Statistical Inference for Symmetric NMF Parameters

Performs statistical inference on the parameter matrix \(C\) of a symmetric NMF model (\(Y \approx XCX^\top\)).

This is a wrapper around nmfkc.inference that automatically sets the covariate matrix to \(A = X^\top\), which is the defining property of symmetric NMF.

Usage

nmfkc.net.inference(object, Y, wild.bootstrap = TRUE, ...)

Arguments

object: A fitted model returned by nmfkc() with Y.symmetric = "bi" or "tri", or the newer nmfkc.net with type = "bi" or "tri".
Y: The original symmetric matrix (P x P).
wild.bootstrap: Logical; if TRUE (default), perform wild bootstrap inference for the C matrix.
...: Additional arguments passed to nmfkc.inference() (e.g., wild.B, wild.seed, C.p.side).

Value

The object augmented with inference fields (same as nmfkc.inference), with class c("nmfkc.net.inference", "nmfkc.inference", "nmf.inference", "nmfkc", "nmf").

Lifecycle

This function is experimental. The interface may change in future versions; details are to be described in an upcoming paper.

Examples

# \donttest{
library(nmfkc)
Y <- matrix(c(0,1,1,0,0,0,
              1,0,1,0,0,0,
              1,1,0,1,0,0,
              0,0,1,0,1,1,
              0,0,0,1,0,1,
              0,0,0,1,1,0), 6, 6)
res <- nmfkc.net(Y, rank = 2, type = "tri", nstart = 20)
res_inf <- nmfkc.net.inference(res, Y)
summary(res_inf)
#> 
#> Call:
#> nmfkc.net(Y = Y, rank = 2, type = "tri", nstart = 20)
#> 
#> Dimensions: 6 
#> Rank (Q):    2 
#> Runtime:     0.06 
#> Iterations:  25 
#> 
#> Statistics:
#>   Objective function:   5.193 
#>   Multiple R-squared:   0.3957 
#>   Residual Std Error:   0.1623 
#>   Mean Absolute Error:  0.3031 
#> 
#> Structure Diagnostics:
#>   Basis (X) Sparsity:    33.3% (< 1e-4)
#> 
#> Symmetric NMF type: unknown
#> Inference (conditional on X):
#>   sigma^2:   0.1623 
#>   C matrix:  2 x 2
#> 
#> C coefficients: 1 total, 0 significant
#>       Row:Col  Estimate Std. Error (Boot) z value   Pr(>z) 
#> Basis1:Basis2     0.053      0.222  0.104    0.24   0.4062  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
# }