# fvbmHess: Hessian of the log-pseudolikelihood function for a fitted... In BoltzMM: Boltzmann Machines with MM Algorithms

## Description

Computes the Hessian with respect to 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

 `1` ```fvbmHess(data, model) ```

## 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`.

## Value

The n+choose(n,2) by n+choose(n,2) Hessian matrix, summed over the N rows of `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, bias bias, interaction[1,2], interaction[1,3], and interaction[2,3].

## 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

 ```1 2 3 4 5 6 7 8 9``` ```# 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 Hessian matrix summed over all num rows of data. fvbmHess(data,model) ```

BoltzMM documentation built on May 2, 2019, 11:02 a.m.