Last active
December 23, 2020 02:02
-
-
Save nanxstats/4b64f81aa258959bef6ca06572307298 to your computer and use it in GitHub Desktop.
Bayesian lasso with greta, compared to lasso and msaenet
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
# https://nanx.me/blog/post/bayesian-lasso-with-greta/ | |
# generate synthetic data ------------------------------------------------------ | |
library("msaenet") | |
n <- 500 | |
p <- 1000 | |
pnz <- 10 | |
dat <- msaenet.sim.gaussian( | |
n = n * 2, p = p, | |
rho = 0.5, coef = rep(5, pnz), snr = 3, | |
p.train = 0.5, seed = 42 | |
) | |
x <- dat$x.tr | |
y <- dat$y.tr | |
beta <- c(rep(5, pnz), rep(0, p - pnz)) | |
# msaenet ---------------------------------------------------------------------- | |
library("doParallel") | |
registerDoParallel(detectCores()) | |
fit_msaenet <- msaenet( | |
x, y, | |
family = "gaussian", | |
init = "ridge", alphas = seq(0.05, 0.95, 0.05), | |
tune = "cv", nfolds = 10, rule = "lambda.min", | |
nsteps = 20, tune.nsteps = "ebic", | |
seed = 42, parallel = TRUE, verbose = FALSE | |
) | |
msaenet.nzv(fit_msaenet) | |
png("greta-msaenet-coef.png", res = 300, height = 1500, width = 2100) | |
par() | |
opar <- par() | |
par(mar = c(2, 4, 1, 2) + 0.1) | |
layout(matrix(c(1, 2), 2, 1), heights = c(2, 1)) | |
plot(fit_msaenet, type = "coef") | |
plot(fit_msaenet, type = "criterion", ylab = "EBIC") | |
par(opar) | |
dev.off() | |
(tp_msaenet <- msaenet.tp(fit_msaenet, 1:pnz)) | |
(fp_msaenet <- msaenet.fp(fit_msaenet, 1:pnz)) | |
pred_msaenet <- predict(fit_msaenet, dat$x.te) | |
(mse_msaenet <- msaenet.mse(dat$y.te, pred_msaenet)) | |
# lasso ------------------------------------------------------------------------ | |
library("glmnet") | |
set.seed(42) | |
cv_lasso <- cv.glmnet(x, y, family = "gaussian", alpha = 1, nfolds = 10) | |
png("greta-glmnet-cv.png", res = 300, height = 1500, width = 2100) | |
plot(cv_lasso) | |
dev.off() | |
fit_lasso <- glmnet(x, y, family = "gaussian", alpha = 1, lambda = cv_lasso$lambda.min) | |
selected_lasso <- (abs(as.vector(fit_lasso$beta)) > .Machine$double.eps) | |
(tp_lasso <- sum((selected_lasso & beta)[1:pnz])) | |
(fp_lasso <- sum((selected_lasso | beta)[-(1:pnz)])) | |
pred_lasso <- predict(fit_lasso, dat$x.te) | |
(mse_lasso <- msaenet.mse(dat$y.te, pred_lasso)) | |
# bayesian lasso --------------------------------------------------------------- | |
library("greta") | |
set.seed(42) | |
# define data model | |
intercept <- normal(0, 10) | |
sd <- cauchy(0, 3, truncation = c(0, Inf)) | |
coefs <- laplace(0, 1, dim = ncol(x)) | |
mu <- intercept + x %*% coefs | |
distribution(y) <- normal(mu, sd) | |
m <- model(intercept, coefs, sd) | |
plot(m) | |
draws_blasso <- mcmc(m, warmup = 1000, n_samples = 5000, chains = 8) | |
# utility functions for posterior ---------------------------------------------- | |
# get beta posterior estimate from a chain | |
get_betahat <- function(df) { | |
betahat <- apply(df[, 2:(ncol(df) - 1)], 2, mean, na.rm = TRUE) | |
