Boltzmann Machines with MM Algorithms.
BoltzMM
The BoltzMM package allows for computation of probability mass functions of fully-visible Boltzmann machines (FVBMs) via pfvbm and allpfvbm. Random data can be generated using rfvbm. Maximum pseudolikelihood estimation of parameters via the MM algorithm can be conducted using fitfvbm. Computation of partial derivatives and Hessians can be performed via fvbmpartiald and fvbmHessian. Covariance estimation and normal standard errors can be computed using fvbmcov and fvbmstderr.
Installation
If devtools has already been installed, then the most current build of BoltzMM can be obtained via the command:
devtools::install_github('andrewthomasjones/BoltzMM',build_vignettes = TRUE)
The latest stable build of BoltzMM can be obtain from CRAN via the command:
install.packages("BoltzMM", repos='http://cran.us.r-project.org')
An archival build of BoltzMM is available at http://doi.org/10.5281/zenodo.2538256. Manual installation instructions can be found within the R installation and administration manual https://cran.r-project.org/doc/manuals/r-release/R-admin.html.
Examples
Compute the probability of every length n=3 binary spin vector under bvec and Mmat:
library(BoltzMM)
set.seed(1)
bvec <- c(0,0.5,0.25)
Mmat <- matrix(0.1,3,3) - diag(0.1,3,3)
allpfvbm(bvec,Mmat)
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.0666189 0.04465599 0.1213876 0.1213876 0.07362527 0.07362527
#> [,7] [,8]
#> [1,] 0.2001342 0.2985652
Generate num=1000 random strings of n=3 binary spin variables under bvec and Mmat.
library(BoltzMM)
set.seed(1)
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)
head(data)
#> [,1] [,2] [,3]
#> [1,] 1 1 -1
#> [2,] -1 -1 1
#> [3,] -1 1 1
#> [4,] 1 1 1
#> [5,] -1 1 -1
#> [6,] 1 1 1
Fit a fully visible Boltzmann machine to data, starting from parameters bvec and Mmat.
library(BoltzMM)
set.seed(1)
bvec <- c(0,0.5,0.25)
Mmat <- matrix(0.1,3,3) - diag(0.1,3,3)
data <- rfvbm(num,bvec,Mmat)
fitfvbm(data,bvec,Mmat)
#> $pll
#> [1] -1892.661
#>
#> $bvec
#> [1] 0.02607382 0.46484595 0.27640931
#>
#> $Mmat
#> [,1] [,2] [,3]
#> [1,] 0.0000000 0.1179001 0.1444486
#> [2,] 0.1179001 0.0000000 0.0351134
#> [3,] 0.1444486 0.0351134 0.0000000
#>
#> $itt
#> [1] 5
Example with real data from https://hal.archives-ouvertes.fr/hal-01927188v1.
# Load bnstruct library & package
library(bnstruct)
#> Loading required package: bitops
#> Loading required package: Matrix
#> Loading required package: igraph
#>
#> Attaching package: 'igraph'
#> The following objects are masked from 'package:stats':
#>
#> decompose, spectrum
#> The following object is masked from 'package:base':
#>
#> union
library(BoltzMM)
# Load data
data(senate)
# Turn data into a matrix
senate_data <- as.matrix(senate)
# Recode Yes as 1, and No as -1
senate_data[senate=="Yes"] <- 1
senate_data[senate=="No"] <- -1
# Conduct imputation
imp_data <- knn.impute(suppressWarnings(matrix(as.numeric(senate_data),
dim(senate_data))),
k=1)
# No governement - using as reference level
data_nogov <- imp_data[,-1]
# Initialize parameters
bvec <- rep(0,8)
Mmat <- matrix(0,8,8)
nullmodel<-list(bvec=bvec,Mmat=Mmat)
# Fit a fully visible Boltzmann machine to data, starting from parameters bvec and Mmat.
model <- fitfvbm(data_nogov,bvec,Mmat)
# Compute the sandwich covariance matrix using the data and the model.
covarmat <- fvbmcov(data_nogov,model,fvbmHess)
