# Mutual Information

### Description

KNN Mutual Information Estimators.

### Usage

1 |

### Arguments

`X` |
an input data matrix. |

`Y` |
an input data matrix. |

`k` |
the maximum number of nearest neighbors to search. The default value is set to 10. |

`direct` |
Directly compute or via entropies. |

### Details

The direct computation is based on the first estimator of A. Kraskov, H. Stogbauer and P.Grassberger (2004) and the indirect computation is done via entropy estimates, i.e., I(X, Y) = H (X) + H(Y) - H(X, Y). The direct method has smaller bias and variance but the indirect method is faster, see Evans (2008).

### Value

For direct method, one mutual information estimate;
For indirect method,a vector of length `k`

for mutual information estimates using `1:k`

nearest neighbors, respectively.

### Author(s)

Shengqiao Li. To report any bugs or suggestions please email: shli@stat.wvu.edu.

### References

A. Kraskov, H. Stogbauer and P.Grassberger (2004).
“Estimating mutual information”.
*Physical Review E*, **69**:066138, 1–16.

D. Evans (2008).
“A Computationally efficient estimator for mutual information”.
*Proc. R. Soc. A*, **464**, 1203–1215.