adding likelihood to theano implementation

3 files changed, 80 insertions, 41 deletions

diff --git a/simulation/main.py b/simulation/main.py
index c2446d7..decdf8f 100644
--- a/simulation/main.py
+++ b/simulation/main.py
@@ -19,9 +19,9 @@ def simulate_cascade(x, graph):
         - susc: the nodes susceptible at the beginning of this time step
         - x: the subset of susc who became infected
     """
+    yield x, np.zeros(graph.shape[0], dtype=bool)
     susc = np.ones(graph.shape[0], dtype=bool)
-    susc = susc ^ x  # t=0, the source is not susceptible
-    yield x, susc
+    #yield x, susc
     while np.any(x):
         susc = susc ^ x  # nodes infected at previous step are now inactive
         if not np.any(susc):
@@ -60,13 +60,16 @@ if __name__ == "__main__":
     g = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
     p = 0.5
     g = np.log(1. / (1 - p * g))
-    error = []
-    sizes = [10, 10**2, 10**3]
-    for s in sizes:
-        cascades = simulate_cascades(s, g)
-        cascade, y_obs = mn.build_matrix(cascades, 0)
-        conf = mn.bootstrap(cascade, y_obs, n_iter=100)
-        estimand = np.linalg.norm(np.delete(conf - g[0], 0, axis=1), axis=1)
-        error.append(mn.confidence_interval(*np.histogram(estimand, bins=50)))
-        plt.semilogx(sizes, error)
-        plt.show()
+    print(g)
+    sizes = [10**3]
+    for si in sizes:
+        cascades = simulate_cascades(si, g)
+        cascade, y_obs = mn.build_matrix(cascades, 2)
+        print(mn.infer(cascade, y_obs))
+        #conf = mn.bootstrap(cascade, y_obs, n_iter=100)
+        #estimand = np.linalg.norm(np.delete(conf - g[0], 0, axis=1), axis=1)
+        #plt.hist(estimand, bins=40)
+        #plt.show()
+        #error.append(mn.confidence_interval(*np.histogram(estimand, bins=50)))
+    #plt.plot(sizes, error)
+    #plt.show()
diff --git a/simulation/vi.py b/simulation/vi.py
index aeccb69..1e45761 100644
--- a/simulation/vi.py
+++ b/simulation/vi.py
@@ -50,7 +50,7 @@ def kl(params1, params0):
 grad_kl = grad(kl)
 
 
-def sgd(mu1, sig1, mu0, sig0, cascades, n_e=100, lr=lambda t: 1e-2, n_print=10):
+def sgd(mu1, sig1, mu0, sig0, cascades, n_e=100, lr=lambda t: 1e-1, n_print=10):
     g_mu1, g_sig1 = grad_kl((mu1, sig1), (mu0, sig0))
     for t in xrange(n_e):
         lrt = lr(t)  # learning rate
@@ -61,19 +61,19 @@ def sgd(mu1, sig1, mu0, sig0, cascades, n_e=100, lr=lambda t: 1e-2, n_print=10):
             sig1 = np.maximum(sig1 + lrt * g_sig1, 1e-3)
             res = np.sum(ll_full((mu1, sig1), x, s) for x, s in zip(*cascades))\
                     + kl((mu1, sig1), (mu0, sig0))
-            if step % n_print == 0:
-                logging.info("Epoch:{}\tStep:{}\tLB:{}\t".format(t, step, res))
-                print mu1[0:2, 0:2]
-                print sig1[0:2, 0:2]
+            #if step % n_print == 0:
+        logging.info("Epoch:{}\tStep:{}\tLB:{}\t".format(t, step, res))
+        print mu1
+        print sig1
 
 
 if __name__ == '__main__':
-    #graph = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
-    graph = np.random.binomial(2, p=.2, size=(10, 10))
+    graph = np.array([[0, 0, 1], [0, 0, 0.5], [0, 0, 0]])
+    #graph = np.random.binomial(2, p=.2, size=(4, 4))
     p = 0.5
     graph = np.log(1. / (1 - p * graph))
-    print(graph[0:2, 0:2])
-    cascades = mn.build_cascade_list(mn.simulate_cascades(500, graph))
+    print(graph)
+    cascades = mn.build_cascade_list(mn.simulate_cascades(100, graph))
     mu0, sig0 = (1. + .2 * np.random.normal(size=graph.shape),
                  1 + .2 * np.random.normal(size=graph.shape))
     mu1, sig1 = (1. + .2 * np.random.normal(size=graph.shape),
diff --git a/simulation/vi_theano.py b/simulation/vi_theano.py
index 562fa67..9e8fdb0 100644
--- a/simulation/vi_theano.py
+++ b/simulation/vi_theano.py
@@ -8,29 +8,29 @@ n_cascades = 1000
 n_nodes = 4
 n_samples = 100
 srng = tsr.shared_randomstreams.RandomStreams(seed=123)
-lr = 1e-2
-n_epochs = 10
+lr = 5*1e-3
+n_epochs = 20
 
