Package 'infoxtr'

Title: Information-Theoretic Measures for Revealing Variable Interactions
Description: Implements information-theoretic measures to explore variable interactions, including KSG mutual information estimation for continuous variables from Kraskov et al. (2004) <doi:10.1103/PhysRevE.69.066138>, knockoff conditional mutual information described in Zhang & Chen (2025) <doi:10.1126/sciadv.adu6464>, synergistic-unique-redundant decomposition introduced by Martinez-Sanchez et al. (2024) <doi:10.1038/s41467-024-53373-4>, and information imbalance gain following Del Tatto et al. (2024) <doi:10.1073/pnas.2317256121>, allowing detection of complex and diverse relationships among variables.
Authors: Wenbo Lyu [aut, cre, cph] (ORCID: <https://orcid.org/0009-0002-6003-3800>)
Maintainer: Wenbo Lyu <[email protected]>
License: GPL-3
Version: 0.4
Built: 2026-10-03 08:35:37 UTC
Source: https://github.com/stscl/infoxtr

Help Index

Conditional Entropy

Description

Conditional Entropy

Usage

ce(data, target, conds, base = exp(1), type = c("cont", "disc"), k = 3)

Arguments

data

Observation data.
target

Integer vector of column indices for the target variables.
conds

Integer vector of column indices for the conditioning variables.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
type

(optional) Estimation method: "disc" for discrete entropy or "cont" for continuous entropy (KSG estimator).
k

(optional) Number of nearest neighbors used by the continuous estimator. Ignored when type = "disc".

Value

A numerical value.

Examples

infoxtr::ce(matrix(1:100,ncol=2),1,2)

Conditional Mutual Information

Description

Conditional Mutual Information

Usage

cmi(
  data,
  target,
  interact,
  conds,
  base = exp(1),
  type = c("cont", "disc"),
  k = 3,
  normalize = FALSE
)

Arguments

data

Observation data.
target

Integer vector of column indices for the target variables.
interact

Integer vector of column indices for the interacting variables.
conds

Integer vector of column indices for the conditioning variables.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
type

(optional) Estimation method: "disc" for discrete entropy or "cont" for continuous entropy (KSG estimator).
k

(optional) Number of nearest neighbors used by the continuous estimator. Ignored when type = "disc".
normalize

(optional) Logical; if TRUE, return normalized mutual information.

Value

A numerical value.

Examples

set.seed(42)
infoxtr::cmi(matrix(stats::rnorm(99,1,10),ncol=3),1,2,3)

Discretization

Description

Discretization

Usage

discretize(
  x,
  n = 5,
  method = "natural",
  large = 3000,
  prop = 0.15,
  seed = 42,
  thr = 0.4,
  iter = 100,
  bps = NULL,
  right_closed = TRUE
)

Arguments

x

A vector.
n

(optional) Number of classes.
method

(optional) Discretization method. One of "sd", "equal", "geometric", "quantile", "manual", ⁠"natural("jenks")"⁠, or "headtail"("headtails").
large

(optional) Threshold sample size for natural breaks sampling.
prop

(optional) Sampling proportion used when method = "natural" and the input size exceeds large.
seed

(optional) Random seed used for sampling in natural breaks.
thr

(optional) Threshold used in the head/tail breaks algorithm.
iter

(optional) Maximum number of iterations for head/tail breaks.
bps

(optional) Numeric vector of manual breakpoints used when method = "manual".
right_closed

(optional) Logical. If TRUE, intervals are right-closed (e.g., ⁠(a, b]⁠). If FALSE, intervals are left-closed ⁠[a, b)⁠.

Value

A discretized integer vector.

Note

If x is not numeric, or if the number of unique non-NA values is less than or equal to n (except for the "headtail"("headtails") method), the function falls back to integer encoding via as.factor(). In all cases, missing values (NA/NaN) are ignored and returned as class 0.

Examples

set.seed(42)
infoxtr::discretize(stats::rnorm(99,1,10))

Shannon Entropy

Description

Shannon Entropy

Usage

entropy(vec, base = exp(1), type = c("cont", "disc"), k = 3)

Arguments

vec

A vector.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
type

(optional) Estimation method: "disc" for discrete entropy or "cont" for continuous entropy (KSG estimator).
k

(optional) Number of nearest neighbors used by the continuous estimator. Ignored when type = "disc".

Value

A numerical value.

