Package 'fastmit'

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)

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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	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.
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

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.

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)

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