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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 1eba385 | Matthew Stephens | 2025-11-11 | workflowr::wflow_publish("flash_pca.rmd") |
library(flashier)Loading required package: ebnmlibrary(fastICA)
library(PMA)Motivated by some results from ICA I want to try fitting \(X = M + lf' + E\) where M is low rank.
Given \(l\) and \(f\), the maximum likelihood estimate for \(M\) is given by truncated SVD of \(X-lf'\), so I can iterate between estimating \(l,f\) and estimating \(M\). This approach shoudl work for either using flashier or PMD to estimate \(l,f\).
These are the same simulations as in (fastica_01.html)
M <- 10000 # Number of variants/samples (rows)
L <- 10 # True number of latent factors
T <- 100 # Number of traits/phenotypes (columns)
s_1 <- 1 # Standard Deviation 1 (Spike component)
s_2 <- 5 # Standard Deviation 2 (Slab component)
eps <- 1e-2 # Standard Deviation for observation noise
# Set seed for reproducibility
set.seed(42)
# Data Simulation (G = X %*% Y + noise)
# 3.1. Generating Standard Deviation Matrices (a and b)
# Elements are sampled from {s_1, s_2} [1, 2].
sd_choices <- c(s_1, s_2)
# Matrix 'a' (M x L): Standard deviations for X (Probabilities p=[0.7, 0.3]) [4]
p_a <- c(0.7, 0.3)
a_vector <- sample(sd_choices, size = M * L, replace = TRUE, prob = p_a)
a <- matrix(a_vector, nrow = M, ncol = L)
# Matrix 'b' (L x T): Standard deviations for Y (Probabilities p=[0.8, 0.2]) [4]
p_b <- c(0.8, 0.2)
b_vector <- sample(sd_choices, size = L * T, replace = TRUE, prob = p_b)
b <- matrix(b_vector, nrow = L, ncol = T)
# Generating Latent Factors (X and Y)
# X is drawn from Normal(0, a)
X <- matrix(rnorm(M * L, mean = 0, sd = a), nrow = M, ncol = L)
# Y is drawn from Normal(0, b)
Y <- matrix(rnorm(L * T, mean = 0, sd = b), nrow = L, ncol = T)
# Generating Noise and Final Data Matrix G
# Noise is generated from Normal(0, eps)
noise <- matrix(rnorm(M * T, mean = 0, sd = eps), nrow = M, ncol = T)
# Calculate the final data matrix G = X @ Y + noise
G <- X %*% Y + noiseHere I try the iterative approach with rank of M=9. I find that it chooses a laplace prior with all its weight on non-null component, and does not find a great solution.
fit.fl = flash(G, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.for(i in 1:5){
M.svd = svd(G - fitted(fit.fl) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
#fit.fl = flash(G-M, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)
fit.fl = flash_update_data(fit.fl,G-M)
fit.fl = flash_backfit(fit.fl)
print(fit.fl$elbo)
}Backfitting 1 factors (tolerance: 1.49e-02)...
Difference between iterations is within 1.0e+06...
Difference between iterations is within 1.0e+05...
Difference between iterations is within 1.0e+04...
Difference between iterations is within 1.0e+03...
Difference between iterations is within 1.0e+02...
Difference between iterations is within 1.0e+01...
Wrapping up...
Done.
[1] 3111599
Backfitting 1 factors (tolerance: 1.49e-02)...
Difference between iterations is within 1.0e+01...
Wrapping up...
Done.
[1] 3141269
Backfitting 1 factors (tolerance: 1.49e-02)...
Wrapping up...
Done.
[1] 3141269
Backfitting 1 factors (tolerance: 1.49e-02)...
Wrapping up...
Done.
[1] 3141269
Backfitting 1 factors (tolerance: 1.49e-02)...
Wrapping up...
Done.