# Compute the standard errors of the parameter elements according to a normal approximation.
st_errors <- fvbmstderr(data_nogov,covarmat)
# Compute z-scores and p-values under null
test_results<-fvbmtests(data_nogov,model,nullmodel)
test_results
#> $bvec_z
#> [1] -1.3871285 3.0958110 1.8099814 -0.4957960 -0.8230061 -0.1625973
#> [7] 0.5715010 2.4308532
#>
#> $bvec_p
#> [1] 0.165402598 0.001962754 0.070298676 0.620038322 0.410504513 0.870835547
#> [7] 0.567660056 0.015063316
#>
#> $Mmat_z
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] NA -0.6596632 -1.3152156 -2.0181850 0.1936413 3.8587216
#> [2,] -0.6596632 NA -0.9536614 -2.0795939 -0.4947831 6.1625534
#> [3,] -1.3152156 -0.9536614 NA 1.3258059 -1.0861345 2.6332797
#> [4,] -2.0181850 -2.0795939 1.3258059 NA 3.0115924 0.4798541
#> [5,] 0.1936413 -0.4947831 -1.0861345 3.0115924 NA -1.2899547
#> [6,] 3.8587216 6.1625534 2.6332797 0.4798541 -1.2899547 NA
#> [7,] 0.5671620 0.5877623 5.8430378 -0.9769979 1.5757127 -1.0129338
#> [8,] 0.3126387 -3.4715041 -0.9287578 4.0101249 0.7587521 2.3224311
#> [,7] [,8]
#> [1,] 0.5671620 0.3126387
#> [2,] 0.5877623 -3.4715041
#> [3,] 5.8430378 -0.9287578
#> [4,] -0.9769979 4.0101249
#> [5,] 1.5757127 0.7587521
#> [6,] -1.0129338 2.3224311
#> [7,] NA 2.2571849
#> [8,] 2.2571849 NA
#>
#> $Mmat_p
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] NA 5.094700e-01 1.884374e-01 4.357200e-02 0.846456748
#> [2,] 0.5094699872 NA 3.402551e-01 3.756280e-02 0.620753227
#> [3,] 0.1884374472 3.402551e-01 NA 1.849040e-01 0.277419500
#> [4,] 0.0435719956 3.756280e-02 1.849040e-01 NA 0.002598813
#> [5,] 0.8464567475 6.207532e-01 2.774195e-01 2.598813e-03 NA
#> [6,] 0.0001139817 7.158116e-10 8.456467e-03 6.313312e-01 0.197066396
#> [7,] 0.5706041434 5.566918e-01 5.125738e-09 3.285702e-01 0.115092039
#> [8,] 0.7545551426 5.175514e-04 3.530146e-01 6.068665e-05 0.448000891
#> [,6] [,7] [,8]
#> [1,] 1.139817e-04 5.706041e-01 7.545551e-01
#> [2,] 7.158116e-10 5.566918e-01 5.175514e-04
#> [3,] 8.456467e-03 5.125738e-09 3.530146e-01
#> [4,] 6.313312e-01 3.285702e-01 6.068665e-05
#> [5,] 1.970664e-01 1.150920e-01 4.480009e-01
#> [6,] NA 3.110918e-01 2.020973e-02
#> [7,] 3.110918e-01 NA 2.399652e-02
#> [8,] 2.020973e-02 2.399652e-02 NA
For more examples, see individual help files.
Technical references
Please refer to the following sources regarding various facets of the FVBM models that are implemented in the package.
The FVBM model and the consistency of their maximum pseudolikelihood estimators (MPLEs) was first considered in http://doi.org/10.1162/neco.2006.18.10.2283. The MM algorithm implemented in the main function fitfvbm was introduced in http://doi.org/10.1162/NECO_a_00813. Here various convergence results regarding the algorithm is proved. Next, the asymptotic normality results pertaining to the use of the functions fvbmstderr and fvbmtests are proved in http://doi.org/10.1109/TNNLS.2015.2425898. Finally, the senate data was introduced and analysed in https://hal.archives-ouvertes.fr/hal-01927188v1.
Reference to package
If you find this package useful in your work, then please follow the usual R instructions for citing the package in your publications. That is, follow the instructions from citation('BoltzMM').
# Citation instructions
citation('BoltzMM')
#> Warning in citation("BoltzMM"): no date field in DESCRIPTION file of
#> package 'BoltzMM'
#> Warning in citation("BoltzMM"): could not determine year for 'BoltzMM' from
#> package DESCRIPTION file
#>
#> To cite package 'BoltzMM' in publications use:
#>
#> Andrew Thomas Jones, Hien Duy Nguyen and Jessica Juanita Bagnall
#> (NA). BoltzMM: Boltzmann Machines with MM Algorithms. R package
#> version 0.1.3.
#>
#> A BibTeX entry for LaTeX users is
#>
#> @Manual{,
#> title = {BoltzMM: Boltzmann Machines with MM Algorithms},
#> author = {Andrew Thomas Jones and Hien Duy Nguyen and Jessica Juanita Bagnall},
#> note = {R package version 0.1.3},
#> }
#>
#> ATTENTION: This citation information has been auto-generated from
#> the package DESCRIPTION file and may need manual editing, see
#> 'help("citation")'.
Authorship statement
The BoltzMM package is co-authored by Andrew T. Jones, Hien D. Nguyen, and Jessica J. Bagnall. The initial development of the package, in native R was conducted by HDN. Implementation of the core loops of the package in the C language was performed by ATJ. JJB formatted and contributed the senate data set as well as the example analysis on the senate data. All three co-authors contributed to the documentation of the software as well as troubleshooting and testing.
Unit testing
Using the package testthat, we have conducted the following unit test for the GitHub build, on the date: 31 January, 2019. The testing files are contained in the tests folder of the repository.
Bug reporting and contributions
Thank you for your interest in BoltzMM. If you happen to find any bugs in the program, then please report them on the Issues page (https://github.com/andrewthomasjones/BoltzMM/issues). Support can also be sought on this page. Furthermore, if you would like to make a contribution to the software, then please forward a pull request to the owner of the repository.