+###############Variational Inference####################
 
 # Declare Theano variables
-mu = theano.shared(.5 * np.random.rand(1, n_nodes, n_nodes), name="mu",
-                    broadcastable=(True, False, False))
-sig = theano.shared(.3 * np.random.rand(1, n_nodes, n_nodes), name="sig",
-                    broadcastable=(True, False, False))
-mu0 = theano.shared(.5 * np.random.rand(1, n_nodes, n_nodes), name="mu",
-                    broadcastable=(True, False, False))
-sig0 = theano.shared(.3 * np.random.rand(1, n_nodes, n_nodes), name="sig",
-                    broadcastable=(True, False, False))
+mu = theano.shared(.5 + .2 * np.random.normal(size=(1, n_nodes, n_nodes)),
+                    name="mu", broadcastable=(True, False, False))
+sig = theano.shared(.1 + .04 * np.random.normal(size=(1, n_nodes, n_nodes)),
+                    name="sig", broadcastable=(True, False, False))
+mu0 = theano.shared(.5 + .2 * np.random.normal(size=(1, n_nodes, n_nodes)),
+                    name="mu", broadcastable=(True, False, False))
+sig0 = theano.shared(.1 + .04 * np.random.normal(size=(1, n_nodes, n_nodes)),
+                    name="sig", broadcastable=(True, False, False))
 x = tsr.matrix(name='x', dtype='int8')
 s = tsr.matrix(name='s', dtype='int8')
 
 # Construct Theano graph
 theta = srng.normal((n_samples, n_nodes, n_nodes)) * sig + mu
-y = tsr.clip(tsr.dot(x, theta), 1e-3, 1)
+y = tsr.maximum(tsr.dot(x, theta), 1e-3)
 infect = tsr.log(1. - tsr.exp(-y[0:-1])).dimshuffle(1, 0, 2)
 lkl_pos = tsr.sum(infect * (x[1:] & s[1:])) / n_samples
 lkl_neg = tsr.sum(-y[0:-1].dimshuffle(1, 0, 2) * (~x[1:] & s[1:])) / n_samples
-
 lkl = lkl_pos + lkl_neg
 kl = tsr.sum(tsr.log(sig / sig0) + (sig0**2 + (mu0 - mu)**2)/(2*sig)**2)
 res = lkl + kl
@@ -48,8 +48,24 @@ train_kl = theano.function(inputs=[], outputs=[],
                                    (sig, tsr.clip(sig + lr * gsigkl, 1e-3, 1))))
 
 
+###############Maximum Likelihood#####################
+
+x = tsr.matrix(name='x', dtype='int8')
+s = tsr.matrix(name='s', dtype='int8')
+params = theano.shared(.5 + .01*np.random.normal(size=(n_nodes, n_nodes)),
+                        name='params')
+y = tsr.maximum(tsr.dot(x, params), 1e-5)
+infect = tsr.log(1. - tsr.exp(-y[0:-1]))
+lkl_pos = tsr.sum(infect * (x[1:] & s[1:]))
+lkl_neg = tsr.sum(-y[0:-1] * (~x[1:] & s[1:]))
+lkl_mle = lkl_pos + lkl_neg
+gparams = theano.gradient.grad(lkl_mle, params)
+train_mle = theano.function(inputs=[x, s], outputs=lkl_mle, updates=[(params,
+                                        tsr.clip(params + lr * gparams, 0, 1))])
+
+
 if __name__ == "__main__":
-    graph = np.random.binomial(2, p=.2, size=(n_nodes, n_nodes))
+    graph = .5 * np.random.binomial(2, p=.5, size=(n_nodes, n_nodes))
     for k in range(len(graph)):
         graph[k, k] = 0
     p = 0.5
@@ -57,10 +73,30 @@ if __name__ == "__main__":
     cascades = mn.build_cascade_list(mn.simulate_cascades(n_cascades, graph),
                                      collapse=True)
     x_obs, s_obs = cascades[0], cascades[1]
-    for i in range(n_epochs):
-        train_kl()
-        for k in xrange(len(x_obs)/100):
-            cost = train(x_obs[k*100:(k+1)*100], s_obs[k*100:(k+1)*100])
-        print(cost)
-    print(mu.get_value())
-    print(graph)
+
+    #mle
+    lkl_plot = []
+    if 0:
+        for i in range(n_epochs):
+            for xt, st in zip(x_obs, s_obs):
+                lkl = train_mle(xt, st)
+                lkl_plot.append(lkl)
+        print(graph)
+        w = params.get_value()
+        for k in range(len(w)):
+            w[k, k] = 0
+        print(w)
+        import matplotlib.pyplot as plt
+        plt.plot(lkl_plot)
+        plt.show()
+
+    #variational inference
+    if 1:
+        for i in range(n_epochs):
+            train_kl()
+            for k in xrange(len(x_obs)/100):
+                cost = train(x_obs[k*100:(k+1)*100], s_obs[k*100:(k+1)*100])
+            print(cost)
+        print(graph)
+        print(mu.get_value())
+        print(sig.get_value())