README

The goal of vsp is to enable fast, spectral estimation of latent factors in random dot product graphs. Under mild assumptions, the vsp estimator is consistent for (degree-corrected) stochastic blockmodels, (degree-corrected) mixed-membership stochastic blockmodels, and degree-corrected overlapping stochastic blockmodels.

More generally, the vsp estimator is consistent for random dot product graphs that can be written in the form

where Z and Y satisfy the varimax assumptions of [1]. vsp works on directed and undirected graphs, and on weighted and unweighted graphs. Note that vsp is a semi-parametric estimator.

Installation

install.packages("vsp")

install.packages("devtools")
devtools::install_github("RoheLab/vsp")

Example

Obtaining estimates from vsp is straightforward. We recommend representing networks as igraph objects or sparse adjacency matrices using the Matrix package. Once you have your network in one of these formats, you can get estimates by calling the vsp() function. The result is a vsp_fa S3 object.

Here we demonstrate vsp usage on an igraph object, using the enron network from igraphdata package to demonstrate this functionality. First we peak at the graph:

library(igraph)
data(enron, package = "igraphdata")

image(sign(get.adjacency(enron, sparse = FALSE)))

library(vsp)

fa <- vsp(enron, rank = 30)
fa
#> Vintage Sparse PCA Factor Analysis
#> 
#> Rows (n):   184
#> Cols (d):   184
#> Factors (rank): 30
#> Lambda[rank]:   0.2077
#> Components
#> 
#> Z: 184 x 30 [matrix] 
#> B: 30 x 30 [matrix] 
#> Y: 184 x 30 [matrix] 
#> u: 184 x 30 [matrix] 
#> d: 30      [numeric] 
#> v: 184 x 30 [matrix]

get_varimax_z(fa)
#> # A tibble: 184 × 31
#>    id         z01      z02      z03      z04      z05      z06      z07      z08
#>    <chr>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>    <dbl>
#>  1 row0…  2.42e-4 -0.00245 -2.99e-2  3.37e-4  9.96e-5 -0.0114  -0.00849  0.502  
#>  2 row0… -2.52e-3  0.00135  6.70e-4 -1.63e-1 -1.47e-2  0.0471   0.190    0.00181
#>  3 row0…  2.98e-4 -0.100    1.17e-4 -3.62e-3 -2.06e-2  0.187   -0.158    0.00303
#>  4 row0… -7.75e-5 -0.0183   1.17e-4  5.42e-2 -5.58e-3  0.00165 -0.0367  -0.00106
#>  5 row0… -2.31e-3  0.00150  2.57e-1 -1.42e-2 -4.38e-2  0.00629  1.18    -0.0179 
#>  6 row0… -3.46e-2 -0.0527  -2.61e-2 -1.26e-2 -1.83e-2  0.0282   0.408   -0.0286 
#>  7 row0… -1.08e-3 -0.327   -6.01e-1 -6.98e-2 -9.85e-2 -0.0709   0.509    0.0511 
#>  8 row0…  1.58e-2 -0.0518  -1.34e-2 -1.03e-2 -4.12e-3 -0.0139   0.225   -0.0244 
#>  9 row0…  2.22e-3  0.0752   3.30e-2 -6.50e-4 -5.00e-1 -0.0278  -0.0740  -0.00556
#> 10 row0…  7.13e-4 -0.0119   1.95e-2 -5.06e-3 -7.08e-3  0.00341 -0.00369 13.4    
#> # ℹ 174 more rows
#> # ℹ 22 more variables: z09 <dbl>, z10 <dbl>, z11 <dbl>, z12 <dbl>, z13 <dbl>,
#> #   z14 <dbl>, z15 <dbl>, z16 <dbl>, z17 <dbl>, z18 <dbl>, z19 <dbl>,
#> #   z20 <dbl>, z21 <dbl>, z22 <dbl>, z23 <dbl>, z24 <dbl>, z25 <dbl>,
#> #   z26 <dbl>, z27 <dbl>, z28 <dbl>, z29 <dbl>, z30 <dbl>

At the moment, we also enjoy using pairs plots of the factors as a diagnostic measure:

plot_varimax_z_pairs(fa, 1:5)

plot_varimax_y_pairs(fa, 1:5)

Similarly, an IPR pairs plot can be a good way to check for singular vector localization (and thus overfitting!).

plot_ipr_pairs(fa)

plot_mixing_matrix(fa)

References

[1] Rohe, Karl, and Muzhe Zeng. “Vintage Factor Analysis with Varimax Performs Statistical Inference.” Journal of the Royal Statistical Society Series B: Statistical Methodology 85, no. 4 (September 29, 2023): 1037–60. https://doi.org/10.1093/jrsssb/qkad029.