diff options
Diffstat (limited to 'gi/posterior-regularisation')
| -rw-r--r-- | gi/posterior-regularisation/train_pr_agree.py | 90 |
1 files changed, 81 insertions, 9 deletions
diff --git a/gi/posterior-regularisation/train_pr_agree.py b/gi/posterior-regularisation/train_pr_agree.py index bbd6e007..9d41362d 100644 --- a/gi/posterior-regularisation/train_pr_agree.py +++ b/gi/posterior-regularisation/train_pr_agree.py @@ -250,7 +250,10 @@ class ProductModel: # return the overall objective return llh1 + llh2 + kl -class InterpolatedModel: +class RegularisedProductModel: + # as above, but with a slack regularisation term which kills the + # closed-form solution for the E-step + def __init__(self, epsilon): self.pcm = PhraseToContextModel() self.cpm = ContextToPhraseModel() @@ -260,7 +263,7 @@ class InterpolatedModel: def prob(self, pid, cid): p1 = self.pcm.prob(pid, cid) p2 = self.cpm.prob(pid, cid) - return (p1 + p2) / 2 + return (p1 / sum(p1)) * (p2 / sum(p2)) def dual(self, lamba): return self.logz(lamba) + self.epsilon * dot(lamba, lamba) ** 0.5 @@ -272,17 +275,19 @@ class InterpolatedModel: # PR-step: optimise lambda to minimise log(z_lambda) + eps ||lambda||_2 self.lamba = scipy.optimize.fmin_slsqp(self.dual, self.lamba, bounds=[(0, 1e100)] * num_tags, - fprime=self.dual_gradient, iprint=0) + fprime=self.dual_gradient, iprint=1) # E,M-steps: collect expected counts under q_lambda and normalise - #llh1 = self.pcm.expectation_maximisation_step(self.lamba) - #llh2 = self.cpm.expectation_maximisation_step(-self.lamba) + llh1 = self.pcm.expectation_maximisation_step(self.lamba) + llh2 = self.cpm.expectation_maximisation_step(-self.lamba) - # return the overall objective: llh1 + llh2 - KL(q||p1.p2) - pass + # return the overall objective: llh - KL(q||p1.p2) + # llh = llh1 + llh2 + # kl = sum q log q / p1 p2 = sum q { lambda . phi } - log Z + return llh1 + llh2 + self.logz(self.lamba) \ + - dot(self.lamba, self.expected_features(self.lamba)) def logz(self, lamba): - # FIXME: complete this! lz = 0 for pid, cid, cnt in edges: p1 = self.pcm.prob(pid, cid) @@ -306,14 +311,81 @@ class InterpolatedModel: fs -= cnt * q2 / sum(q2) return fs + +class InterpolatedModel: + def __init__(self, epsilon): + self.pcm = PhraseToContextModel() + self.cpm = ContextToPhraseModel() + self.epsilon = epsilon + self.lamba = zeros(num_tags) + + def prob(self, pid, cid): + p1 = self.pcm.prob(pid, cid) + p2 = self.cpm.prob(pid, cid) + return (p1 + p2) / 2 + + def dual(self, lamba): + return self.logz(lamba) + self.epsilon * dot(lamba, lamba) ** 0.5 + + def dual_gradient(self, lamba): + return self.expected_features(lamba) + self.epsilon * 2 * lamba + + def expectation_maximisation_step(self): + # PR-step: optimise lambda to minimise log(z_lambda) + eps ||lambda||_2 + self.lamba = scipy.optimize.fmin_slsqp(self.dual, self.lamba, + bounds=[(0, 1e100)] * num_tags, + fprime=self.dual_gradient, iprint=2) + + # E,M-steps: collect expected counts under q_lambda and normalise + llh1 = self.pcm.expectation_maximisation_step(self.lamba) + llh2 = self.cpm.expectation_maximisation_step(self.lamba) + + # return the overall objective: llh1 + llh2 - KL(q||p1.p2) + # kl = sum_y q log q / 0.5 * (p1 + p2) = sum_y q(y) { -lambda . phi(y) } - log Z + # = -log Z + lambda . (E_q1[-phi] + E_q2[-phi]) / 2 + kl = -self.logz(self.lamba) + dot(self.lamba, self.expected_features(self.lamba)) + return llh1 + llh2 - kl, llh1, llh2, kl + # FIXME: KL comes out negative... + + def logz(self, lamba): + lz = 0 + for pid, cid, cnt in edges: + p1 = self.pcm.prob(pid, cid) + q1 = p1 / sum(p1) * exp(-lamba) + q1z = sum(q1) + + p2 = self.cpm.prob(pid, cid) + q2 = p2 / sum(p2) * exp(-lamba) + q2z = sum(q2) + + lz += log(0.5 * (q1z + q2z)) * cnt + return lz + + # z = 1/2 * (sum_y p1(y|x) exp (-lambda . phi(y)) + sum_y p2(y|x) exp (-lambda . phi(y))) + # = 1/2 (z1 + z2) + # d (log z) / dlambda = 1/2 (E_q1 [ -phi ] + E_q2 [ -phi ] ) + def expected_features(self, lamba): + fs = zeros(num_tags) + for pid, cid, cnt in edges: + p1 = self.pcm.prob(pid, cid) + q1 = (p1 / sum(p1)) * exp(-lamba) + fs -= 0.5 * cnt * q1 / sum(q1) + + p2 = self.cpm.prob(pid, cid) + q2 = (p2 / sum(p2)) * exp(-lamba) + fs -= 0.5 * cnt * q2 / sum(q2) + return fs + if style == 'p2c': m = PhraseToContextModel() elif style == 'c2p': m = ContextToPhraseModel() elif style == 'prod': m = ProductModel() +elif style == 'prodslack': + m = RegularisedProductModel(0.5) elif style == 'sum': - m = InterpolatedModel() + m = InterpolatedModel(0.5) for iteration in range(30): obj = m.expectation_maximisation_step() |