added plots to appendix

1 files changed, 67 insertions, 6 deletions

diff --git a/src/convex_optimization.py b/src/convex_optimization.py
index 000143f..fbfeb29 100644
--- a/src/convex_optimization.py
+++ b/src/convex_optimization.py
@@ -4,7 +4,7 @@ from theano import tensor, function
 import numpy as np
 import timeout
 import cvxopt
-
+import scipy
 
 @timeout.timeout(20)
 def sparse_recovery(lbda, n_cascades):
@@ -124,28 +124,89 @@ def diff_and_opt(M_val, w_val, f_x, f_xz):
     return 1 - np.exp(theta), theta
 
 
+def restrictedEigenvalue(M_val, w_val, theta_val, gramMatrix=False):
+    """
+    returns the smallest restricted eigenvalue of the matrix on the set S
+    gramMatrix (bool) : If true, use the gram matrix instead of the Hessian
+    theta_val : true vector of parameters
+    """
+    m, n = M_val.shape
+
+    if gramMatrix:
+        H = 1./m * np.dot(M_val.T,M_val)
+    else:
+        #compute the Hessian
+        #theta = tensor.row().T
+        #theta_ = theta.flatten()
+
+        #M = tensor.matrix(name='M', dtype=theano.config.floatX)
+        #w = tensor.vector(name='w', dtype=theano.config.floatX)
+
+        #y =   - 1./n*( (w).dot(tensor.log(1-tensor.exp(M.dot(theta_)))) +
+                #(1-w).dot(tensor.dot(M, theta_)))
+
+        #f = theano.function([theta, M, w], [theano.gradient.hessian(y,
+            #theta_)], allow_input_downcast=True)
+
+        #print(theta_val)
+        #H = f(np.atleast_2d(theta_val).T, M_val.astype('float64'), w_val)
+
+    #print(H)
+
+    #evals_small, evecs_small = scipy.sparse.linalg.eigsh(H.astype('float64'), 1,
+            #which="LM")
+    #print(evals_small)
+
+        theta = tensor.vector()
+
+        M = tensor.matrix(name='M', dtype=theano.config.floatX)
+        w = tensor.vector(name='w', dtype=theano.config.floatX)
+
+        y =   - 1./n*((w).dot(tensor.log(1-tensor.exp(M.dot(theta)))) +
+                (1-w).dot(tensor.dot(M, theta)))
+
+        f = theano.function([theta, M, w], [theano.gradient.hessian(y,
+            theta)], allow_input_downcast=True)
+
+        H = f(theta_val, M_val.astype('float32'), w_val)
+
+        print(H)
+
+    evals_small, evecs_small = scipy.sparse.linalg.eigsh(H, 1,
+            which="LM")
+    print(evals_small)
+
+
 def test():
     """
     unit test
     """
     lbda = .0001
-    G = cascade_creation.InfluenceGraph(max_proba=.9)
+    G = cascade_creation.InfluenceGraph(max_proba=.9, min_proba=.2)
     G.erdos_init(n=20, p = .3)
     A = cascade_creation.generate_cascades(G, .1, 500)
-    M_val, w_val = cascade_creation.icc_matrixvector_for_node(A, 2)
-    print(len(M_val))
+    M_val, w_val = cascade_creation.icc_matrixvector_for_node(A, 0)
+    print(M_val.shape)
+    print(w_val.shape)
 
     #Type lasso
     if 0:
-        f_x, f_xz = type_lasso(lbda)
+        f_x, f_xz = type_lasso(lbda, 500)
         p_vec, _ = diff_and_opt(M_val, w_val, f_x, f_xz)
         print(G.mat[2])
 
     #Sparse recovery
-    if 1:
+    if 0:
         f_x, f_xz = sparse_recovery(lbda, 500)
         p_vec, _ = diff_and_opt(M_val, w_val, f_x, f_xz)
         print(G.mat[2])
 
+    #Restricted Eigenvalue
+    if 2:
+        node = 1
+        parents = np.nonzero(G.mat[:, node])[0]
+        theta_val = G.logmat[:,node]
+        restrictedEigenvalue(M_val, w_val, theta_val)
+
 if __name__=="__main__":
     test()