MFKnockoffs.filter: Model-Free Knockoff Filter
In MFKnockoffs: Model-Free Knockoff Filter for Controlled Variable Selection

Description Usage Arguments Details Value References Examples

Run the model-free knockoff procedure from start to finish, selecting variables relevant for predicting the outcome of interest.

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MFKnockoffs.filter(X, y, knockoffs = MFKnockoffs.create.approximate_gaussian,
  statistic = MFKnockoffs.stat.glmnet_coef_difference, q = 0.1,
  threshold = c("knockoff+", "knockoff"))

`X`	matrix or data frame of predictors
`y`	response vector
`knockoffs`	the method used to construct knockoffs for the X variables. It must be a function taking a n-by-p matrix X as input and returning a n-by-p matrix of knockoff variables
`statistic`	the test statistic (by default, a lasso statistic with cross validation). See the Details section for more information.
`q`	target FDR (false discovery rate)
`threshold`	either 'knockoff+' or 'knockoff' (default: 'knockoff+').

This function creates the knockoffs, computes the test statistics, and selects variables. It is the main entry point for the model-free knockoff package.

The parameter knockoffs controls how knockoff variables are created. By default, a multivariate normal distribution is fitted to the original variables in X. The estimated mean vector and covariance matrix are used to generate second-order approximate Gaussian knockoffs. In general, knockoffs should be a function taking a n-by-p matrix of observed variables X and returning a n-by-p matrix of knockoff variables. Two optional functions for creating knockoffs are provided with this package.

If the rows of X are distributed as a multivariate Gaussian with known parameters, then the function MFKnockoffs.create.gaussian can be used to generate valid Gaussian knockoff variables, as shown in the examples below.

If the design matrix X is assumed to be fixed instead of random, one can create knockoff variables using the function MFKnockoffs.create.fixed. This corresponds to the original framework of the (non Model-Free) knockoff filter.

For more information about creating knockoffs, type ??MFKnockoffs.create.

The default test statistic is MFKnockoffs.stat.glmnet_coef_difference. For a complete list of the statistics provided with this package, type ??MFKnockoffs.stat.

It is also possible to provide custom test statistics. An example can be found in the vignette.

An object of class "MFKnockoffs.result". This object is a list containing at least the following components:

`X`	matrix of original variables
`X_k`	matrix of knockoff variables
`statistic`	computed test statistics
`threshold`	computed selection threshold
`selected`	named vector of selected variables

Candes et al., Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection, arXiv:1610.02351 (2016). https://statweb.stanford.edu/~candes/MF_Knockoffs/index.html

Barber and Candes, Controlling the false discovery rate via knockoffs. Ann. Statist. 43 (2015), no. 5, 2055–2085. https://projecteuclid.org/euclid.aos/1438606853

p=100; n=200; k=15
mu = rep(0,p); Sigma = diag(p)
X = matrix(rnorm(n*p),n)
nonzero = sample(p, k)
beta = 3.5 * (1:p %in% nonzero)
y = X %*% beta + rnorm(n)

# Basic usage with default arguments
result = MFKnockoffs.filter(X, y)
print(result$selected)

# Advanced usage with custom arguments
knockoffs = function(X) MFKnockoffs.create.gaussian(X, mu, Sigma)
k_stat = function(X, X_k, y) MFKnockoffs.stat.glmnet_coef_difference(X, X_k, y, nfolds=5)
result = MFKnockoffs.filter(X, y, knockoffs=knockoffs, statistic=k_stat)
print(result$selected)