%pylab inline
import numpy as np
import matplotlib.pyplot as plt

n = 100
mu_x0, sigma_x0 = 0.5, 0.5
x = np.random.normal(mu_x0, sigma_x0, n)
mu_e, sigma_e = 0., 0.3
e = np.random.normal(mu_e, sigma_e, n)
y = -x + x**3 + e
plt.figure()
plt.plot(x,y,'*r')
plt.ylabel('x')
plt.ylabel('y')
min_x, max_x = np.min(x), np.max(x)
x_range = np.linspace(min_x, max_x, n)
y_true = -x_range + x_range**3
plt.plot(x_range,y_true,'b',label='true')

x_add_ones =np.column_stack((x, ones(shape(x)[0])))
x_range_add_ones =np.column_stack((x_range, ones(shape(x_range)[0])))


# OLS for d=1
theta_0 = np.dot(numpy.linalg.inv(np.dot(np.transpose(x_add_ones),x_add_ones)),
                 np.dot(y,x_add_ones))
y_0 = np.dot(x_range_add_ones,theta_0)
plt.plot(x_range,y_0,'g',label='OLS')

# compute weights from q1(x)/q0(x)
mu_w, sigma_w = -0.28, 0.38
w = exp(-((x-mu_w)**2)/float(2*sigma_w**2))
x_w = x * w
x_w_add_ones  =np.column_stack((x_w, ones(shape(x_w)[0])))

# weighted log-likelihood
theta_1 = np.dot(numpy.linalg.inv(np.dot(np.transpose(x_w_add_ones),x_w_add_ones)),
                 np.dot(y,x_w_add_ones))
y_1 = np.dot(x_range_add_ones,theta_1)
plt.plot(x_range,y_1,'m',label='WLS')
plt.legend()
plt.title('Training data set')

# test set
mu_x0, sigma_x0 = 0., 0.3
x1 = np.random.normal(mu_x0, sigma_x0, n)
y1 = -x1 + x1**3 + e

plt.figure()
plt.plot(x1,y1,'*r')
plt.ylabel('x')
plt.ylabel('y')
min_x, max_x = np.min(x1), np.max(x1)
x_range = np.linspace(min_x, max_x, n)
y_true = -x_range + x_range**3
plt.plot(x_range,y_true,'b',label='true')

x1_add_ones =np.column_stack((x1, ones(shape(x1)[0])))
x1_range_add_ones =np.column_stack((x_range, ones(shape(x1)[0])))


# OLS for d=1
theta_0 = np.dot(numpy.linalg.inv(np.dot(np.transpose(x1_add_ones),x1_add_ones)),
                 np.dot(y1,x1_add_ones))
y_0 = np.dot(x1_range_add_ones,theta_0)
plt.plot(x_range,y_0,'g',label='OLS')
plt.legend()
plt.title('Test data set')

I would assign probability of connections based on common features such as location, skills and etc.