pfvbm function

Probability mass function of a fully-visible Boltzmann machine evaluated for an individual vector.

Compute the probability of a string of n>1 binary spin variables (i.e. each element is -1 or 1) arising from a fully-visible Boltzmann machine with some specified bias vector and interaction matrix.

pfvbm(xval, bvec, Mmat)

Arguments

• xval: Vector of length n containing binary spin variables.
• bvec: Vector of length n containing real valued bias parameters.
• Mmat: Symmetric n by n matrix, with zeros along the diagonal, containing the interaction parameters.

Returns

The probability of the random string xval under a fully-visible Boltzmann machine with bias vector bvec and interaction matrix Mmat.

Examples

# Compute the probability of the vector xval=(-1,1,-1), under bvec and Mmat.
xval <- c(-1,1,-1)
bvec <- c(0,0.5,0.25)
Mmat <- matrix(0.1,3,3) - diag(0.1,3,3)
pfvbm(xval,bvec,Mmat)

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.

Author(s)

Andrew T. Jones and Hien D. Nguyen