Maximal Information Coefficient

It estimates the Maximal Information Coefficient (MIC) for a continuous predicted-observed dataset.

Usage

MIC(data = NULL, obs, pred, tidy = FALSE, na.rm = TRUE)

Arguments

data: (Optional) argument to call an existing data frame containing the data.
obs: Vector with observed values (numeric).
pred: Vector with predicted values (numeric).
tidy: logical operator (TRUE/FALSE) to decide the type of return. TRUE returns a data.frame, FALSE returns a list (default).
na.rm: Logic argument to remove rows with missing values (NA). Default is na.rm = TRUE.

Value

an object of class numeric within a list (if tidy = FALSE) or within a data frame (if tidy = TRUE).

Details

The MIC function is a wrapper for the mine_stat function of the minerva-package, a collection of Maximal Information-Based Nonparametric statistics (MINE). See Reshef et al. (2011).

For the predicted-observed case (PO), the MIC is defined as follows: $$\textrm{MIC}(D)=\max_{PO<B(n)} M(D)_{X,Y} = \max_{PO<B(n)} \frac{I^ * (D,P,O)} {log(\min{P,O})},$$ where $B(n)=n^{\alpha}$ is the search-grid size, $I^*(D,P,O)$ is the maximum mutual information over all grids P-by-O, of the distribution induced by D on a grid having P and O bins (where the probability mass on a cell of the grid is the fraction of points of D falling in that cell). Albanese et al. (2013).

For the formula and more details, see online-documentation

References

Reshef, D., Reshef, Y., Finucane, H., Grossman, S., McVean, G., Turnbaugh, P., Lander, R., Mitzenmacher, M., and Sabeti, P. (2011). Detecting novel associations in large datasets. Science 334, 6062. doi:10.1126/science.1205438 .

Albanese, D., M. Filosi, R. Visintainer, S. Riccadonna, G. Jurman, C. Furlanello. minerva and minepy: a C engine for the MINE suite and its R, Python and MATLAB wrappers. Bioinformatics (2013) 29(3):407-408. doi:10.1093/bioinformatics/bts707 .

Examples

# \donttest{
set.seed(1)
X <- rnorm(n = 100, mean = 0, sd = 10)
Y <- X + rnorm(n=100, mean = 0, sd = 3)
MIC(obs = X, pred = Y)
#> [1] 0.8546051
# }