The Class Imbalance Problem

class_imbalance.py

import numpy as np
from numpy.random import binomial, beta
import pandas as pd

N = np.r_[ 750*np.arange(1,30) ] 
p_assignment = 0.5

def sample_beta_posterior(N, C):
    return beta(1+C,N-C+1)

trials = 10000
conversion = np.linspace(0.01,.5,20)

def pprint(results, p, N):
    print """Total participants: %d, conversion probability: %.3f"""%(N, p)
    print """Sample var. of delta: %.3f"""%results.var()
    print """Sample mean of delta: %.4f"""%results.mean()
    print "---------------------------------"
    print

var_results = pd.DataFrame(np.zeros((len(N), len(conversion))), index=N, columns=conversion)


for n in N:
    for p in conversion:
        _results = np.zeros(trials)
        for i in range(trials):
            split = binomial(n, p_assignment)
            N_A, N_B = split, n - split 
            C_A, C_B = binomial(N_A, p), binomial(N_B, p)
            delta = 1.0*C_A/N_A - 1.0*C_B/N_B
            _results[i] = delta
        pprint(_results, p, n)
        var_results[p].ix[n] = _results.var()
var_results.columns = map(lambda r: "%.2f"%r, var_results.columns)


plt.imshow(np.log(var_results.values), cmap=plt.cm.gist_heat, interpolation='none')
plt.yticks(np.arange(0.5, len(var_results.index), 1)[::4], var_results.index[::4])
plt.xticks(np.arange(0.5, len(var_results.columns), 1)[::3], var_results.columns[::3])