1 files changed, 114 insertions, 0 deletions
diff --git a/simulation/vi_beta.py b/simulation/vi_beta.py
new file mode 100644
index 0000000..e3bcbf6
--- /dev/null
+++ b/simulation/vi_beta.py
@@ -0,0 +1,114 @@
+import time
+import main as mn
+import numpy as np
+import logging
+import scipy.special as ssp
+from itertools import product
+
+logging.basicConfig(format='%(asctime)s - %(levelname)s - %(message)s',
+                    level=logging.INFO)
+
+def g(m):
+    assert (m > 0).all()
+    return np.log(1 - np.exp(-m))
+
+
+def h(m):
+    return -m
+
+
+def ll(x, s, theta):
+    """
+    x : infected
+    s : susceptible
+    """
+    res = 0
+    for t in range(1, x.shape[0]):
+        w = np.dot(x[t-1], theta)
+        res += g(w)[x[t]].sum() + h(w)[~x[t] & s[t]].sum()
+    return res
+
+
+def sample(params):
+    mu, v = params
+    size = mu.shape
+    return np.clip(np.random.beta(mu, v, size=size), 1e-3, 1e5)
+
+
+def ll_full(params, x, s, nsamples=50):
+    return np.mean([ll(x, s, sample(params)) for _ in xrange(nsamples)])
+
+
+def kl(params1, params0):
+    mu0, sig0 = params0
+    mu1, sig1 = params1
+    return (ssp.betaln(mu0, sig0) - ssp.betaln(mu1, sig1) + (mu0 - mu1) *
+            ssp.psi(mu0) + (sig0 - sig1) * ssp.psi(sig0) + (mu1 - mu0 + sig1 -
+                sig0) * ssp.psi(mu0 + sig0)).sum()
+
+
+def aux(var, res, i, j, f, eps):
+    var[i,j] += eps
+    res[i,j] += f(var)
+    var[i,j] -= 2 * eps
+    res[i,j] -= f(var)
+    res[i,j] /= 2 * eps
+    var[i, j] += eps
+
+
+def grad_ll_full(params, x, s, nsamples=50, eps=1e-5):
+    mu, v = params
+    n, m = mu.shape
+    mugrad = np.empty((n,m))
+    vgrad = np.empty((n,m))
+    for (i, j) in product(xrange(n), xrange(m)):
+        aux(mu, mugrad, i, j, lambda t: ll_full((t, v), x, s, nsamples), eps)
+        aux(v, vgrad, i, j, lambda t: ll_full((mu, t), x, s, nsamples), eps)
+
+    return mugrad, vgrad
+
+
+def grad_kl(params1, params0, eps=1e-5):
+    mu0, sig0 = params0
+    mu1, sig1 = params1
+
+    n, m = mu0.shape
+    mugrad = np.empty((n,m))
+    vgrad = np.empty((n,m))
+    for (i, j) in product(xrange(n), xrange(m)):
+        aux(mu1, mugrad, i, j, lambda t: kl((t, sig1), params0), eps)
+        aux(sig1, vgrad, i, j, lambda t: kl((mu1, t), params0), eps)
+
+    return mugrad, vgrad
+
+
+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
+        mu1 = np.clip(mu1 + lrt * g_mu1, 1e-3, 1e5)
+        sig1 = np.clip(sig1 + lrt * g_sig1, 1e-3, 1e5)
+        for step, (x, s) in enumerate(zip(*cascades)):
+            g_mu1, g_sig1 = grad_ll_full((mu1, sig1), x, s)
+            mu1 = np.clip(mu1 + lrt * g_mu1, 1e-3, 1e5)
+            sig1 = np.clip(sig1 + lrt * g_sig1, 1e-3, 1e5)
+            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
+        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=(4, 4))
+    p = 0.5
+    graph = np.log(1. / (1 - p * 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),
+                 1 + .2 * np.random.normal(size=graph.shape))
+    sgd(mu1, sig1, mu0, sig0, cascades, n_e=30, n_print=1)