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query.py
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# queries
import random
import collections
from utils import *
import numpy as np
import networkx as nx
"""
All the querying strategies are implemented here
"""
def pagerank(bgt, step_size, partial_net, edge_wt):
"""
PageRank query strategy
"""
# pagerank is obtained when setting nan as 0.
cur_A = partial_net['A'].copy()
A = np.zeros_like(partial_net['A'])
n = A.shape[0]
known_eid = partial_net['known_eid']
known_e = np.array(eid_to_e(n, known_eid))
A[known_e[:, 0], known_e[:, 1]] = cur_A[known_e[:, 0], known_e[:, 1]]
A[known_e[:, 1], known_e[:, 0]] = cur_A[known_e[:, 0], known_e[:, 1]]
G = nx.from_numpy_matrix(np.matrix(A))
pg = nx.pagerank(G, alpha=0.85)
utility = []
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
for i in range(len(pool_eid)):
l_e = pool_e[i, :]
utility.append(pg[l_e[0]]+pg[l_e[1]])
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k], reverse=True)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return utility, pool_eid[inds]
def degree_sum(bgt, step_size, partial_net, edge_wt):
"""
Degree sum query strategy
"""
cur_A = partial_net['A'].copy()
A = np.zeros_like(partial_net['A'])
n = A.shape[0]
known_eid = partial_net['known_eid']
known_e = eid_to_e(n, known_eid)
A[known_e[:, 0], known_e[:, 1]] = cur_A[known_e[:, 0], known_e[:, 1]]
A[known_e[:, 1], known_e[:, 0]] = cur_A[known_e[:, 0], known_e[:, 1]]
degrees = A.sum(axis=0)
utility = []
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
for i in range(len(pool_eid)):
l_e = pool_e[i]
utility.append(degrees[l_e[0]] + degrees[l_e[1]])
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k], reverse=True)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return utility, pool_eid[inds]
def probability(bgt, step_size, partial_net, post_P, edge_wt):
"""
Maximum Probability based query strategy
"""
n = partial_net['A'].shape[0]
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
utility = post_P[pool_e[:, 0], pool_e[:, 1]]
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k].sum(), reverse=True)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return utility, pool_eid[inds]
def distance(bgt, step_size, partial_net, X, edge_wt):
"""
Minimum distance based query strategy
"""
n = partial_net['A'].shape[0]
utility = []
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
for i in range(len(pool_eid)):
l_e = pool_e[i]
diff = X[l_e[0], :] - X[l_e[1], :]
utility.append(np.linalg.norm(diff))
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k], reverse=False)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return utility, pool_eid[inds]
def entropy(bgt, step_size, partial_net, post_P, edge_wt):
"""
Maximum entropy based query strategy
"""
A = partial_net['A']
n = A.shape[0]
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
Ps = post_P[pool_e[:, 0], pool_e[:, 1]]
P_te = Ps
utility = -P_te*np.log(P_te) - (1-P_te)*np.log(1-P_te)
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k], reverse=True)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return utility, pool_eid[inds]
def fisher_x_ii_k(partial_net, post_P, X, ne_params, i):
# sum over only the known neighbours of i
d = ne_params['d']
gamma = (1/ne_params['s1']**2 - 1/ne_params['s2']**2)
known_i = partial_net['known_dic'][i]
post_P = post_P[i, known_i]
p = post_P*(1 - post_P)
tmp = (p*(X[i, :] - X[known_i, :]).T).dot(X[i, :] - X[known_i, :])
FI_ii = gamma**2*tmp + np.diag(np.ones(d)*np.finfo(float).eps)
return FI_ii
def d_optimality(bgt, step_size, partial_net, post_P, X, ne_params, edge_wt):
"""
Parameter Variance reduction strategy
"""
A = partial_net['A']
gamma = (1/ne_params['s1']**2 - 1/ne_params['s2']**2)
n = A.shape[0]
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
fishers = [fisher_x_ii_k(partial_net, post_P, X, ne_params, idx) for idx in range(n)]
utility = []
for eid in range(len(pool_eid)):
i, j = pool_e[eid]
diff_ij = X[i, :] - X[j, :]
P_ij = post_P[i, j]
I_ij_X = fishers[i] + fishers[j]
tmp = diff_ij.dot(np.linalg.inv(I_ij_X)).dot(diff_ij.T)
