Investigate V after every iteration in SuSiE RSS
Dat Do
2025-09-08
Last updated: 2025-09-10
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Knit directory: Improved_LD_SuSiE/
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Here we want to investigate why using out-of-sample LD matrix can cause many false discovery by looking that the result after every training iteration. Recall that SuSiE_rss work by iteratively fitting Single Effect Model to the residuals: \[\overline{r} = X^{\top} y - X^{\top} X \overline{b} = v - R \overline{b} \] where \(\overline{b} = \sum_{\ell=1}^{L} \overline{b}_{\ell}\) is the sum of the posterior mean of all effects.
We expect that after detecting all ``true’’ causal SNP, \(\overline{r}\) will be a vector of \(J\) equally small numbers so that the PIP of over-fitted \(\ell\) will be close to 0 (diffused). Hence the purity of over-fitted \(\ell\)-th CS is small and is not reported.
However, it can be seen that because of mis-specified \(R\), after controlling for all causal SNP, the residual \(\overline{r}\) of other SNPs can ``increase’’, leading to large PIP, thus creates false discovery. The second (related) case is that when subtracting \(\widehat{R} \overline{b}\) from \(v\), because of the mismatch between \(\widehat{R}\) and \(R\), some of the correlated SNP to the causal SNP is not subtracted enough. Consider an example: \(v_i = 5, v_j = 6\) and \(R_{ij} \approx 1\), all other \(v_{k}= 0\). After one iteration that SuSiE pick the credible set \(\{i, j\}\), we expect \(\overline{v}_{i} = \overline{v}_j = 0\). However, if \(\widehat{R}_{ij} \ll R_{ij}\), then the PIP of SNP \(i\) in the first CS will be much smaller, leading to smaller subtraction term \(R \overline{b}\), which causes big residual \(\overline{r}_j\).
We will also see that our method (projected \(R\)) will experience the second behavior (not subtracting enough) much less.
In the experiment below, the true \(L = 1\) and causal SNP’s position is randomly chosen between 1 and \(J = 200\). Set \(L = 3\) in SuSiE and in every iteration, we will look at three figures: (1) \(\overline{r}\) after adding back \(\ell\)-th CS; (2) PIP got from Single Effect Model; (3) \(\overline{r}\) after subtracting \(R \overline{b}\). We consider In-sample, Out-of-sample, and Projected (our method) covariance matrices.
Note that the title of the figure corresponds to SuSiE’s outer loop. Each figure has 3 rows correspond to the inner loop from 1 to \(L = 3\). The algorithm often converges after around 5 iteration (outer loop) so we only look at the first 5.
It is helpful to pay attention to the scale of \(y\)-axis (of \(v\) and of PIP) in each figure, as it can change from figure to figure.
First we look at In-sample Covariance matrix. All is good
knitr::opts_chunk$set(echo = TRUE, fig.width=8, fig.height=7, dpi=150)
library(susieR)
source("code/SuSiE_rss.R")
source("code/R_algorithms.R")
## using gtex data
gtex = readRDS("./data/Thyroid_ENSG00000132855.rds")
## seed present: 1, 2
seed = 1
set.seed(seed)
print(paste("This is seed number", seed))[1] "This is seed number 1"# Remove SNPs with MAF < 0.01
maf = apply(gtex, 2, function(x) sum(x)/2/length(x))
X0 = gtex[, maf > 0.01]
X = na.omit(X0)
snp_total = ncol(X0)
n = nrow(X0)
J = 200
# Start from a random point on the genome
indx_start = sample(1: (snp_total - J), 1)
X = X0[, indx_start:(indx_start + J -1)]
# View(cor(X)[1:10, 1:10])
## sub-sample into two
out_sample = sample(1:n, 100)
X_out = X[out_sample, ]
X_in = X[setdiff(1:n, out_sample), ]
rm_p = c(which(diag(cov(X_in))==0), which(diag(cov(X_out))==0))
indx_p = setdiff(1:J, rm_p)
X_in = X_in[, indx_p]
X_out = X_out[, indx_p]
## Standardize both sample matrices
X_in <- scale(X_in)
X_out <- scale(X_out)
## out-sample LD matrix
R_hat = cor(X_out)
R = cor(X_in)
## generate data from in-sample X matrix
J = ncol(X_in)
beta <- rep(0, J)
n = nrow(X_in)
num_causal_SNP = 1
gamma = sample(c(1:J), size = num_causal_SNP, replace = FALSE)
b = rnorm(num_causal_SNP) * 3
beta = rep(0, J)
beta[gamma] = b
y = X_in %*% beta + rnorm(n)
y = scale(y)
V_xy = t(X_in) %*% y / (n-1)
## 1. In-sample covariance matrix
V_xx = R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("In-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
Out-sample Covariance matrix: We can see that after subtracting the first CS, the remaining \(\overline{v}\) is still big (not subtracting enough; compare to the in-sample covariance matrix).
