fvbmstderr {BoltzMM}

Standard errors for the parameter elements of a fitted fully-visible Boltzmann machine.

Description

Computes the normal approximation standard errors from the sandwich estimator of the covariance matrix for a maximum pseudolikelihood estimated fully-visible Boltzmann machine.

Usage

fvbmstderr(data, covarmat)

Arguments

data

An N by n matrix, where each of the N rows contains a length n string of spin variables (i.e. each element is -1 or 1).

covarmat

A covariance matrix generated from fvbmcov.

Value

A list containing 2 objects: a vector containing the standard errors corresponding to the bias parameters bvec_se, and a matrix containing the standard errors corresponding to the interaction parameters Mmat_se.

Author(s)

Andrew T. Jones and Hien D. Nguyen

References

H.D. Nguyen and I.A. Wood (2016), Asymptotic normality of the maximum pseudolikelihood estimator for fully-visible Boltzmann machines, IEEE Transactions on Neural Networks and Learning Systems, vol. 27, pp. 897-902.

Examples

# Generate num=1000 random strings of n=3 binary spin variables under bvec and Mmat.
num <- 1000
bvec <- c(0,0.5,0.25)
Mmat <- matrix(0.1,3,3) - diag(0.1,3,3)
data <- rfvbm(num,bvec,Mmat)
# Fit a fully visible Boltzmann machine to data, starting from parameters bvec and Mmat.
model <- fitfvbm(data,bvec,Mmat)
# Compute the sandwich covariance matrix using the data and the model.
covarmat <- fvbmcov(data,model,fvbmHess)
# Compute the standard errors of the parameter elements according to a normal approximation.
fvbmstderr(data,covarmat)