Approximate bayesian inference using EP

In [1]:

    

import choix
import numpy as np

np.set_printoptions(precision=3, suppress=True)


    

In [2]:

    

n_items = 8
data = [
    (7, 3), (2, 0), (5, 2), (4, 2), (2, 1),
    (4, 5), (6, 3), (5, 4), (7, 0), (2, 3),
    (4, 0), (0, 4), (6, 5), (3, 2), (3, 4),
    (3, 4), (5, 2), (7, 3), (7, 6), (6, 5),
]


    

In [3]:

    

mean, cov = choix.ep_pairwise(n_items, data, 0.1, model="logit")
print("mean:")
print(mean)
print("\ncovariance:")
print(cov)
print("\ntotal variance: {:3f}".format(np.trace(cov)))


    

    




mean:
[-1.638 -2.752 -1.011 -0.016 -0.94  -0.047  2.324  4.081]

covariance:
[[ 2.767  0.659  1.275  1.127  1.492  1.13   0.814  0.738]
 [ 0.659  5.367  1.033  0.689  0.681  0.695  0.485  0.391]
 [ 1.275  1.033  2.     1.333  1.318  1.345  0.939  0.757]
 [ 1.127  0.689  1.333  2.204  1.358  1.158  1.098  1.033]
 [ 1.492  0.681  1.318  1.358  2.043  1.368  0.959  0.782]
 [ 1.13   0.695  1.345  1.158  1.368  2.229  1.256  0.818]
 [ 0.814  0.485  0.939  1.098  0.959  1.256  3.022  1.426]
 [ 0.738  0.391  0.757  1.033  0.782  0.818  1.426  4.055]]

total variance: 23.687252

In [4]:

    

mean, cov = choix.ep_pairwise(n_items, data, 0.1, model="probit")
print("mean:")
print(mean)
print("\ncovariance:")
print(cov)
print("\ntotal variance: {:3f}".format(np.trace(cov)))


    

    




mean:
[-1.198 -2.927 -0.797 -0.126 -0.742 -0.15   2.019  3.922]

covariance:
[[ 1.896  0.835  1.355  1.299  1.455  1.306  1.014  0.84 ]
 [ 0.835  4.451  0.99   0.857  0.843  0.839  0.654  0.53 ]
 [ 1.355  0.99   1.607  1.392  1.37   1.363  1.062  0.861]
 [ 1.299  0.857  1.392  1.708  1.373  1.294  1.124  0.953]
 [ 1.455  0.843  1.37   1.373  1.621  1.398  1.074  0.867]
 [ 1.306  0.839  1.363  1.294  1.398  1.705  1.192  0.903]
 [ 1.014  0.654  1.062  1.124  1.074  1.192  2.417  1.462]
 [ 0.84   0.53   0.861  0.953  0.867  0.903  1.462  3.584]]

total variance: 18.990294