BoltzMM (version 0.1.5)

fvbmtests: Hypothesis testing for a fully-visible Boltzmann machine.

Description

Tests the hypothesis that the true bias and interaction parameter values are those in nullmodel, given data and model.

Usage

fvbmtests(data, model, nullmodel)

Value

A list containing 4 objects: a vector containing the z-scores corresponding to the bias parameters bvec_z,a vector containing the p-values corresponding to the bias parameters bvec_p,a matrix containing the z-scores corresponding to the interaction parameters Mmat_z, and a matrix containing the standard errors corresponding to the interaction parameters Mmat_p.

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.

nullmodel

A list containing two elements: a vector of length n bvec, and an n by n matrix Mmat. A list generated by fitfvbm is also sufficient.

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)

#Propose a null hypothesis model
nullmodel <- list(bvec = c(0,0,0), Mmat = matrix(0,3,3))

# Compute z-scores
fvbmtests(data,model,nullmodel)