/h).sum())/((1.0/z) + (1.0/h).sum())
alpha_change = (grad - c)/h
n_bad = (alpha_change > alpha).sum()
while n_bad > 0:
alpha_change/=2.0
n_bad = (alpha_change > alpha).sum()
alpha_new = alpha - alpha_change
pos = np.where(alpha_new <= SMALL_NUMBER)[0]
alpha_new[pos] = SMALL_NUMBER
# if (alpha_new < 0).sum() > 0:
# init_alpha /= 10.0
# return self.alpha_nr(maxit=maxit,init_alpha = init_alpha)
diff = np.sum(np.abs(alpha-alpha_new))
alpha = alpha_new
if diff < 1e-6 and it > 1:
return alpha
except:
alpha = old_alpha
return alpha
def alpha_nr(self,maxit=20,init_alpha=[]): M,K = self.gamma_matrix.shape if not len(init_alpha) > 0: init_alpha = self.gamma_matrix.mean(axis=0)/K alpha = init_alpha.copy() alphap = init_alpha.copy() 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()) alpha_new = alpha - np.dot(np.linalg.inv(H),grad) if (alpha_new < 0).sum() > 0: init_alpha /= 10.0 return self.alpha_nr(maxit=maxit,init_alpha = init_alpha) diff = np.sum(np.abs(alpha-alpha_new)) alpha = alpha_new if diff < 1e-6 and it > 1: return alpha return alpha
def tell(self,X,fit):
'''Updates the model parameters with the function values.
'''
fit = self.utility(fit) # Map to utility values
# Compute information differentials
p0a = pg(0,self.a)
p0b = pg(0,self.b)
p0ab = pg(0,self.a+self.b)
p1a = pg(1,self.a)
p1b = pg(1,self.b)
p1ab = pg(1,self.a+self.b)
N = len(X)
dA = p0ab - p0a + sum([f*np.log(x) for x,f in zip(X,fit)])/N
dB = p0ab - p0b + sum([f*np.log(1-x) for x,f in zip(X,fit)])/N
# Compute the Riemannian metric and raise the derivatives
gdet = p1a*p1b - p1ab*(p1a+p1b)
gA = ((p1b - p1ab)*dA + p1ab*dB)/(self.a*gdet)
gB = ((p1a - p1ab)*dB + p1ab*dA)/(self.b*gdet)
# Update parameters w/ exponential map
self.a *= np.exp(self.step*gA)
self.b *= np.exp(self.step*gB)
def _train_m_step(self):
self.obj.pull()
# update beta
self.new_beta[:, :] = np.maximum(self.new_beta, EPS)
self.beta[:, :] = self.new_beta / np.sum(self.new_beta,
axis=0)[None, :]
self.new_beta[:, :] = 0
# update alpha
alpha_sum = np.sum(self.alpha)
gvec = np.sum(self.grad_alpha, axis=0)
gvec += self.num_docs * (pg(0, alpha_sum) - pg(0, self.alpha))
hvec = self.num_docs * pg(1, self.alpha)
z_0 = pg(1, alpha_sum)
c_nume = np.sum(gvec / hvec)
c_deno = 1 / z_0 + np.sum(1 / hvec)
c_0 = c_nume / c_deno
delta = (gvec - c_0) / hvec
self.alpha -= delta
self.alpha[:] = np.maximum(self.alpha, EPS)
self.grad_alpha[:, :] = 0
self.obj.push()