## 2. Out-sample covariance matrix
V_xx = R_hat
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Out-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
Projected Covariance matrix: After subtracting the first CS, the remaining \(\overline{v}\) is better controlled.
## 3. Projected R
ret = proj_Dykstra(R=R_hat, v=V_xy)
V_xx = ret$R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Projected R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
Consider multiplying \(vv^{\top}\) with some \(\alpha > 1\). We find that it does not improve control of the residual. When setting \(\alpha > 1.4\), SuSiE often gives error in training….
alpha = 1.1
ret = proj_Dykstra(R=R_hat, v= sqrt(alpha) * V_xy)
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Projected R w/ alpha =", alpha, "Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
Let us experiment with interpolating between Projected \(\tilde{R}\) and \(vv^{\top}\) Consider \(R = \lambda \tilde{R} + (1-\lambda) vv^{\top}\) and set \(diag(R) = 1\). We find it helps controlling the residual a little bit.
lam = 0.5
ret = proj_Dykstra(R=R_hat, v = V_xy)
V_xx = lam * ret$R + (1-lam) * tcrossprod(V_xy)
diag(V_xx) <- 1
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Projected R w/ lam =", lam, "Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
Let us look at some other seeds.
seed = 1
set.seed(seed)
print(paste("This is seed number", seed))[1] "This is seed number 1"# Remove SNPs with MAF < 0.01
maf = apply(gtex, 2, function(x) sum(x)/2/length(x))
X0 = gtex[, maf > 0.01]
X = na.omit(X0)
snp_total = ncol(X0)
n = nrow(X0)
J = 200
# Start from a random point on the genome
indx_start = sample(1: (snp_total - J), 1)
X = X0[, indx_start:(indx_start + J -1)]
# View(cor(X)[1:10, 1:10])
## sub-sample into two
out_sample = sample(1:n, 100)
X_out = X[out_sample, ]
X_in = X[setdiff(1:n, out_sample), ]
rm_p = c(which(diag(cov(X_in))==0), which(diag(cov(X_out))==0))
indx_p = setdiff(1:J, rm_p)
X_in = X_in[, indx_p]
X_out = X_out[, indx_p]
## Standardize both sample matrices
X_in <- scale(X_in)
X_out <- scale(X_out)
## out-sample LD matrix
R_hat = cor(X_out)
R = cor(X_in)
## generate data from in-sample X matrix
J = ncol(X_in)
beta <- rep(0, J)
n = nrow(X_in)
num_causal_SNP = 1
gamma = sample(c(1:J), size = num_causal_SNP, replace = FALSE)
b = rnorm(num_causal_SNP) * 3
beta = rep(0, J)
beta[gamma] = b
y = X_in %*% beta + rnorm(n)
y = scale(y)
V_xy = t(X_in) %*% y / (n-1)
## 1. In-sample covariance matrix
V_xx = R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("In-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
## 2. Out-sample covariance matrix
V_xx = R_hat
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Out-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
## 3. Projected R
ret = proj_Dykstra(R=R_hat, v=V_xy)
V_xx = ret$R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Projected R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