res_eid = 2*gamma**2*P_ij*(1-P_ij)*tmp*np.linalg.det(I_ij_X)
utility.append(res_eid)
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k], reverse=True)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return np.array(utility), pool_eid[inds]
def v_optimality_k(bgt, step_size, partial_net, post_P, X, ne_params, edge_wt):
"""
Prediction Variance reduction strategy
"""
A = partial_net['A']
gamma = (1/ne_params['s1']**2 - 1/ne_params['s2']**2)
n = A.shape[0]
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
fishers = [fisher_x_ii_k(partial_net, post_P, X, ne_params, idx) for idx in range(n)]
l_target_e = partial_net['target_e'].tolist()
target_dict = collections.defaultdict(list)
for u, v in l_target_e:
target_dict[u].append(v)
target_dict[v].append(u)
Ps = post_P[pool_e[:, 0], pool_e[:, 1]]
Ps = Ps*(1-Ps)
djj_i = [(X[i, :] - X[j, :]).dot(np.linalg.inv(fishers[i])).dot(X[i, :] - X[j, :]) for i, j in pool_e]
dii_j = [(X[i, :] - X[j, :]).dot(np.linalg.inv(fishers[j])).dot(X[i, :] - X[j, :]) for i, j in pool_e]
deno_i = 1/(1+gamma**2*Ps*djj_i)
deno_j = 1/(1+gamma**2*Ps*dii_j)
utility = []
for eid in range(len(pool_eid)):
i, j = pool_e[eid]
X_diff_ij = X[i, :] - X[j, :]
Pis = post_P[i, target_dict[i]]
dkj_i = (X[i, :] - X[target_dict[i], :]).dot(np.linalg.inv(fishers[i])).dot(X_diff_ij.T)
score_i = ((Pis*(1-Pis))**2*dkj_i**2*deno_i[eid])
Pjs = post_P[j, target_dict[j]]
dli_j = (X[j, :] - X[target_dict[j], :]).dot(np.linalg.inv(fishers[j])).dot(-X_diff_ij.T)
score_j = ((Pjs*(1-Pjs))**2*dli_j**2*deno_j[eid])
res_eid = gamma**4*Ps[eid]*(np.sum(score_i) + np.sum(score_j))
utility.append(res_eid)
utility = utility * edge_wt
sorted_e_ind = sorted(range(len(utility)), key=lambda k: utility[k], reverse=True)
if bgt >= step_size:
inds = sorted_e_ind[:step_size]
else:
inds = sorted_e_ind[:min(bgt, len(pool_eid))]
return np.array(utility), pool_eid[inds]
def distance_weight(partial_net, X):
"""
Information Density technique with
cosine-similarity distance weighting.
"""
A = partial_net['A']
n = A.shape[0]
pool_eid = partial_net['pool_eid']
pool_e = eid_to_e(n, pool_eid)
X_norm_sq = np.linalg.norm(X, axis = 1)**2
node1_embed = X[pool_e[:,0],:]
node2_embed = X[pool_e[:,1],:]
node11_dot = node1_embed @ node1_embed.T
node12_dot = node1_embed @ node2_embed.T
node22_dot = node2_embed @ node2_embed.T
dir1_dot = node11_dot + node22_dot
dir2_dot = node12_dot + node12_dot.T
assert(dir1_dot.shape == (len(pool_eid), len(pool_eid)))
assert(dir2_dot.shape == (len(pool_eid), len(pool_eid)))
dist = np.minimum(dir1_dot, dir2_dot)
edge_norms = X_norm_sq[pool_e[:,0]] + X_norm_sq[pool_e[:,1]]
edge_norms = np.sqrt(edge_norms)
norm_prod = edge_norms.T @ edge_norms
cos_dist = dist / norm_prod
assert(cos_dist.shape == (len(pool_eid), len(pool_eid)))
dist_weight = np.mean(cos_dist, axis = 1)
return dist_weight
def get_query(partial_net, post_P, X, step_size, bgt, ne_params, strategy, use_dist_wt = False):
print('pool_eid length left', len(partial_net['pool_eid']))
if strategy == 'random_1' or strategy == 'random_2' or strategy == 'random_3':
pool_eid = partial_net['pool_eid']
set_pool = set(pool_eid)
if bgt >= step_size:
query = np.array(random.sample(list(set_pool), step_size))
else:
query = np.array(random.sample(list(set_pool), min(bgt, len(pool_eid))))
else:
if use_dist_wt:
wts = distance_weight(partial_net, X)
else:
wts = np.ones(len(partial_net['pool_eid']))
if strategy == 'pagerank':
utility, query = pagerank(bgt, step_size, partial_net, wts)
elif strategy == 'max_degree_sum':
utility, query = degree_sum(bgt, step_size, partial_net, wts)
elif strategy == 'max_probability':
utility, query = probability(bgt, step_size, partial_net, post_P, wts)
elif strategy == 'min_distance':
utility, query = distance(bgt, step_size, partial_net, X, wts)
elif strategy == 'max_entropy':
utility, query = entropy(bgt, step_size, partial_net, post_P, wts)
elif strategy == 'd_optimality':
utility, query = d_optimality(bgt, step_size, partial_net, post_P, X, ne_params, wts)
elif strategy == 'v_optimality':
utility, query = v_optimality_k(bgt, step_size, partial_net, post_P, X, ne_params, wts)
else:
query = []
return query