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
.
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.
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.
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.
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")'.
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.
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.
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.
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