Package 'BCodifSIS'

Ball-Codifference Sure Independence Screening

Description

Computes Ball-codifference scores and performs sure independence screening for high-dimensional predictors. The package provides compiled C routines and R wrappers for ranking predictors by a local codifference-weighted random-ball score.

Details

The main screening function is bcodif_sis(). Lower-level functions are available for computing scores for one predictor pair or for all columns of a predictor matrix.

References

Rezapour, M. and Maroufy, V. (2026). "Ball-Codifference Screening for Heavy-Tailed Predictors". doi:10.48550/arXiv.2607.20821.

See Also

bcodif_sis(), bcodif_scores(), bcodif_score_pair()

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Compute One Ball-Codifference Score

Description

Computes the Ball-codifference score for one predictor-response pair. The function bcodif_score() is an alias for bcodif_score_pair().

Usage

bcodif_score_pair(x, y, normalize = FALSE, absolute_kappa = FALSE,
  ridge = 1e-12)

bcodif_score(x, y, normalize = FALSE, absolute_kappa = FALSE,
  ridge = 1e-12)

Arguments

x	Numeric predictor vector.
y	Numeric response vector.
normalize	Logical. If TRUE, use the normalized score.
absolute_kappa	Logical. If TRUE, use $|\kappa_{ij}|$.
ridge	Nonnegative ridge used only when normalize = TRUE.

Value

One numeric score.

See Also

bcodif_scores(), bcodif_score_slow()

Examples

grid <- seq_len(40)
x <- sin(grid / 4) + cos(grid / 7)
y <- x + 0.5 * sin(grid / 3)
bcodif_score_pair(x, y)

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Slow Pure-R Ball-Codifference Score

Description

Computes the same unnormalized empirical Ball-codifference score as the compiled routine, but using simple R loops. This function is mainly intended for testing and small examples.

Usage

bcodif_score_slow(x, y, absolute_kappa = FALSE)

Arguments

x	Numeric predictor vector.
y	Numeric response vector.
absolute_kappa	Logical. If TRUE, use $|\kappa_{ij}|$.

Value

One numeric score.

See Also

bcodif_score_pair(), quick_check()

Examples

grid <- seq_len(15)
x <- sin(grid / 4) + cos(grid / 7)
y <- x + sin(grid / 3)
fast <- bcodif_score(x, y)
slow <- bcodif_score_slow(x, y)
all.equal(fast, slow, tolerance = 1e-10)

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Compute Ball-Codifference Scores for Predictor Columns

Description

Computes the empirical Ball-codifference score between each column of X and the response y. The compiled implementation uses a sorted sweep and Fenwick-tree updates to avoid a direct cubic loop over all observations for each ball center.

Usage

bcodif_scores(X, y, normalize = FALSE, absolute_kappa = FALSE, ridge = 1e-12)

Arguments

X	Numeric predictor matrix. Rows are observations and columns are predictors.
y	Numeric response vector with length nrow(X).
normalize	Logical. If TRUE, use the normalized Ball-codifference score.
absolute_kappa	Logical. If TRUE, use $|\kappa_{ij}|$ instead of signed $\kappa_{ij}$.
ridge	Nonnegative ridge used only when normalize = TRUE.

Value

A numeric vector of scores, one per predictor column. Column names are preserved when available.

See Also

bcodif_sis(), bcodif_score_pair()

Examples

grid <- seq_len(50)
X <- vapply(seq_len(5), function(j) {
  sin(grid / (j + 1)) + cos(grid * j / 9)
}, numeric(50))
y <- X[, 1] + sin(grid / 3)
bcodif_scores(X, y)

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Ball-Codifference Sure Independence Screening

Description

Ranks predictors by their marginal Ball-codifference score and returns the top d variables. The alias bcodifsis() is provided for users who prefer a compact function name.

Usage

bcodif_sis(X, y, d = NULL, normalize = FALSE, absolute_kappa = FALSE,
  ridge = 1e-12)

bcodifsis(x, y, d = NULL, normalize = FALSE, absolute_kappa = FALSE,
  ridge = 1e-12)

## S3 method for class 'bcodif_sis'
print(x, ...)

Arguments

X	Numeric predictor matrix. Rows are observations and columns are predictors.
x	For bcodifsis(), a numeric predictor matrix. For the print method, an object returned by bcodif_sis().
y	Numeric response vector with length nrow(X).
d	Number of variables to retain. The default is floor(nrow(X) / log(nrow(X))).
normalize	Logical. If TRUE, rank by the normalized score.
absolute_kappa	Logical. If TRUE, use $|\kappa_{ij}|$.
ridge	Nonnegative ridge used only when normalize = TRUE.
...	Additional arguments for the print method, currently unused.

Value

An object of class bcodif_sis, which is a list with components:

ix	Integer indices of the selected variables.
scores	Numeric score for every predictor.
ranking	Integer ranking from largest score to smallest score.
complete.info	Data frame with variable index, name, statistic, rank, and selection flag.
d	Number of retained variables.
method	Name of the screening method used.
normalize	Whether normalized scores were used.
absolute_kappa	Whether the absolute local codifference weight was used.
call	Matched function call.

See Also

bcodif_scores(), quick_check()

Examples

grid <- seq_len(80)
X <- vapply(seq_len(10), function(j) {
  sin(grid / (j + 1)) + cos(grid * j / 9)
}, numeric(80))
y <- X[, 2] + 0.5 * sin(grid / 3)
fit <- bcodif_sis(X, y, d = 3)
fit$ix
head(fit$complete.info)

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Quick Installation and Functionality Check

Description

Runs a small self-test. The test compares the compiled score to the slow pure-R score and then fits a small screening example.

Usage

quick_check()

Value

A list with the compiled score, slow score, their absolute difference, and a fitted bcodif_sis object.

See Also

bcodif_sis(), bcodif_score_slow()

Examples

quick_check()

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