mr.mash: Multiple Regression with Multivariate Adaptive Shrinkage.

In stephenslab/mr.mash.alpha: Multiple Regression with Multivariate Adaptive Shrinkage

Multiple Regression with Multivariate Adaptive Shrinkage.

Description

Performs multivariate multiple regression with mixture-of-normals prior.

Usage

mr.mash(
  X,
  Y,
  S0,
  w0 = rep(1/(length(S0)), length(S0)),
  V = NULL,
  mu1_init = matrix(0, nrow = ncol(X), ncol = ncol(Y)),
  tol = 0.0001,
  convergence_criterion = c("mu1", "ELBO"),
  max_iter = 5000,
  update_w0 = TRUE,
  update_w0_method = "EM",
  w0_penalty = rep(1, length(S0)),
  update_w0_max_iter = Inf,
  w0_threshold = 0,
  compute_ELBO = TRUE,
  standardize = TRUE,
  verbose = TRUE,
  update_V = FALSE,
  update_V_method = c("full", "diagonal"),
  version = c("Rcpp", "R"),
  e = 1e-08,
  ca_update_order = c("consecutive", "decreasing_logBF", "increasing_logBF", "random"),
  nthreads = as.integer(NA)
)

Arguments

X	n x p matrix of covariates.
Y	n x r matrix of responses.
S0	List of length K containing the desired r x r prior covariance matrices on the regression coefficients.
w0	K-vector with prior mixture weights, each associated with the respective covariance matrix in S0.
V	r x r residual covariance matrix.
mu1_init	p x r matrix of initial estimates of the posterior mean regression coefficients. These should be on the same scale as the X provided. If standardize=TRUE, mu1_init will be scaled appropriately after standardizing X.
tol	Convergence tolerance.
convergence_criterion	Criterion to use for convergence check.
max_iter	Maximum number of iterations for the optimization algorithm.
update_w0	If TRUE, prior weights are updated.
update_w0_method	Method to update prior weights. Only EM is currently supported.
w0_penalty	K-vector of penalty terms (>=1) for each mixture component. Default is all components are unpenalized.
update_w0_max_iter	Maximum number of iterations for the update of w0.
w0_threshold	Drop mixture components with weight less than this value. Components are dropped at each iteration after 15 initial iterations. This is done to prevent from dropping some poetentially important components prematurely.
compute_ELBO	If TRUE, ELBO is computed.
standardize	If TRUE, X is "standardized" using the sample means and sample standard deviations. Standardizing X allows a faster implementation, but the prior has a different interpretation. Coefficients and covariances are returned on the original scale.
verbose	If TRUE, some information about the algorithm's process is printed at each iteration.
update_V	if TRUE, residual covariance is updated.
update_V_method	Method to update residual covariance. So far, "full" and "diagonal" are supported. If update_V=TRUE and V is not provided by the user, this option will determine how V is computed (and fixed) internally from mu1_init.
version	Whether to use R or C++ code to perform the coordinate ascent updates.
e	A small number to add to the diagonal elements of the prior matrices to improve numerical stability of the updates.
ca_update_order	The order with which coordinates are updated. So far, "consecutive", "decreasing_logBF", "increasing_logBF", "random" are supported.
nthreads	Number of RcppParallel threads to use for the updates. When nthreads is NA, the default number of threads is used; see defaultNumThreads. This setting is ignored when version = "R".

Value

A mr.mash fit, stored as a list with some or all of the following elements:

mu1	p x r matrix of posterior means for the regression coeffcients.
S1	r x r x p array of posterior covariances for the regression coeffcients.
w1	p x K matrix of posterior assignment probabilities to the mixture components.
V	r x r residual covariance matrix
w0	K-vector with (updated, if update_w0=TRUE) prior mixture weights, each associated with the respective covariance matrix in S0

.

S0	r x r x K array of prior covariance matrices on the regression coefficients

.

intercept	r-vector containing posterior mean estimate of the intercept.
fitted	n x r matrix of fitted values.
G	r x r covariance matrix of fitted values.
pve	r-vector of proportion of variance explained by the covariates.
ELBO	Evidence Lower Bound (ELBO) at last iteration.
progress	A data frame including information regarding convergence criteria at each iteration.
converged	TRUE or FALSE, indicating whether the optimization algorithm converged to a solution within the chosen tolerance level.
Y	n x r matrix of responses at last iteration (only relevant when missing values are present in the input Y).

Examples

###Set seed
set.seed(123)

###Simulate X and Y
##Set parameters
n  <- 1000
p <- 100
p_causal <- 20
r <- 5

###Simulate data
out <- simulate_mr_mash_data(n, p, p_causal, r, pve=0.5, B_cor=1,
                             B_scale=1, X_cor=0, X_scale=1, V_cor=0)

###Split the data in training and test sets
Ytrain <- out$Y[-c(1:200), ]
Xtrain <- out$X[-c(1:200), ]
Ytest <- out$Y[c(1:200), ]
Xtest <- out$X[c(1:200), ]

###Specify the covariance matrices for the mixture-of-normals prior.
univ_sumstats <- compute_univariate_sumstats(Xtrain, Ytrain,
                   standardize=TRUE, standardize.response=FALSE)
grid <- autoselect.mixsd(univ_sumstats, mult=sqrt(2))^2
S0 <- compute_canonical_covs(ncol(Ytrain), singletons=TRUE,
                             hetgrid=c(0, 0.25, 0.5, 0.75, 1))
S0 <- expand_covs(S0, grid, zeromat=TRUE)

###Fit mr.mash
fit <- mr.mash(Xtrain, Ytrain, S0, update_V=TRUE)

# Compare the "fitted" values of Y against the true Y in the training set.
plot(fit$fitted,Ytrain,pch = 20,col = "darkblue",xlab = "true",
     ylab = "fitted")
abline(a = 0,b = 1,col = "magenta",lty = "dotted")

# Predict the multivariate outcomes in the test set using the fitted model.
Ytest_est <- predict(fit,Xtest)
plot(Ytest_est,Ytest,pch = 20,col = "darkblue",xlab = "true",
     ylab = "predicted")
abline(a = 0,b = 1,col = "magenta",lty = "dotted")

stephenslab/mr.mash.alpha documentation built on Feb. 7, 2025, 10:06 p.m.