From 72c705df4fefe32792ed7c75f39b06da5061870e Mon Sep 17 00:00:00 2001
From: "trevor.cohn" <trevor.cohn@ec762483-ff6d-05da-a07a-a48fb63a330f>
Date: Fri, 2 Jul 2010 02:04:18 +0000
Subject: Tweaking the agree model.

git-svn-id: https://ws10smt.googlecode.com/svn/trunk@98 ec762483-ff6d-05da-a07a-a48fb63a330f
---
 gi/posterior-regularisation/train_pr_agree.py | 90 ++++++++++++++++++++++++---
 1 file changed, 81 insertions(+), 9 deletions(-)

(limited to 'gi/posterior-regularisation/train_pr_agree.py')

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()
-- 
cgit v1.2.3