Examples

set.seed(42)
infoxtr::entropy(stats::rnorm(100), type = "cont")
infoxtr::entropy(sample(letters[1:5], 100, TRUE), base = 2, type = "disc")

Imbalance Gain

Description

Imbalance Gain

Usage

imbalance_gain(
  mx,
  my,
  alpha = seq(0, 1, 0.1),
  lib = NULL,
  pred = NULL,
  h = 1,
  k = 3,
  threads = 1,
  method = "euclidean"
)

Arguments

mx

Numeric matrix of hypothesised driving variable measurements.
my

Numeric matrix of hypothesised response variable measurements.
alpha

(optional) Scaling parameter weighting the putative driver measurements.
lib

(optional) Library indices.
pred

(optional) Prediction indices.
h

(optional) Prediction horizon.
k

(optional) Number of nearest neighbors when estimating ranks.
threads

(optional) Number of parallel threads.
method

(optional) Distance measure to be used: "euclidean", "manhattan", or ⁠maximum"⁠.

Value

A numeric vector.

References

Del Tatto, V., Fortunato, G., Bueti, D., Laio, A., 2024. Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks. Proceedings of the National Academy of Sciences 121.

Examples

set.seed(42)
mx = embed(rnorm(100), 3)
my = embed(rnorm(100), 3)
infoxtr::imbalance_gain(mx, my)

Information Imbalance

Description

Information Imbalance

Usage

info_imbalance(
  mx,
  my,
  lib = NULL,
  pred = NULL,
  k = 1,
  threads = 1,
  method = "euclidean"
)

Arguments

mx

Numeric matrix of hypothesised driving variable measurements.
my

Numeric matrix of hypothesised response variable measurements.
lib

(optional) Library indices.
pred

(optional) Prediction indices.
k

(optional) Number of nearest neighbors when estimating ranks.
threads

(optional) Number of parallel threads.
method

(optional) Distance measure to be used: "euclidean", "manhattan", or ⁠maximum"⁠.

Value

A numeric value.

References

Glielmo, A., Zeni, C., Cheng, B., Csanyi, G., Laio, A., 2022. Ranking the information content of distance measures. PNAS Nexus 1.

Examples

set.seed(42)
mx = embed(rnorm(100), 3)
my = embed(rnorm(100), 3)
infoxtr::info_imbalance(mx, my)

Joint Entropy

Description

Joint Entropy

Usage

je(data, indices, base = exp(1), type = c("cont", "disc"), k = 3)

Arguments

data

Observation data.
indices

Integer vector of column indices to include in joint entropy calculation.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
type

(optional) Estimation method: "disc" for discrete entropy or "cont" for continuous entropy (KSG estimator).
k

(optional) Number of nearest neighbors used by the continuous estimator. Ignored when type = "disc".

Value

A numerical value.

Examples

infoxtr::je(matrix(1:100,ncol=2),1:2)

Knockoff Conditional Mutual Information

Description

Knockoff Conditional Mutual Information

Usage

kocmi(
  data,
  target,
  agent,
  conds,
  knockoff,
  null_knockoff = NULL,
  type = c("cont", "disc"),
  nboots = 10000,
  k = 3,
  threads = 1,
  seed = 42,
  base = exp(1),
  method = "equal",
  contain_null = TRUE
)

Arguments

data

Observation data.
target

Integer vector of column indices for the target variables.
agent

Integer vector of column indices for the agent variables.
conds

Integer vector of column indices for the conditioning variables.
knockoff

Knockoff realizations constructed for the agent variable while keeping the target variable unchanged. Each column corresponds to one Monte Carlo knockoff sample generated using the remaining variables except the target.
null_knockoff

(optional) Knockoff realizations generated under the null setting where all variables are jointly used to construct knockoffs. Each column represents one Monte Carlo sample. If contain_null = FALSE, this argument can be NULL.
type

(optional) Estimation method: "disc" for discrete mutual information or "cont" for continuous mutual information (KSG estimator).
nboots

(optional) Number of permutations used in the sign-flipping permutation test for evaluating the significance of the mean information difference.
k

(optional) For type = "cont", the number of nearest neighbors used by the continuous conditional mutual information estimator. For type = "disc", the number of bins used for discretization.
threads

(optional) Number of threads used.
seed

(optional) Random seed used for permutation test.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
method

(optional) Discretization method. One of "sd", "equal", "geometric", "quantile", ⁠"natural("jenks")"⁠, or "headtail"("headtails").
contain_null

(optional) Logical. If TRUE, the test statistic is computed using knockoffs generated under the null model (provided in null_knockoff). In this case the difference is defined as I(Y;Xnull∣Z)−I(Y;Xknockoff∣Z)I(Y; X_{null} | Z) - I(Y; X_{knockoff} | Z). If FALSE, the original conditional mutual information I(Y;X∣Z)I(Y; X | Z) is used instead and compared against the knockoff estimates I(Y;Xknockoff∣Z)I(Y; X_{knockoff} | Z).

