fvbmpartiald {BoltzMM}

Partial derivatives of the log-pseudolikelihood function for a fitted fully-visible Boltzmann machine.

Description

Computes the partial derivatives for all unique parameter elements of the bias vector and interaction matrix of a fully-visible Boltzmann machine, for some random length n string of spin variables (i.e. each element is -1 or 1) and some fitted parameter values.

Usage

fvbmpartiald(data, model)

Arguments

data

Vector of length n containing binary spin variables.

model

List generated from fitfvbm.

Value

A list containing 2 objects: a vector containing the partial derivatives corresponding to the bias parameters bvec, and a matrix containing the partial derivatives corresponding to the interaction parameters Mmat.

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 partial derivatives evaluated at the first observation of data.
fvbmpartiald(data,model)