# [scikit-learn] mutual information for continuous variables with scikit-learn

Gael Varoquaux gael.varoquaux at normalesup.org
Wed Feb 1 09:18:40 EST 2023

```For estimating mutual information on continuous variables, have a look at the corresponding package
https://pypi.org/project/mutual-info/

G

On Wed, Feb 01, 2023 at 02:32:03PM +0100, m m wrote:
> Hello,

> I have two continuous variables (heart rate samples over a period of time), and
> would like to compute mutual information between them as a measure of
> similarity.

> I've read some posts suggesting to use the mutual_info_score from scikit-learn
> but will this work for continuous variables? One stackoverflow answer suggested
> converting the data into probabilities with np.histogram2d() and passing the
> contingency table to the mutual_info_score.

> from sklearn.metrics import mutual_info_score

> def calc_MI(x, y, bins):
>     c_xy = np.histogram2d(x, y, bins)[0]
>     mi = mutual_info_score(None, None, contingency=c_xy)
>     return mi

> # generate data
> L = np.linalg.cholesky( [[1.0, 0.60], [0.60, 1.0]])
> uncorrelated = np.random.standard_normal((2, 300))
> correlated = np.dot(L, uncorrelated)
> A = correlated[0]
> B = correlated[1]
> x = (A - np.mean(A)) / np.std(A)
> y = (B - np.mean(B)) / np.std(B)

> # calculate MI
> mi = calc_MI(x, y, 50)

> Is calc_MI a valid approach? I'm asking because I also read that when variables
> are continuous, then the sums in the formula for discrete data become
> integrals, but I'm not sure if this procedure is implemented in scikit-learn?

> Thanks!

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--
Gael Varoquaux
Research Director, INRIA