[1] 3141269cor(X, fit.fl$L_pm) [,1]
[1,] -0.38113764
[2,] 0.18419586
[3,] -0.08593986
[4,] 0.13029310
[5,] -0.17712154
[6,] 0.56054887
[7,] -0.11792697
[8,] -0.61798516
[9,] 0.25148413
[10,] 0.05945271fit.fl$L_ghat[[1]]
$pi
[1] 1.806438e-07 9.999998e-01
$mean
[1] 0 0
$scale
[1] 0.0000000 0.7150248
attr(,"class")
[1] "laplacemix"
attr(,"row.names")
[1] 1 2fit.fl$elbo[1] 3141269Try a normal mixture prior instead:
fit.fl = flash(G, ebnm_fn = ebnm_normal_scale_mixture, greedy_Kmax = 1)Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.cor(X, fit.fl$L_pm) [,1]
[1,] -0.38140081
[2,] 0.18573512
[3,] -0.08625343
[4,] 0.13224256
[5,] -0.17841814
[6,] 0.55913558
[7,] -0.11852873
[8,] -0.61631534
[9,] 0.25340468
[10,] 0.06051061for(i in 1:5){
M.svd = svd(G - fitted(fit.fl) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
#fit.fl = flash(G-M, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)
fit.fl = flash_update_data(fit.fl,G-M)
fit.fl = flash_backfit(fit.fl)
print(fit.fl$elbo)
}Backfitting 1 factors (tolerance: 1.49e-02)...
Difference between iterations is within 1.0e+06...
Difference between iterations is within 1.0e+05...
Difference between iterations is within 1.0e+04...
Difference between iterations is within 1.0e+03...
Difference between iterations is within 1.0e+02...
Difference between iterations is within 1.0e+01...
Wrapping up...
Done.
[1] 3131196
Backfitting 1 factors (tolerance: 1.49e-02)...
Difference between iterations is within 1.0e+00...
Wrapping up...
Done.
[1] 3141348
Backfitting 1 factors (tolerance: 1.49e-02)...
Wrapping up...
Done.
[1] 3141348
Backfitting 1 factors (tolerance: 1.49e-02)...
Wrapping up...
Done.
[1] 3141348
Backfitting 1 factors (tolerance: 1.49e-02)...
Wrapping up...
Done.
[1] 3141348cor(X, fit.fl$L_pm) [,1]
[1,] -0.3815060
[2,] 0.1857550
[3,] -0.0862240
[4,] 0.1322642
[5,] -0.1784584
[6,] 0.5592986
[7,] -0.1185320
[8,] -0.6164988
[9,] 0.2534772
[10,] 0.0605242fit.fl$L_ghat[[1]]
$pi
[1] 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.18094444
[7] 0.03758443 0.00000000 0.21533611 0.02070509 0.00000000 0.41790590
[13] 0.07271325 0.05481079 0.00000000 0.00000000 0.00000000 0.00000000
[19] 0.00000000 0.00000000 0.00000000 0.00000000
$mean
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
$sd
[1] 0.0000000 0.1229333 0.1891227 0.2529762 0.3202798 0.3940946 0.4768439
[8] 0.5708588 0.6786031 0.8028042 0.9465530 1.1133963 1.3074330 1.5334192
[15] 1.7968879 2.1042857 2.4631315 2.8822015 3.3717434 3.9437279 4.6121413
[22] 5.3933273
attr(,"class")
[1] "normalmix"
attr(,"row.names")
[1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22fit.fl$elbo[1] 3141348Now try with initializing at an ica solution. It still uses a laplace prior, but it essentially converges to the ica solution (ie does not move much) and the elbo is better
fit.ica = fastICA(G, n.comp = 10)
s = fit.ica$S[,1]
a = fit.ica$A[1,]
M.svd = svd(G - s %*% t(a) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
fit.fl2 = flash(G-M, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.fit.fl2$L_ghat[[1]]
$pi
[1] 1.940483e-06 9.999981e-01
$mean
[1] 0 0
$scale
[1] 0.0000000 0.4334429
attr(,"class")
[1] "laplacemix"
attr(,"row.names")
[1] 1 2fit.fl2$elbo[1] 3148073for(i in 1:5){
M.svd = svd(G - fitted(fit.fl2) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
fit.fl2 = flash(G-M, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)
print(fit.fl$elbo)
}Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 3141348
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 3141348
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 3141348
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 3141348
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 3141348cor(X, fit.fl2$L_pm) [,1]
[1,] -2.211661e-03
[2,] -2.436869e-03
[3,] 2.869316e-05
[4,] 7.598077e-03
[5,] 1.470651e-03
[6,] -3.292375e-03
[7,] -9.997270e-01
[8,] -3.886822e-03
[9,] 8.330709e-03
[10,] -4.525288e-03fit.fl2$L_ghat[[1]]
$pi
[1] 1.685282e-06 9.999983e-01
$mean
[1] 0 0
$scale
[1] 0.0000000 0.4334428
attr(,"class")
[1] "laplacemix"
attr(,"row.names")
[1] 1 2fit.fl2$F_ghat[[1]]
$pi
[1] 6.48661e-11 1.00000e+00
$mean
[1] 0 0
$scale
[1] 0.000000 4.767295
attr(,"class")
[1] "laplacemix"
attr(,"row.names")
[1] 1 2fit.fl2$elbo[1] 3149452fit.fl$elbo[1] 3141348Here I try the same thing, but using just the first 8 PCs in an attempt to provide a bit more “wiggle room” for the optimization to move. But I found convergence is very slow here.
fit.fl = flash(G, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.for(i in 1:50){
M.svd = svd(G - fitted(fit.fl) )
M = M.svd$u[,1:8] %*% (M.svd$d[1:8] * t(M.svd$v[,1:8]))
fit.fl = flash(G-M, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)
print(fit.fl$elbo)
}Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740099
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[1] -2740093
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740092
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740092
