# fvbmstderr: Standard errors for the parameter elements of a fitted... In BoltzMM: Boltzmann Machines with MM Algorithms

## Description

Computes the normal approximation standard errors from the sandwich estimator of the covariance matrix for a maximum pseudolikelihood estimated fully-visible Boltzmann machine.

## Usage

 `1` ```fvbmstderr(data, covarmat) ```

## 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). `covarmat` A covariance matrix generated from `fvbmcov`.

## Value

A list containing 2 objects: a vector containing the standard errors corresponding to the bias parameters `bvec_se`, and a matrix containing the standard errors corresponding to the interaction parameters `Mmat_se`.

## 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 10 11``` ```# 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. covarmat <- fvbmcov(data,model,fvbmHess) # Compute the standard errors of the parameter elements according to a normal approximation. fvbmstderr(data,covarmat) ```

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