II {EWSmethods}

Information Imbalance

Description

Estimates the information imbalance of two hypothesised linked system measurements for a given scalar ('alpha').

Usage

II(X, Y, tau = 1, alpha = 1, k = 1, method = "euclidean")

Arguments

X

Numeric matrix of hypothesised driving variable measurements. If univariate, call 'embedTS(X)' prior to calling 'II()'.

Y

Numeric matrix of hypothesised response variable measurements. If univariate, call 'embedTS(Y)' prior to calling 'II()'.

tau

Numeric. Time lag of information transfer between X and Y.

alpha

Numeric. Scaling parameter for X. If information imbalance is minimised at an 'alpha' > 0, this may be indicative of Granger causality.

k

Numeric. Number of nearest neighbours when estimating ranks.

method

String. Distance measure to be used - defaults to 'euclidean' but see '?dist' for options.

Value

Information imbalance

Source

Del Tatto, V., Bueti, D. & Laio, A. (2024) Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks. PNAS 121 (19) e2317256121.

Examples

#Load the multivariate simulated
#dataset `simTransComms`

data(simTransComms)

#Embed the spp_2 and spp_5 of the third community

embedX <- embed_ts(X = simTransComms$community3[,c("time","spp_2")],
E = 5, tau = 1)

embedY <- embed_ts(X = simTransComms$community3[,c("time","spp_5")],
E = 5, tau = 1)

#Estimate the forward information imbalance
#between spp_2 and spp_5

egII_for <- II(X = embedX[,-1], Y = embedY[,-1],
tau = 1, alpha = 1, k = 5)

#Estimate the reverse information imbalance
#between spp_2 and spp_5

egII_rev <- II(X = embedY[,-1], Y = embedX[,-1],
tau = 1, alpha = 1, k = 5)