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740092
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740091
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740091
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740090
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740090
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740090
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740089
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740089
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740089
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740088
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740088
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740088
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740087
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740087
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740087
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740086
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740086
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740086
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740085
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740085
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740085
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740085
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740084
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740084
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740084
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740083
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740083
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740083
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] -2740082
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] -2740082
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] -2740082
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] -2740081
Adding factor 1 to flash object...
Wrapping up...
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Nullchecking 1 factors...
Done.
[1] -2740081cor(X, fit.fl$L_pm) [,1]
[1,] -0.37800842
[2,] 0.17910674
[3,] -0.08737775
[4,] 0.12771926
[5,] -0.17455302
[6,] 0.56250455
[7,] -0.11533349
[8,] -0.62305161
[9,] 0.24789657
[10,] 0.05560268fit.fl$L_ghat[[1]]
$pi
[1] 1.131635e-06 9.999989e-01
$mean
[1] 0 0
$scale
[1] 0.0000000 0.7134562
attr(,"class")
[1] "laplacemix"
attr(,"row.names")
[1] 1 2fit.fl$elbo[1] -2740081Try nuclear norm regularization on M rather than hard rank constraint.
fit.fl = flash(G, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.for(i in 1:50){
M.svd = svd(G - fitted(fit.fl) )
M.svd$d = pmax(0, M.svd$d - 10)
M = M.svd$u %*% (M.svd$d * t(M.svd$v))
fit.fl = flash(G-M, ebnm_fn = ebnm_point_laplace, greedy_Kmax = 1)
print(fit.fl$elbo)
}Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1924275
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1923715
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1936740
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1946657
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1951180
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1953225
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954144
Adding factor 1 to flash object...
Wrapping up...
Done.
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Done.
[1] 1954551
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954727
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954799
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954824
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954827
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954821
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954810
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954797
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954783
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954769
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954755
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954740
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954726
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954712
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954697
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954683
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954669
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954655
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954640
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954626
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954612
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954598
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954584
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954569
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954555
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954541
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954527
Adding factor 1 to flash object...
Wrapping up...
Done.
Nullchecking 1 factors...
Done.
