Help for package fastmit

Type:

Package

Title:

Fast Mutual Information Based Independence Test

Version:

0.1.1

Description:

A mutual information estimator based on k-nearest neighbor method proposed by A. Kraskov, et al. (2004) <doi:10.1103/PhysRevE.69.066138> to measure general dependence and the time complexity for our estimator is only squared to the sample size, which is faster than other statistics. Besides, an implementation of mutual information based independence test is provided for analyzing multivariate data in Euclidean space (T B. Berrett, et al. (2019) <doi:10.1093/biomet/asz024>); furthermore, we extend it to tackle datasets in metric spaces.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

LazyData:

true

LinkingTo:

Rcpp, RcppArmadillo

Imports:

Rcpp, stats

Suggests:

testthat

NeedsCompilation:

yes

Author:

Shiyun Lin [aut, cre], Jin Zhu [aut], Wenliang Pan [aut], Xueqin Wang [aut], SC2S2 [cph]

Maintainer:

Shiyun Lin <linshy27@mail2.sysu.edu.cn>

RoxygenNote:

6.1.1

Packaged:

2019-12-20 00:16:12 UTC; Arwen

Repository:

CRAN

Date/Publication:

2019-12-30 14:00:07 UTC

kNN Mutual Information Estimators

Description

Estimate mutual information based on the distribution of nearest neighborhood distances. The kNN method is described by Kraskov, et. al (2004).

Usage

mi(x, y, k = 5, distance = FALSE)

Arguments

x

A numeric vector, matrix, data.frame or dist object.

y

A numeric vector, matrix, data.frame or dist object.

k

Order of neighborhood to be used in the kNN method.

distance

Bool flag for considering x and y as distance matrices or not. If distance = TRUE, x and y would be considered as distance matrices, otherwise, these arguments are treated as data and Euclidean distance would be implemented for the samples in x and y. Default: distance = FALSE.

Details

If two samples are passed to arguments x and y, the sample sizes (i.e. number of rows of the matrix or length of the vector) must agree. Moreover, data being passed to x and y must not contain missing or infinite values.

Value

mi

The estimated mutual information.

References

Kraskov, A., Stögbauer, H., & Grassberger, P. (2004). Estimating mutual information. Physical review E 69(6): 066138.

Examples

library(fastmit)
set.seed(1)
x <- rnorm(100)
y <- x + rnorm(100)
mi(x, y, k = 5, distance = FALSE)

set.seed(1)
x <- rnorm(100)
y <- 100 * x + rnorm(100)
distx <- dist(x)
disty <- dist(y)
mi(distx, disty, k = 5, distance = TRUE)

Mutual Information Test

Description

Mutual Information test of independence. Mutual Information are generic dependence measures in Banach spaces.

Usage

mi.test(x, y, k = 5, distance = FALSE, num.permutations = 99,
  seed = 1)

Arguments

x

A numeric vector, matrix, data.frame or dist object.

y

A numeric vector, matrix, data.frame or dist object.

k

Order of neighborhood to be used in the kNN method.

distance

num.permutations

The number of permutation replications. If num.permutations = 0, the function just returns the Mutual Information statistic. Default: num.permutations = 99.

seed

The random seed. Default: seed = 1.

Details

mi.test utilizes the Mutual Information statistics (see mi) to measure dependence and derive a p-value via replicating the random permutation num.permutations times.

Value

If num.permutations > 0, mi.test returns a htest class object containing the following components:

statistic

Mutual Information statistic.

p.value

The p-value for the test.

replicates

Permutation replications of the test statistic.

size

Sample size.

alternative

A character string describes the alternative hypothesis.

method

A character string indicates what type of test was performed.

data.name

Description of data.

If num.permutations = 0, mi.test returns a statistic value.

Examples

library(fastmit)
set.seed(1)
error <- runif(50, min = -0.3, max = 0.3)
x <- runif(50, 0, 4*pi)
y <- cos(x) + error
# plot(x, y)
res <- mi.test(x, y)