shapleySubsetMc {sensitivity}

Estimation of Shapley effects from data using nearest neighbors method

Description

shapleySubsetMc implements the estimation of the Shapley effects from data using some nearest neighbors method to generate according to the conditional distributions of the inputs. It can be used with categorical inputs.

Usage

shapleySubsetMc(X,Y, Ntot=NULL, Ni=3, cat=NULL, weight=NULL, discrete=NULL, noise=FALSE)
## S3 method for class 'shapleySubsetMc'
plot(x, ylim = c(0, 1), ...)

Arguments

X

a matrix or a dataframe of the input sample

Y

a vector of the output sample

Ntot

an integer of the approximate cost wanted

Ni

the number of nearest neighbours taken for each point

cat

a vector giving the indices of the input categorical variables

weight

a vector with the same length of cat giving the weight of each categorical variable in the product distance

discrete

a vector giving the indices of the input variable that are real, and not categorical, but that can take several times the same values

noise

logical. If FALSE (the default), the variable Y is a function of X

x

a list of class "shapleySubsetMc" storing the state of the sensitivity study (Shapley effects, cost, names of inputs)

ylim

y-coordinate plotting limits

...

any other arguments for plotting

Details

If weight = NULL, all the categorical variables will have the same weight 1.

If Ntot = NULL, the nearest neighbours will be compute for all the n (2^p-2) points, where n is the length of the sample. The estimation can be very long with this parameter.

Value

shapleySubsetMc returns a list of class "shapleySubsetMc", containing:

shapley

the Shapley effects estimates.

cost

the real total cost of these estimates: the total number of points for which the nearest neighbours were computed.

names

the labels of the input variables.

Author(s)

Baptiste Broto

References

B. Broto, F. Bachoc, M. Depecker, 2020, Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution, SIAM/ASA Journal of Uncertainty Quantification, 8:693-716.

See Also

shapleyPermEx, shapleyPermRand, shapleyLinearGaussian, sobolrank, shapleysobol_knn

Examples

# First example: the linear Gaussian framework

# we generate a covariance matrice Sigma
p <- 4 #dimension
A <- matrix(rnorm(p^2),nrow=p,ncol=p)
Sigma <- t(A)%*%A # it means t(A)%*%A
C <- chol(Sigma)
n <- 500 #sample size (put n=2000 for more consistency)

Z=matrix(rnorm(p*n),nrow=n,ncol=p)
X=Z%*%C # X is a gaussian vector with zero mean and covariance Sigma
Y=rowSums(X) 
Shap=shapleySubsetMc(X=X,Y=Y,Ntot=5000)
plot(Shap)


#Second example: The Sobol model with heterogeneous inputs

p=8 #dimension
A=matrix(rnorm(p^2),nrow=p,ncol=p)
Sigma=t(A)%*%A
C=chol(Sigma)
n=500 #sample size (put n=5000 for more consistency)

Z=matrix(rnorm(p*n),nrow=n,ncol=p)
X=Z

#we create discrete and categorical variables
X[,1]=round(X[,1]/2) 
X[,2]=X[,2]>2
X[,4]=-2*round(X[,4])+4
X[(X[,6]>0 &X[,6]<1),6]=1

cat=c(1,2)  # we choose to take X1 and X2 as categorical variables (with the discrete distance)
discrete=c(4,6) # we indicate that X4 and X6 can take several times the same value

Y=sobol.fun(X)
Ntot <- 2000 # put Ntot=20000 for more consistency
Shap=shapleySubsetMc(X=X,Y=Y, cat=cat, discrete=discrete, Ntot=Ntot, Ni=10)

plot(Shap)