[1] 1954513
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954499
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954485
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954471
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954457
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954443
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954429
Adding factor 1 to flash object...
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Done.
Nullchecking 1 factors...
Done.
[1] 1954415
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954401
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954387
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954373
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954359
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954345
Adding factor 1 to flash object...
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Done.
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Done.
[1] 1954330
Adding factor 1 to flash object...
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Done.
[1] 1954315
Adding factor 1 to flash object...
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Done.
[1] 1954306cor(X, fit.fl$L_pm) [,1]
[1,] -0.38122318
[2,] 0.18435429
[3,] -0.08616472
[4,] 0.13039632
[5,] -0.17723444
[6,] 0.56045909
[7,] -0.11810855
[8,] -0.61778328
[9,] 0.25160371
[10,] 0.05952674fit.fl$L_ghat[[1]]
$pi
[1] 2.814814e-07 9.999997e-01
$mean
[1] 0 0
$scale
[1] 0.000000 0.715645
attr(,"class")
[1] "laplacemix"
attr(,"row.names")
[1] 1 2fit.fl$elbo[1] 1954306Here I try the same with PMD
library(PMA)
fit.pmd = PMD(G,"standard",sumabs=0.5,center=F)Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1234567891011121314151617181920cor(X, fit.pmd$u) [,1]
[1,] 0.26840307
[2,] -0.08054940
[3,] 0.06713861
[4,] -0.01299302
[5,] 0.10758749
[6,] -0.36451223
[7,] 0.05598098
[8,] 0.81813865
[9,] -0.12268001
[10,] -0.07062926for(i in 1:10){
M.svd = svd(G - fit.pmd$u %*% t(fit.pmd$d * fit.pmd$v) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
fit.pmd = PMD(G-M, v = fit.pmd$v, type="standard", sumabs= 0.5, center=F,niter=1)
}Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1cor(X, fit.pmd$u) [,1]
[1,] 0.011377423
[2,] -0.011759704
[3,] -0.008862186
[4,] 0.011258508
[5,] 0.016953914
[6,] -0.055848148
[7,] 0.011011700
[8,] 0.986368084
[9,] -0.014366883
[10,] 0.011987536# fit term
sum((G-M- fit.pmd$u %*% (fit.pmd$d * t(fit.pmd$v)))^2) [1] 2029164# penalty term (seems to be fixed)
sum(abs(fit.pmd$u)) * fit.pmd$sumabsu + sum(abs(fit.pmd$v)) * fit.pmd$sumabsv[1] 2525This worked well. Now I’ll try a lesser penalty.
fit.pmd = PMD(G,"standard",sumabs=0.9,center=F)Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1cor(X, fit.pmd$u) [,1]
[1,] 0.38293438
[2,] -0.19070578
[3,] 0.08766478
[4,] -0.13750981
[5,] 0.18229298
[6,] -0.55618217
[7,] 0.12076554
[8,] 0.61146048
[9,] -0.25850008
[10,] -0.06340065for(i in 1:10){
M.svd = svd(G - fit.pmd$u %*% t(fit.pmd$d * fit.pmd$v) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
fit.pmd = PMD(G-M, v = fit.pmd$v, type="standard", sumabs= 0.9, center=F,niter=1)
print(sum((G-M- fit.pmd$u %*% (fit.pmd$d * t(fit.pmd$v)))^2) )
}Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461Warning in PMDL1L1(x, sumabs = sumabs, sumabsu = sumabsu, sumabsv = sumabsv, :
PMDL1L1 was run without first subtracting out the mean of x.1
[1] 89.97461cor(X, fit.pmd$u) [,1]
[1,] 0.38293438
[2,] -0.19070578
[3,] 0.08766478
[4,] -0.13750981
[5,] 0.18229298
[6,] -0.55618217
[7,] 0.12076554
[8,] 0.61146048
[9,] -0.25850008
[10,] -0.06340065# fit term
sum((G-M- fit.pmd$u %*% (fit.pmd$d * t(fit.pmd$v)))^2) [1] 89.97461# penalty term (seems to be fixed)
sum(abs(fit.pmd$u)) * fit.pmd$sumabsu + sum(abs(fit.pmd$v)) * fit.pmd$sumabsv[1] 6784.095Here I compare the fit and penalty at the fastICA solution to see if this is a convergence issue. It was a bit of a suprise to see that the ICA solution does not get close to the PMD fit term. This is presumably because it does not optimize for mse. Also we see that the M.svd$d has 9 large eigenvalues, and one that is not large but bigger than background. This is the one that ICA is not fitting. That is, ICA does not actually leave a rank 9 matrix but actually a rank 10 matrix. Presumably this is because ICA fits the top 10PCs not the actual data matrix, so it leaves some of the “noise” unfitted, but maybe actually PMD is fitting more noise? (Is this an advantage of an initial step doing PCA? It might be. Maybe we should try PMD on the top PCs rather than the full data matrix?)
