semvec/pypi-packages huggingface dataset:
eummd 0.0.2
Computes maximum mean discrepancy two-sample test for univariate data using the Laplacian kernel. It is also possible to compute the p-value using permutations.
Requires Python: >=3.6

# eummd

## Description 

Computes maximum mean discrepancy two-sample test for univariate data using the Laplacian kernel. It is also possible to compute the p-value using permutations. Also includes implementation for computing the robust median difference statistic 'Q\_n' from Croux and Rousseeuw (1992) <doi:10.1007/978-3-662-26811-7_58> based on Johnson and Mizoguchi (1978) <doi:10.1137/0207013>.


## Installation instructions

Install using `pip`:

```
python3 -m pip install eummd
```

Methods are implemented in C++, and then called using Cython.


## Functions 

There are various functions for computing the maximum mean discrepancy (MMD).

  - `eummd`: efficient univariate MMD with the Laplacian kernel, O(n log n) 
  for a total of n samples.
  - `mmd`: MMD (univariate/multivariate).
  - `meammd`: multivariate efficient approximate MMD, using either random 
  projections or interpoint distances.
  - `mediandiff`: computes the median difference. If univariate, can 
  be computed in O(n log n), otherwise is O(n^2).
  - `medianheuristic`: the inverse of the median difference.

`eummd` and `mmd` return a dictionary with the items `pval` for 
p-value (if specified), `stat` for the statistic and `beta` for the
kernel parameter value that was used. If `beta` is specified as a 
non-positive number, then the median heuristic will be calculated.


## Examples:

```
from eummd import eummd
from eummd import mediandiff

X = np.array([7.1, 1.2, 4.3, 0.4]).astype(np.float64)
Y = np.array([5.5, 2.6, 8.7]).astype(np.float64)
beta = 0.1

# only computes statistic, 
d = eummd(X, Y, beta, pval=False)
print(d['stat'])

# computes statistic and p-value, and used median heuristic for beta
d = eummd(X, Y, beta=-0.1, pval=True)
print("p-value for univariate data: ", d['pval'])
print("statistic for univariate data: ", d['stat'])
print("beta for univariate data: ", d['beta'])

# show median heuristic was used
print(1.0 / mediandiff(X, Y, fast=True))

# a multivariate example, using median heuristic for beta
X = np.array([[1, 2, 3, 4, 5, 6], [7, 8, 9, 10, 11, 12]]).reshape((6, 2))
Y = np.array([[13, 14, 15, 16], [17, 18, 19, 20]]).reshape((4, 2))

d = mmd(X=X, Y=Y, beta=-0.5, pval=True, kernel="Laplacian")
print("p-value for multivariate data: ", d['pval'])
print("statistic for multivariate data: ", d['stat'])
print("beta for multivariate data: ", d['beta'])
```