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bayeslex_opt.py
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bayeslex_opt.py
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import numpy as np
import admm
from bayeslex_stats import getCoCountsTwoLex, getEMu, computeS, estimateK
# slsqp only
import scipy as sp
from bayeslex_stats import e_co_diff
class BayesLexOptimizer:
def __init__(self,x,pos_lex,neg_lex,prefilter=False,max_k=0.9,verbosity=0):
if prefilter: #try to eliminate words that don't cooccur more in-lexicon
co_pn, e_co_pn = getCoCountsTwoLex(x,pos_lex,neg_lex)
self.pos_lex = list(np.array(pos_lex)[co_pn.sum(axis=1) < e_co_pn.sum(axis=1)])
self.neg_lex = list(np.array(neg_lex)[co_pn.sum(axis=0) < e_co_pn.sum(axis=0)])
print "prefiltering from %d,%d to %d,%d"%(co_pn.shape[0],co_pn.shape[1],len(self.pos_lex),len(self.neg_lex))
else:
self.pos_lex = pos_lex
self.neg_lex = neg_lex
# now reload the counts using the lexicon
co_pn, self.e_co_pn = getCoCountsTwoLex(x,self.pos_lex,self.neg_lex)
e_mu = getEMu(x)
self.N_pos = len(self.pos_lex)
self.N_neg = len(self.neg_lex)
self.mu_pos = e_mu[self.pos_lex]
self.mu_neg = e_mu[self.neg_lex]
self.s = computeS(x)
self.co_pos = co_pn.sum(axis=1) #co-counts for each pos lex word
self.co_neg = co_pn.T.sum(axis=1) #co-counts for each neg lex word
rval = estimateK(x,self.pos_lex,self.neg_lex)
ratio = np.sqrt(self.mu_neg.sum() / self.mu_pos.sum())
#ratio = 1.
self.k_pos = rval * ratio * np.ones(self.N_pos)
self.k_neg = (rval / ratio) * np.ones(self.N_neg)
self.x_sum = x.sum() #TODO! count only lexicon words
self.max_k = max_k
self.verbosity = verbosity
def estimateADMM(self,n_epochs=100,max_iter=100,rho=1.0,adaptive_rho=True,max_k=0.9,grad_based=False):
'''
This is the biconvex method in Sec 9 of Boyd et al.
'''
if grad_based:
raise ValueError("Gradient-based optimization is not currently supported")
u = 0.
projector = lambda x : np.clip(x,0,max_k)
for it in xrange(n_epochs):
# solve k_pos = argmin(k_pos \in C) F(k_pos,k_neg) + penalty
P_diag, P_low_rank, q, r = self.getLowRankQuadraticParams(self.co_pos,self.co_neg,self.mu_pos,self.mu_neg,self.k_neg,self.s,u,rho)
self.k_pos = admm.admmQuadBounded(P_diag.copy(),P_low_rank,q.copy(), projector, max_iter=max_iter,rho=1.)
# todo: offer L-BFGS based optimization here
# solve k_neg = argmin(k_pos \in C) F(k_pos,k_neg) + penalty
P_diag, P_low_rank, q, r = self.getLowRankQuadraticParams(self.co_neg,self.co_pos,self.mu_neg,self.mu_pos,self.k_pos,self.s,-u,rho)
old_k_neg = self.k_neg
self.k_neg = admm.admmQuadBounded(P_diag.copy(),P_low_rank,q.copy(), projector, max_iter=max_iter,rho=1.)