M.svd = svd(G - s %*% t(a) )
M = M.svd$u[,1:9] %*% (M.svd$d[1:9] * t(M.svd$v[,1:9]))
sum((G-M- s %*% t(a))^2)[1] 93.62801M.svd$d [1] 9176.2905200 8113.6850689 7919.9268198 7220.2153718 7120.6590558
[6] 6467.8700988 6108.6111561 5314.9885635 3673.8448242 1.9145568
[11] 1.0879917 1.0818923 1.0781103 1.0769687 1.0749752
[16] 1.0737024 1.0705980 1.0673045 1.0639946 1.0618220
[21] 1.0600228 1.0576188 1.0561401 1.0532369 1.0514490
[26] 1.0486938 1.0472644 1.0449246 1.0417742 1.0408329
[31] 1.0397812 1.0379476 1.0359387 1.0348096 1.0338034
[36] 1.0318856 1.0307806 1.0301591 1.0260115 1.0235496
[41] 1.0227009 1.0217301 1.0191786 1.0173757 1.0149219
[46] 1.0140178 1.0121285 1.0109634 1.0095153 1.0065901
[51] 1.0061486 1.0041182 1.0010232 0.9995755 0.9977064
[56] 0.9975979 0.9957359 0.9946129 0.9941258 0.9918242
[61] 0.9886653 0.9882669 0.9858695 0.9823833 0.9814767
[66] 0.9807947 0.9802120 0.9787143 0.9766344 0.9738211
[71] 0.9730331 0.9720059 0.9702359 0.9665484 0.9661569
[76] 0.9645165 0.9629077 0.9604952 0.9594310 0.9568659
[81] 0.9551573 0.9545256 0.9520256 0.9492639 0.9462706
[86] 0.9448512 0.9440892 0.9428766 0.9397537 0.9378132
[91] 0.9356203 0.9344767 0.9306737 0.9276352 0.9267261
[96] 0.9249556 0.9239296 0.9199207 0.9158973 0.9126204svd((G-fit.pmd$u %*% (fit.pmd$d * t(fit.pmd$v))))$d [1] 8.117499e+03 7.920111e+03 7.256598e+03 7.134314e+03 6.478365e+03
[6] 6.148451e+03 5.338734e+03 4.748096e+03 3.608830e+03 1.088411e+00
[11] 1.081894e+00 1.078265e+00 1.076970e+00 1.075021e+00 1.073817e+00
[16] 1.070731e+00 1.067332e+00 1.064023e+00 1.061822e+00 1.060127e+00
[21] 1.057620e+00 1.056216e+00 1.053259e+00 1.051613e+00 1.048720e+00
[26] 1.047286e+00 1.044964e+00 1.042030e+00 1.040842e+00 1.039811e+00
[31] 1.037961e+00 1.035977e+00 1.034845e+00 1.033894e+00 1.032034e+00
[36] 1.030914e+00 1.030176e+00 1.026102e+00 1.023608e+00 1.022779e+00
[41] 1.021776e+00 1.019187e+00 1.017391e+00 1.014994e+00 1.014120e+00
[46] 1.012301e+00 1.010972e+00 1.009856e+00 1.006717e+00 1.006161e+00
[51] 1.004120e+00 1.001031e+00 9.995807e-01 9.977976e-01 9.976091e-01
[56] 9.957384e-01 9.946141e-01 9.942168e-01 9.921946e-01 9.888689e-01
[61] 9.883603e-01 9.859798e-01 9.824715e-01 9.814767e-01 9.810739e-01