| Version | Author | Date |
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| 2f35f45 | dodat97 | 2025-09-09 |
| Version | Author | Date |
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| 2f35f45 | dodat97 | 2025-09-09 |
| Version | Author | Date |
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| 2f35f45 | dodat97 | 2025-09-09 |
| Version | Author | Date |
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| 2f35f45 | dodat97 | 2025-09-09 |
| Version | Author | Date |
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| 2f35f45 | dodat97 | 2025-09-09 |
seed = 2
set.seed(seed)
print(paste("This is seed number", seed))[1] "This is seed number 2"# Remove SNPs with MAF < 0.01
maf = apply(gtex, 2, function(x) sum(x)/2/length(x))
X0 = gtex[, maf > 0.01]
X = na.omit(X0)
snp_total = ncol(X0)
n = nrow(X0)
J = 200
# Start from a random point on the genome
indx_start = sample(1: (snp_total - J), 1)
X = X0[, indx_start:(indx_start + J -1)]
# View(cor(X)[1:10, 1:10])
## sub-sample into two
out_sample = sample(1:n, 100)
X_out = X[out_sample, ]
X_in = X[setdiff(1:n, out_sample), ]
rm_p = c(which(diag(cov(X_in))==0), which(diag(cov(X_out))==0))
indx_p = setdiff(1:J, rm_p)
X_in = X_in[, indx_p]
X_out = X_out[, indx_p]
## Standardize both sample matrices
X_in <- scale(X_in)
X_out <- scale(X_out)
## out-sample LD matrix
R_hat = cor(X_out)
R = cor(X_in)
## generate data from in-sample X matrix
J = ncol(X_in)
beta <- rep(0, J)
n = nrow(X_in)
num_causal_SNP = 1
gamma = sample(c(1:J), size = num_causal_SNP, replace = FALSE)
b = rnorm(num_causal_SNP) * 3
beta = rep(0, J)
beta[gamma] = b
y = X_in %*% beta + rnorm(n)
y = scale(y)
V_xy = t(X_in) %*% y / (n-1)
## 1. In-sample covariance matrix
V_xx = R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("In-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
## 2. Out-sample covariance matrix
V_xx = R_hat
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Out-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
## 3. Projected R
ret = proj_Dykstra(R=R_hat, v=V_xy)
V_xx = ret$R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Projected R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
seed = 3
set.seed(seed)
print(paste("This is seed number", seed))[1] "This is seed number 3"# Remove SNPs with MAF < 0.01
maf = apply(gtex, 2, function(x) sum(x)/2/length(x))
X0 = gtex[, maf > 0.01]
X = na.omit(X0)
snp_total = ncol(X0)
n = nrow(X0)
J = 200
# Start from a random point on the genome
indx_start = sample(1: (snp_total - J), 1)
X = X0[, indx_start:(indx_start + J -1)]
# View(cor(X)[1:10, 1:10])
## sub-sample into two
out_sample = sample(1:n, 100)
X_out = X[out_sample, ]
X_in = X[setdiff(1:n, out_sample), ]
rm_p = c(which(diag(cov(X_in))==0), which(diag(cov(X_out))==0))
indx_p = setdiff(1:J, rm_p)
X_in = X_in[, indx_p]
X_out = X_out[, indx_p]
## Standardize both sample matrices
X_in <- scale(X_in)
X_out <- scale(X_out)
