BoltzMM (version 0.1.5)

fvbmcov: Sandwich estimator of the covariance matrix for a fitted fully-visible Boltzmann machine.

Description

Computes the sandwich estimator of the covariance matrix for a maximum pseudolikelihood estimated fully-visible Boltzmann machine.

Usage

fvbmcov(data, model, fvbmHess)

Value

The n+choose(n,2) by n+choose(n,2) sandwich covariance matrix, estimated using data and evaluated at the fitted parameter values provided in model. Each row (column) is a unique element of the bias vector and interaction matrix. The rows are arranged in lexicographical order with the bias elements first, followed by the interaction elements. For example, if n=3, the order would be bias[1], bias[2] bias[3], interaction[1,2], interaction[1,3], and interaction[2,3].

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).

model

List generated from fitfvbm.

fvbmHess

A function that computes the Hessian of the parameter elements. Currently, the only implemented method is the default fvbmHess function.

Author

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.
fvbmcov(data,model,fvbmHess)