[66] 9.803592e-01 9.787418e-01 9.766685e-01 9.738279e-01 9.730336e-01
[71] 9.720156e-01 9.702887e-01 9.665486e-01 9.661805e-01 9.646655e-01
[76] 9.629099e-01 9.605022e-01 9.594346e-01 9.568751e-01 9.551861e-01
[81] 9.545383e-01 9.521384e-01 9.493240e-01 9.463089e-01 9.449444e-01
[86] 9.440933e-01 9.430927e-01 9.397773e-01 9.378201e-01 9.356860e-01
[91] 9.344981e-01 9.307157e-01 9.276357e-01 9.267522e-01 9.249570e-01
[96] 9.240263e-01 9.199398e-01 9.159090e-01 9.126318e-01 1.617511e-11
sessionInfo()R version 4.4.2 (2024-10-31)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.6.1
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/Chicago
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] PMA_1.2-4 fastICA_1.2-7 flashier_1.0.56 ebnm_1.1-34
loaded via a namespace (and not attached):
[1] softImpute_1.4-3 gtable_0.3.6 xfun_0.52
[4] bslib_0.9.0 ggplot2_3.5.2 htmlwidgets_1.6.4
[7] ggrepel_0.9.6 lattice_0.22-6 quadprog_1.5-8
[10] vctrs_0.6.5 tools_4.4.2 generics_0.1.4
[13] parallel_4.4.2 Polychrome_1.5.4 tibble_3.3.0
[16] pkgconfig_2.0.3 Matrix_1.7-2 data.table_1.17.6
[19] SQUAREM_2021.1 RColorBrewer_1.1-3 RcppParallel_5.1.10
[22] scatterplot3d_0.3-44 lifecycle_1.0.4 truncnorm_1.0-9
[25] compiler_4.4.2 farver_2.1.2 stringr_1.5.1
[28] git2r_0.35.0 progress_1.2.3 RhpcBLASctl_0.23-42
[31] httpuv_1.6.15 htmltools_0.5.8.1 sass_0.4.10
[34] lazyeval_0.2.2 yaml_2.3.10 plotly_4.11.0
[37] crayon_1.5.3 tidyr_1.3.1 later_1.4.2
[40] pillar_1.10.2 jquerylib_0.1.4 whisker_0.4.1
[43] uwot_0.2.3 cachem_1.1.0 trust_0.1-8
[46] gtools_3.9.5 tidyselect_1.2.1 digest_0.6.37
[49] Rtsne_0.17 stringi_1.8.7 purrr_1.0.4
[52] dplyr_1.1.4 ashr_2.2-66 splines_4.4.2
[55] cowplot_1.1.3 rprojroot_2.0.4 fastmap_1.2.0
[58] grid_4.4.2 colorspace_2.1-1 cli_3.6.5
[61] invgamma_1.1 magrittr_2.0.3 prettyunits_1.2.0
[64] scales_1.4.0 promises_1.3.3 horseshoe_0.2.0
[67] httr_1.4.7 rmarkdown_2.29 fastTopics_0.7-07
[70] deconvolveR_1.2-1 workflowr_1.7.1 hms_1.1.3
[73] pbapply_1.7-2 evaluate_1.0.4 knitr_1.50
[76] viridisLite_0.4.2 irlba_2.3.5.1 rlang_1.1.6
[79] Rcpp_1.0.14 mixsqp_0.3-54 glue_1.8.0
[82] rstudioapi_0.17.1 jsonlite_2.0.0 R6_2.6.1
[85] fs_1.6.6