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Peter Carbonetto
Last updated: 2021-03-06
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Knit directory: fastTopics-experiments/analysis/
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| File | Version | Author | Date | Message |
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| html | 59a8594 | Peter Carbonetto | 2021-03-05 | Revised the simulations slightly. |
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| Rmd | cfc44e5 | Peter Carbonetto | 2021-03-05 | workflowr::wflow_publish(“smallsim.Rmd”) |
| html | 52759e5 | Peter Carbonetto | 2021-03-05 | Added first simulation to “smallsim” demo. |
| Rmd | fe510f0 | Peter Carbonetto | 2021-03-05 | workflowr::wflow_publish(“smallsim.Rmd”) |
| html | b6458fe | Peter Carbonetto | 2021-03-05 | Built a first draft of the “smallsim” demo. |
| Rmd | d0db5de | Peter Carbonetto | 2021-03-05 | workflowr::wflow_publish(“smallsim.Rmd”) |
| Rmd | 275fb51 | Peter Carbonetto | 2021-03-05 | Implemented functions simulate_sizes and simulate_factors. |
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Load the packages used in the analysis below, as well as additional functions that we will use to simulate the data.
library(fastTopics)
library(mvtnorm)
library(ggplot2)
library(cowplot)
source("../code/smallsim_functions.R")Set the seed so that the results can be reproduced.
set.seed(1)Independent topics scenario
In this first example, we simulate counts from a multinomial topic model with 6 topics.
n <- 100
m <- 400
k <- 6
S <- 13*diag(k) - 2
F <- simulate_factors(m,k)
L <- simulate_loadings(n,k,S)
s <- simulate_sizes(n)
X <- simulate_multinom_counts(L,F,s)
X <- X[,colSums(X > 0) > 0]The topic proportions for each sample are randomly drawn from the correlated topic model in which \(\eta_i\) for each sample \(i\) is drawn from the multivariate normal with mean zero and covariance matrix \(S\), such that \(s_{kk} = 11\), \(s_{jk} = -2\) for all \(j \neq k\). Generated in this way, the topic proportions tend to be roughly orthogonal. For example, compare the proportions for topics 5 and 6:
ggplot(data.frame(x = L[,5],y = L[,6]),aes(x = x,y = y)) +
geom_point(shape = 21,size = 1.75,color = "white",fill = "black") +
labs(x = "topic 5 proportion",y = "topic 6 proportion") +
theme_cowplot(font_size = 10)
We compare two different updates for fitting a Poisson NMF model to the simulated counts: the EM updates, and the sequential coordinate descent (SCD) updates. We initialize the model fitting by first running 50 EM updates so that the updates are more likely to be moving toward the same local maximum of the Poisson NMF likelihood surface.
fit0 <- fit_poisson_nmf(X,k,numiter = 50,method = "em",
control = list(extrapolate = FALSE,numiter = 4))
fit1 <- fit_poisson_nmf(X,fit0 = fit0,numiter = 1000,method = "em",
control = list(extrapolate = FALSE,numiter = 4))
fit2 <- fit_poisson_nmf(X,fit0 = fit0,numiter = 1000,method = "scd",
control = list(extrapolate = FALSE,numiter = 4))
fit1 <- poisson2multinom(fit1)
fit2 <- poisson2multinom(fit2)Add text here.
plot_progress(list(em = fit1,scd = fit2),x = "iter",add.point.every = 100)
Correlated topics scenario
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set.seed(1)
S[5,6] <- 10
S[6,5] <- 10
L <- simulate_loadings(n,k,S)
X <- simulate_multinom_counts(L,F,s)
X <- X[,colSums(X > 0) > 0]TO DO: Plot mixture proportions for topics 5 and 6.
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fit0 <- fit_poisson_nmf(X,k,numiter = 50,method = "em",
control = list(extrapolate = FALSE,numiter = 4))
fit1 <- fit_poisson_nmf(X,fit0 = fit0,numiter = 800,method = "em",
control = list(extrapolate = FALSE,numiter = 4))
fit2 <- fit_poisson_nmf(X,fit0 = fit0,numiter = 1000,method = "scd",
control = list(extrapolate = FALSE,numiter = 4))
fit3 <- fit_poisson_nmf(X,fit0 = fit1,numiter = 200,method = "scd",
control = list(extrapolate = FALSE,numiter = 4))
fit1 <- fit_poisson_nmf(X,fit0 = fit1,numiter = 200,method = "scd",
control = list(extrapolate = FALSE,numiter = 4))Add text here.
fit1 <- poisson2multinom(fit1)
fit2 <- poisson2multinom(fit2)
fit3 <- poisson2multinom(fit3)
plot_progress(list(em = fit1,scd = fit2,"scd+em" = fit3),
x = "iter",add.point.every = 100)
sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
#
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
#
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#
# attached base packages:
# [1] stats graphics grDevices utils datasets methods base
#
# other attached packages:
# [1] cowplot_1.0.0 ggplot2_3.3.0 mvtnorm_1.0-11 fastTopics_0.5-24
#
# loaded via a namespace (and not attached):
# [1] httr_1.4.2 tidyr_1.0.0 jsonlite_1.6
# [4] viridisLite_0.3.0 RcppParallel_4.4.2 assertthat_0.2.1
# [7] mixsqp_0.3-44 yaml_2.2.0 progress_1.2.2
# [10] ggrepel_0.9.0 pillar_1.4.3 backports_1.1.5
# [13] lattice_0.20-38 quantreg_5.54 glue_1.3.1
# [16] quadprog_1.5-8 digest_0.6.23 promises_1.1.0
# [19] colorspace_1.4-1 htmltools_0.4.0 httpuv_1.5.2
# [22] Matrix_1.2-18 pkgconfig_2.0.3 invgamma_1.1
# [25] SparseM_1.78 purrr_0.3.3 scales_1.1.0
# [28] whisker_0.4 later_1.0.0 Rtsne_0.15
# [31] MatrixModels_0.4-1 git2r_0.26.1 tibble_2.1.3
# [34] farver_2.0.1 withr_2.1.2 ashr_2.2-51
# [37] lazyeval_0.2.2 magrittr_1.5 crayon_1.3.4
# [40] mcmc_0.9-6 evaluate_0.14 fs_1.3.1
# [43] MASS_7.3-51.4 truncnorm_1.0-8 tools_3.6.2
# [46] data.table_1.12.8 prettyunits_1.1.1 hms_0.5.2
# [49] lifecycle_0.1.0 stringr_1.4.0 MCMCpack_1.4-5
# [52] plotly_4.9.2 munsell_0.5.0 irlba_2.3.3
# [55] compiler_3.6.2 rlang_0.4.5 grid_3.6.2
# [58] htmlwidgets_1.5.1 labeling_0.3 rmarkdown_2.3
# [61] gtable_0.3.0 R6_2.4.1 knitr_1.26
# [64] dplyr_0.8.3 zeallot_0.1.0 workflowr_1.6.2.9000
# [67] rprojroot_1.3-2 stringi_1.4.3 SQUAREM_2017.10-1
# [70] Rcpp_1.0.5 vctrs_0.2.1 tidyselect_0.2.5
# [73] xfun_0.11 coda_0.19-3