Python API

class minepy.MINE(alpha=0.6, c=15, est="mic_approx")

Maximal Information-based Nonparametric Exploration.

Parameters:
alpha : float (0, 1.0]

the exponent in B(n) = n^alpha.

c : float (> 0)

determines how many more clumps there will be than columns in every partition. Default value is 15, meaning that when trying to draw x grid lines on the x-axis, the algorithm will start with at most 15*x clumps.

est : str (“mic_approx”, “mic_e”)

estimator. With est=”mic_approx” the original MINE statistics will be computed, with est=”mic_e” the equicharacteristic matrix is is evaluated and the mic() and tic() methods will return MIC_e and TIC_e values respectively.
compute_score(x, y)

Computes the maximum normalized mutual information scores between x and y.

mic()

Returns the Maximal Information Coefficient (MIC or MIC_e).

mas()

Returns the Maximum Asymmetry Score (MAS).

mev()

Returns the Maximum Edge Value (MEV).

mcn(eps=0)

Returns the Minimum Cell Number (MCN) with eps >= 0.

mcn_general()

Returns the Minimum Cell Number (MCN) with eps = 1 - MIC.

gmic()

Returns the Generalized Maximal Information Coefficient (GMIC).

tic()

Returns the Total Information Coefficient (TIC or TIC_e).

get_score()

Returns the maximum normalized mutual information scores M (i.e. the characteristic matrix if est=”mic_approx”, the equicharacteristic matrix instead). M is a list of 1d numpy arrays where M[i][j] contains the score using a grid partitioning x-values into i+2 bins and y-values into j+2 bins.

computed()

Return True if the scores ((equi)characteristic matrix) are computed.

First Example

The example is located in examples/python_example.py.

import numpy as np
from minepy import MINE

def print_stats(mine):
    print "MIC", mine.mic()
    print "MAS", mine.mas()
    print "MEV", mine.mev()
    print "MCN (eps=0)", mine.mcn(0)
    print "MCN (eps=1-MIC)", mine.mcn_general()
    print "GMIC", mine.gmic()
    print "TIC", mine.tic()

x = np.linspace(0, 1, 1000)
y = np.sin(10 * np.pi * x) + x
mine = MINE(alpha=0.6, c=15, est="mic_approx")
mine.compute_score(x, y)

print "Without noise:"
print_stats(mine)
print

np.random.seed(0)
y +=np.random.uniform(-1, 1, x.shape[0]) # add some noise
mine.compute_score(x, y)

print "With noise:"
print_stats(mine)

Run the example:

$ python python_example.py
Without noise:
MIC 1.0
MAS 0.726071574374
MEV 1.0
MCN (eps=0) 4.58496250072
MCN (eps=1-MIC) 4.58496250072
GMIC 0.779360251901
TIC 67.6612295532

With noise:
MIC 0.505716693417
MAS 0.365399904262
MEV 0.505716693417
MCN (eps=0) 5.95419631039
MCN (eps=1-MIC) 3.80735492206
GMIC 0.359475501353
TIC 28.7498326953

Second Example

The example is located in examples/relationships.py.

Warning

Requires the matplotlib library.

from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
from minepy import MINE


rs = np.random.RandomState(seed=0)

def mysubplot(x, y, numRows, numCols, plotNum,
              xlim=(-4, 4), ylim=(-4, 4)):

    r = np.around(np.corrcoef(x, y)[0, 1], 1)
    mine = MINE(alpha=0.6, c=15, est="mic_approx")
    mine.compute_score(x, y)
    mic = np.around(mine.mic(), 1)
    ax = plt.subplot(numRows, numCols, plotNum,
                     xlim=xlim, ylim=ylim)
    ax.set_title('Pearson r=%.1f\nMIC=%.1f' % (r, mic),fontsize=10)
    ax.set_frame_on(False)
    ax.axes.get_xaxis().set_visible(False)
    ax.axes.get_yaxis().set_visible(False)
    ax.plot(x, y, ',')
    ax.set_xticks([])
    ax.set_yticks([])
    return ax

def rotation(xy, t):
    return np.dot(xy, [[np.cos(t), -np.sin(t)], [np.sin(t), np.cos(t)]])

def mvnormal(n=1000):
    cors = [1.0, 0.8, 0.4, 0.0, -0.4, -0.8, -1.0]
    for i, cor in enumerate(cors):
        cov = [[1, cor],[cor, 1]]
        xy = rs.multivariate_normal([0, 0], cov, n)
        mysubplot(xy[:, 0], xy[:, 1], 3, 7, i+1)

def rotnormal(n=1000):
    ts = [0, np.pi/12, np.pi/6, np.pi/4, np.pi/2-np.pi/6,
          np.pi/2-np.pi/12, np.pi/2]
    cov = [[1, 1],[1, 1]]
    xy = rs.multivariate_normal([0, 0], cov, n)
    for i, t in enumerate(ts):
        xy_r = rotation(xy, t)
        mysubplot(xy_r[:, 0], xy_r[:, 1], 3, 7, i+8)

def others(n=1000):
    x = rs.uniform(-1, 1, n)
    y = 4*(x**2-0.5)**2 + rs.uniform(-1, 1, n)/3
    mysubplot(x, y, 3, 7, 15, (-1, 1), (-1/3, 1+1/3))

    y = rs.uniform(-1, 1, n)
    xy = np.concatenate((x.reshape(-1, 1), y.reshape(-1, 1)), axis=1)
    xy = rotation(xy, -np.pi/8)
    lim = np.sqrt(2+np.sqrt(2)) / np.sqrt(2)
    mysubplot(xy[:, 0], xy[:, 1], 3, 7, 16, (-lim, lim), (-lim, lim))

    xy = rotation(xy, -np.pi/8)
    lim = np.sqrt(2)
    mysubplot(xy[:, 0], xy[:, 1], 3, 7, 17, (-lim, lim), (-lim, lim))

    y = 2*x**2 + rs.uniform(-1, 1, n)
    mysubplot(x, y, 3, 7, 18, (-1, 1), (-1, 3))

    y = (x**2 + rs.uniform(0, 0.5, n)) * \
        np.array([-1, 1])[rs.random_integers(0, 1, size=n)]
    mysubplot(x, y, 3, 7, 19, (-1.5, 1.5), (-1.5, 1.5))

    y = np.cos(x * np.pi) + rs.uniform(0, 1/8, n)
    x = np.sin(x * np.pi) + rs.uniform(0, 1/8, n)
    mysubplot(x, y, 3, 7, 20, (-1.5, 1.5), (-1.5, 1.5))

    xy1 = np.random.multivariate_normal([3, 3], [[1, 0], [0, 1]], int(n/4))
    xy2 = np.random.multivariate_normal([-3, 3], [[1, 0], [0, 1]], int(n/4))
    xy3 = np.random.multivariate_normal([-3, -3], [[1, 0], [0, 1]], int(n/4))
    xy4 = np.random.multivariate_normal([3, -3], [[1, 0], [0, 1]], int(n/4))
    xy = np.concatenate((xy1, xy2, xy3, xy4), axis=0)
    mysubplot(xy[:, 0], xy[:, 1], 3, 7, 21, (-7, 7), (-7, 7))

plt.figure(facecolor='white')
mvnormal(n=800)
rotnormal(n=200)
others(n=800)
plt.tight_layout()
plt.show()
_images/relationships.png