# update dual parameter u
violation = np.dot(self.mu_pos,self.k_pos) - np.dot(self.mu_neg,self.k_neg)
u += violation
# compute residuals (Boyd et al, page 18)
#s^{k+1} in Boyd et al
dual_residual = np.linalg.norm(rho * self.mu_pos * np.dot(self.mu_neg,self.k_neg - old_k_neg))**2
#r^{k+1} in Boyd et al
primal_residual = np.linalg.norm(violation)**2
# first part is primal, second part is augmented lagrangian
f_eval = admm.lowRankPlusDiagonalQuadProd(P_diag,P_low_rank,self.k_neg) + q.dot(self.k_neg) + r + rho * np.linalg.norm(violation)**2
# update Rho
rho,u = admm.updateRho(u,rho,primal_residual,dual_residual)
# consider terminating
# termination (page 19) p=1, n=size(pos_words), m=size(neg_words)
if self.verbosity >= 2:
print it, 'u =',u, f_eval, violation
if self.verbosity >= 1:
print "%d.\tDual residual=%.8f\tPrimal residual=%.8f\tRho=%.3f"%(it,dual_residual,primal_residual,rho)
if self.verbosity >= 2:
print ""
eps_abs = 1e-3 / self.x_sum
eps_rel = 1e-3 / self.x_sum
eps_primal = 1. * eps_abs + eps_rel * np.max([np.dot(self.mu_pos,self.k_pos),
np.dot(self.mu_neg,self.k_neg)])
eps_dual1 = np.sqrt(self.k_pos.shape[0]) * eps_abs + eps_rel * np.linalg.norm(u * self.mu_pos)**2
eps_dual2 = np.sqrt(self.k_neg.shape[0]) * eps_abs + eps_rel * np.linalg.norm(u * self.mu_neg)**2
if dual_residual < eps_dual1 + eps_dual2 and primal_residual < eps_primal:
if self.verbosity >= 0:
print "done!\tit=%d\tdual=%.2e<min(%.2e,%.2e)\tprimal=%.2e<%.2e"%(it,dual_residual,eps_dual1,eps_dual2,primal_residual,eps_primal)
break
## ADMM stuff
def getLowRankQuadraticParams(self,counts_in,counts_out,mu_in,mu_out,k_out,s,u,rho1=1.):
'''
The augmented Lagrangian can be expressed as \frac{1}{2}x'Px + q'x + r
with P = Diag(d) + UU'
'''
out_weight = mu_out.dot(k_out)
counts_multiplier = self.s/self.x_sum
# rho2 is due to the Lagrangian from the boundary constraint
P_diag = ((s * out_weight * mu_in)**2)/self.x_sum #+rho2
# there are two columns, corresponding to the primal and the Lagrangian arising from the equality constraint
P_low_rank = np.outer(np.array([s*np.sqrt((k_out**2).dot(mu_out**2)/self.x_sum),np.sqrt(rho1)]), mu_in).T
# P = np.diag(P_diag) + P_low_rank.dot(P_low_rank.T)
resid_in = counts_in - s * mu_out.sum() * mu_in
resid_out = counts_out - s * mu_in.sum() * mu_out
diff = u - out_weight
q = counts_multiplier * out_weight * (resid_in * mu_in)\
+ counts_multiplier * (resid_out * mu_out * k_out).sum() * mu_in\
+ rho1 * diff * mu_in#\
#+ rho2 * (v - a)
r = .5 * ((resid_in**2).sum() + (resid_out**2).sum())/self.x_sum\
+ .5*rho1*diff**2#\
#+ .5*rho2*np.linalg.norm(v-a)**2# + np.linalg.norm(w-b)**2)
return P_diag,P_low_rank,q,r
## SQSLP Stuff
def getDiffPos(self,p_k):
return self.co_pos - e_co_diff(self.e_co_pn,p_k,self.k_neg).sum(axis=1)
def getDiffNeg(self,p_k):
return self.co_neg - e_co_diff(self.e_co_pn,self.k_pos,p_k).T.sum(axis=1)
def sqErrPos(self,p_k):
return (.5 * np.linalg.norm(self.getDiffPos(p_k))**2)/self.x_sum
def sqErrNeg(self,p_k):
return (.5 * np.linalg.norm(self.getDiffNeg(p_k))**2)/self.x_sum
def jaccPos(self,p_k):
return self.getDiffPos(p_k) * self.s * self.mu_pos * \
(((1-self.k_neg)*self.mu_neg).sum()) / self.x_sum
def jaccNeg(self,p_k):
return self.getDiffNeg(p_k) * self.s * self.mu_neg * \
(((1-self.k_pos)*self.mu_pos).sum()) / self.x_sum
def con_fun_pos(self,p_k):
return np.array(np.dot(self.mu_pos, p_k) -
np.dot(self.mu_neg, self.k_neg))
def con_jac_pos(self,p_k):
return self.mu_pos
def con_fun_neg(self,p_k):
return np.array(np.dot(self.mu_pos, self.k_pos) -
np.dot(self.mu_neg, p_k))
def con_jac_neg(self,p_k):
return self.mu_neg
def estimateSLSQP(self,n_epochs=10,max_iter=5):
for it in xrange(n_epochs):
result_pos = sp.optimize.minimize\
(self.sqErrPos,
self.k_pos,
method='SLSQP',
bounds=[(0,0.9)]*self.N_pos,
jac=self.jaccPos,
constraints = ({'type':'eq',
'fun':self.con_fun_pos,
'jac':self.con_jac_pos}),
options={'maxiter':max_iter,'disp': False})
self.k_pos = result_pos.x
result_neg = sp.optimize.minimize\
(self.sqErrNeg,
self.k_neg,
method='SLSQP',
bounds=[(0,0.9)]*self.N_neg,
jac=self.jaccNeg,
constraints = ({'type':'eq',
'fun':self.con_fun_neg,
'jac':self.con_jac_neg}),
options={'maxiter':max_iter,'disp': False})
self.k_neg = result_neg.x
if self.verbosity > 0:
print it, result_pos.fun + result_neg.fun