## out-sample LD matrix
R_hat = cor(X_out)
R = cor(X_in)
## generate data from in-sample X matrix
J = ncol(X_in)
beta <- rep(0, J)
n = nrow(X_in)
num_causal_SNP = 1
gamma = sample(c(1:J), size = num_causal_SNP, replace = FALSE)
b = rnorm(num_causal_SNP) * 3
beta = rep(0, J)
beta[gamma] = b
y = X_in %*% beta + rnorm(n)
y = scale(y)
V_xy = t(X_in) %*% y / (n-1)
## 1. In-sample covariance matrix
V_xx = R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("In-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
## 2. Out-sample covariance matrix
V_xx = R_hat
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Out-sample R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
## 3. Projected R
ret = proj_Dykstra(R=R_hat, v=V_xy)
V_xx = ret$R
sigma2 = 1
sigma02 = 1
L = 3
max_iter = 5
b_bar = matrix(0, nrow = L, ncol = J)
b_bar2 = matrix(0, nrow = L, ncol = J)
alphas = matrix(0, nrow = L, ncol = J)
mus = matrix(0, nrow = L, ncol = J)
sigmas = matrix(0, nrow = L, ncol = J)
for (iter in (1:max_iter)){
par(mfrow = c(3, 3), mar = c(4, 4, 2, 1), oma = c(0, 0, 4, 0))
V_xy_bar = V_xy - V_xx %*% colSums(b_bar) ## residual signal
for (ell in 1:L){
V_xy_bar_ell = V_xy_bar + V_xx %*% b_bar[ell, ] ## add back ell-th signal
susie_plot(V_xy_bar_ell, y = "z", b=beta)
ret = SER(V_xx, V_xy_bar_ell, n, sigma2, sigma02)
alphas[ell, ] = ret$alpha
mus[ell, ] = ret$mus
sigmas[ell, ] = ret$sigma12
b_bar[ell, ] = alphas[ell, ] * mus[ell, ]
b_bar2[ell, ] = alphas[ell, ] * (mus[ell, ]^2 + sigmas[ell, ])
V_xy_bar = V_xy_bar_ell - V_xx %*% b_bar[ell, ]
susie_plot(ret$alpha, y = "PIP", b=beta)
susie_plot(V_xy_bar, y = "z", b=beta)
}
mtext(paste0("Projected R, Iteration ", iter), outer = TRUE, cex = 1.5, line = 1)
}
It remains a question whether we can make it as good as the in-sample LD matrix…
sessionInfo()R version 4.5.1 (2025-06-13)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.6.1
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
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] RSpectra_0.16-2 Matrix_1.7-3 susieR_0.14.2 workflowr_1.7.1
loaded via a namespace (and not attached):
[1] sass_0.4.10 generics_0.1.4 stringi_1.8.7 lattice_0.22-7
[5] digest_0.6.37 magrittr_2.0.3 evaluate_1.0.4 grid_4.5.1
[9] RColorBrewer_1.1-3 fastmap_1.2.0 plyr_1.8.9 rprojroot_2.1.0
[13] jsonlite_2.0.0 processx_3.8.6 whisker_0.4.1 reshape_0.8.10
[17] ps_1.9.1 mixsqp_0.3-54 promises_1.3.3 httr_1.4.7
[21] scales_1.4.0 jquerylib_0.1.4 cli_3.6.5 rlang_1.1.6
[25] crayon_1.5.3 cachem_1.1.0 yaml_2.3.10 tools_4.5.1
[29] dplyr_1.1.4 ggplot2_3.5.2 httpuv_1.6.16 vctrs_0.6.5
[33] R6_2.6.1 matrixStats_1.5.0 lifecycle_1.0.4 git2r_0.36.2
[37] stringr_1.5.1 fs_1.6.6 irlba_2.3.5.1 pkgconfig_2.0.3
[41] callr_3.7.6 pillar_1.11.0 bslib_0.9.0 later_1.4.2
[45] gtable_0.3.6 glue_1.8.0 Rcpp_1.1.0 xfun_0.52
[49] tibble_3.3.0 tidyselect_1.2.1 rstudioapi_0.17.1 knitr_1.50
[53] farver_2.1.2 htmltools_0.5.8.1 rmarkdown_2.29 compiler_4.5.1
[57] getPass_0.2-4