Value

A named numeric vector.

Note

kocmi only support numeric data.

References

Zhang, X., Chen, L., 2025. Quantifying interventional causality by knockoff operation. Science Advances 11.

Examples

set.seed(42)
kn1 = replicate(50, stats::rnorm(100))
kn2 = replicate(50, stats::rnorm(100))
mat = replicate(3, stats::rnorm(100))
infoxtr::kocmi(mat, 1, 2, 3, kn1, kn2)

Mutual Information

Description

Mutual Information

Usage

mi(
  data,
  target,
  interact,
  base = exp(1),
  type = c("cont", "disc"),
  k = 3,
  normalize = FALSE
)

Arguments

data

Observation data.
target

Integer vector of column indices for the target variables.
interact

Integer vector of column indices for the interacting variables.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
type

(optional) Estimation method: "disc" for discrete entropy or "cont" for continuous entropy (KSG estimator).
k

(optional) Number of nearest neighbors used by the continuous estimator. Ignored when type = "disc".
normalize

(optional) Logical; if TRUE, return normalized mutual information.

Value

A numerical value.

Examples

infoxtr::mi(matrix(1:100,ncol=2),1,2)

Synergistic-Unique-Redundant Decomposition

Description

Synergistic-Unique-Redundant Decomposition

Usage

## S4 method for signature 'data.frame'
surd(
  data,
  target,
  agent,
  lag = 1,
  bin = 5,
  method = "equal",
  max.order = 10,
  threads = 1,
  base = 2,
  normalize = TRUE
)

## S4 method for signature 'sf'
surd(
  data,
  target,
  agent,
  lag = 1,
  bin = 5,
  method = "equal",
  max.order = 10,
  threads = 1,
  base = 2,
  normalize = TRUE,
  nb = NULL
)

## S4 method for signature 'SpatRaster'
surd(
  data,
  target,
  agent,
  lag = 1,
  bin = 5,
  method = "equal",
  max.order = 10,
  threads = 1,
  base = 2,
  normalize = TRUE
)

Arguments

data

Observation data.
target

Integer vector of column indices for the target variables.
agent

Integer vector of column indices for the agent variables.
lag

(optional) Lag of the agent variables.
bin

(optional) Number of discretization bins.
method

(optional) Discretization method. One of "sd", "equal", "geometric", "quantile", ⁠"natural("jenks")"⁠, or "headtail"("headtails").
max.order

(optional) Maximum combination order.
threads

(optional) Number of threads used.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
normalize

(optional) Logical; if TRUE, return normalized mutual information.
nb

(optional) Neighbours list.

Value

A list.

vars

Character vector indicating the variable combination associated with each information component.

types

Character vector indicating the information type of each component.

values

Numeric vector giving the magnitude of each information component.

Note

surd only supports numeric input data. Both bin and method support variable-specific settings using R-style recycling:

  • length 1: applied to the target and all agent variables

  • length 2: first for the target, second for all agents

  • length > 2: first for the target, remaining values are recycled across agents

References

Martinez-Sanchez, A., Arranz, G., Lozano-Duran, A., 2024. Decomposing causality into its synergistic, unique, and redundant components. Nature Communications 15.

Examples

columbus = sf::read_sf(system.file("case/columbus.gpkg", package="spEDM"))
infoxtr::surd(columbus, 1, 2:3)

Transfer Entropy

Description

Transfer Entropy

Usage

te(
  data,
  target,
  agent,
  lag_p = 3,
  lag_q = 3,
  base = exp(1),
  type = c("cont", "disc"),
  k = 3,
  normalize = FALSE,
  lag_single = FALSE
)

Arguments

data

Observation data.
target

Integer vector of column indices for the target variables.
agent

Integer vector of column indices for the agent variables.
lag_p

(optional) Lag of the target variables.
lag_q

(optional) Lag of the agent variables.
base

(optional) Logarithm base of the entropy. Defaults to exp(1) (nats). Use 2 for bits or 10 for dits.
type

(optional) Estimation method: "disc" for discrete entropy or "cont" for continuous entropy (KSG estimator).
k

(optional) Number of nearest neighbors used by the continuous estimator. Ignored when type = "disc".
normalize

(optional) Logical; if TRUE, return normalized mutual information.
lag_single

(optional) Logical; if FALSE, use full lag embedding.

Value

A numerical value.

References

Schreiber, T., 2000. Measuring Information Transfer. Physical Review Letters 85, 461–464.

Examples

set.seed(42)
infoxtr::te(matrix(stats::rnorm(100,1,10),ncol=2),1,2)