names(betahat) <- NULL | |
betahat | |
} | |
# get intercept posterior estimate from a chain | |
get_intercept <- function(df) { | |
alphahat <- mean(df[, 1], na.rm = TRUE) | |
names(alphahat) <- NULL | |
alphahat | |
} | |
# get credible interval from a chain | |
get_ci <- function(df, prob) { | |
ci <- apply(df[, 2:(ncol(df) - 1)], 2, quantile, probs = prob, na.rm = TRUE) | |
names(ci) <- NULL | |
ci | |
} | |
# variable selection - checks whether 0 is contained in the credible interval | |
# ported from horseshoe::HS.var.select(method = "intervals") | |
threshold <- function(lower_ci, upper_ci) { | |
as.numeric(1 - ((lower_ci <= 0) & (upper_ci >= 0))) | |
} | |
# get MSE from each chain | |
mse_chain <- function(draws, x, y) { | |
k <- length(draws) | |
mse <- rep(NA, k) | |
for (i in 1:k) { | |
chain <- draws[[i]] | |
post_mean <- get_betahat(chain) | |
lower_ci <- get_ci(chain, 0.025) | |
upper_ci <- get_ci(chain, 0.975) | |
beta <- threshold(lower_ci, upper_ci) * post_mean | |
alpha <- get_intercept(chain) | |
pred <- x %*% as.matrix(beta) + alpha | |
mse[i] <- msaenet.mse(y, pred) | |
} | |
mse | |
} | |
# select the chain with the minimal MSE on training set | |
idx_chain <- which.min(mse_chain(draws_blasso, dat$x.tr, dat$y.tr)) | |
chain_blasso <- draws_blasso[[idx_chain]] | |
# create data frame for plotting | |
df_blasso <- data.frame( | |
index = 1:ncol(x), | |
truth = beta, | |
post_mean = get_betahat(chain_blasso), | |
lower_ci = get_ci(chain_blasso, 0.025), | |
upper_ci = get_ci(chain_blasso, 0.975) | |
) | |
df_blasso$selected <- threshold(df_blasso$lower_ci, df_blasso$upper_ci) | |
library("ggplot2") | |
library("ggsci") | |
ggplot(data = df_blasso, aes(x = index, y = truth)) + | |
geom_point(size = 2) + | |
theme_classic(base_size = 24) + | |
ylab("") + | |
geom_point(aes(x = index, y = post_mean, col = factor(selected)), size = 2) + | |
geom_errorbar(aes(ymin = lower_ci, ymax = upper_ci, col = factor(selected)), width = 0.1) + | |
theme(legend.position = "none") + | |
scale_color_aaas() + | |
ggtitle("black = truth, red = selected, blue = not selected") | |
ggsave("greta-bayesian-lasso-coef.png", dpi = 300, width = 24, height = 12) | |
(tp_blasso <- sum((threshold(df_blasso$lower_ci, df_blasso$upper_ci) & beta)[1:pnz])) | |
(fp_blasso <- sum((threshold(df_blasso$lower_ci, df_blasso$upper_ci) | beta)[-(1:pnz)])) | |
beta_blasso <- threshold(df_blasso$lower_ci, df_blasso$upper_ci) * df_blasso$post_mean | |
pred_blasso <- dat$x.te %*% as.matrix(beta_blasso) + get_intercept(chain_blasso) | |
(mse_blasso <- msaenet.mse(dat$y.te, pred_blasso)) | |
# summary table ---------------------------------------------------------------- | |
tbl <- data.frame( | |
"Method" = c("msaenet", "Lasso", "Bayesian Lasso"), | |
"TP" = c(tp_msaenet, tp_lasso, tp_blasso), | |
"FP" = c(fp_msaenet, fp_lasso, fp_blasso), | |
"MSE" = c(mse_msaenet, mse_lasso, mse_blasso) | |
) | |
knitr::kable(tbl, digits = 0) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment