set_hyper: Gather model hyperparameters provided by the user.

In hruffieux/locus: Large-Scale Variational Inference for Combined Selection of Covariate and Response Variables in Regression Models

Gather model hyperparameters provided by the user.

Description

This function must be used to provide hyperparameter values for the model used in locus.

Usage

set_hyper(
  d,
  p,
  lambda,
  nu,
  a,
  b,
  eta,
  kappa,
  link = "identity",
  ind_bin = NULL,
  q = NULL,
  phi = NULL,
  xi = NULL,
  m0 = NULL,
  s02 = NULL,
  G = NULL,
  struct = FALSE
)

Arguments

d	Number of responses.
p	Number of candidate predictors.
lambda	Vector of length 1 providing the values of hyperparameter \lambda for the prior distribution of \sigma^{-2}. \sigma represents the typical size of nonzero effects.
nu	Vector of length 1 providing the values of hyperparameter \nu for the prior distribution of \sigma^{-2}. \sigma represents the typical size of nonzero effects.
a	Vector of length 1 or p providing the values of hyperparameter a for the prior distributions for the proportion of responses associated with each candidate predictor, \omega (vector of length p). If of length 1, the provided value is repeated p times.
b	Vector of length 1 or p providing the values of hyperparameter b for the prior distributions for the proportion of responses associated with each candidate predictor, \omega (vector of length p). If of length 1, the provided value is repeated p times.
eta	Vector of length 1 or d for link = "identity", and of length 1 or d_cont = d - length(ind_bin) (the number of continuous response variables) for link = "mix". Provides the values of hyperparameter \eta for the prior distributions of the continuous response residual precisions, \tau. If of length 1, the provided value is repeated d, resp. d_cont, times. Must be NULL for link = "logit" and link = "probit".
kappa	Vector of length 1 or d for link = "identity", and of length 1 or d_cont = d - length(ind_bin) (the number of continuous response variables) for link = "mix". Provides the values of hyperparameter \kappa for the prior distributions of the response residual precisions, \tau. If of length 1, the provided value is repeated d, resp. d_cont, times. Must be NULL for link = "logit" and link = "probit".
link	Response link. Must be "identity" for linear regression, "logit" for logistic regression, "probit" for probit regression, or "mix" for a mix of identity and probit link functions (in this case, the indices of the binary responses must be gathered in argument ind_bin, see below).
ind_bin	If link = "mix", vector of indices corresponding to the binary variables in Y. Must be NULL if link != "mix".
q	Number of covariates. Default is NULL, for Z NULL.
phi	Vector of length 1 or q providing the values of hyperparameter \phi for the prior distributions for the sizes of the nonzero covariate effects, \zeta. If of length 1, the provided value is repeated q times. Default is NULL, for Z NULL.
xi	Vector of length 1 or q providing the values of hyperparameter \xi for the prior distributions for the sizes of the nonzero covariate effects, \zeta. If of length 1, the provided value is repeated q times. Default is NULL, for Z NULL.
m0	Vector of length 1 or p. Hyperparameter when list_struct non-NULL. Default is NULL.
s02	Variance hyperparameter when list_struct is non-NULL. Default is NULL.
G	Number of candidate predictor groups when using the group selection model from the locus function. Default is NULL, for no group selection.
struct	Boolean indicating the use of structured sparse priors set through the set_struct function. Default is FALSE, for no structured selection.

Details

The locus function can also be used with default hyperparameter choices (without using set_hyper) by setting its argument list_hyper to NULL.

Value

An object of class "hyper" preparing user hyperparameter in a form that can be passed to the locus function.

See Also

set_init, locus

Examples

seed <- 123; set.seed(seed)

###################
## Simulate data ##
###################

## Examples using small problem sizes:
##
n <- 200; p <- 200; p0 <- 20; d <- 20; d0 <- 15; q <- 2

## Candidate predictors (subject to selection)
##
# Here we simulate common genetic variants (but any type of candidate
# predictors can be supplied).
# 0 = homozygous, major allele, 1 = heterozygous, 2 = homozygous, minor allele

X_act <- matrix(rbinom(n * p0, size = 2, p = 0.25), nrow = n)
X_inact <- matrix(rbinom(n * (p - p0), size = 2, p = 0.25), nrow = n)

shuff_x_ind <- sample(p)
X <- cbind(X_act, X_inact)[, shuff_x_ind]

bool_x_act <- shuff_x_ind <= p0

pat_act <- beta <- matrix(0, nrow = p0, ncol = d0)
pat_act[sample(p0*d0, floor(p0*d0/5))] <- 1
beta[as.logical(pat_act)] <-  rnorm(sum(pat_act))

## Covariates (not subject to selection)
##
Z <- matrix(rnorm(n * q), nrow = n)

alpha <-  matrix(rnorm(q * d), nrow = q)

## Gaussian responses
##
Y_act <- matrix(rnorm(n * d0, mean = X_act %*% beta, sd = 0.5), nrow = n)
Y_inact <- matrix(rnorm(n * (d - d0), sd = 0.5), nrow = n)
shuff_y_ind <- sample(d)
Y <- cbind(Y_act, Y_inact)[, shuff_y_ind] + Z %*% alpha

## Binary responses
##
Y_bin <- ifelse(Y > 0, 1, 0)

########################
## Infer associations ##
########################

## Continuous responses
##

# No covariate
#
# a and b chosen so that the prior mean number of responses associated with
# each candidate predictor is 1/4.
list_hyper_g <- set_hyper(d, p, lambda = 1, nu = 1, a = 1, b = 4*d-1,
                          eta = 1, kappa = apply(Y, 2, var),
                          link = "identity")

# We take p0_av = p0 (known here); this choice may result in variable
# selections that are (too) conservative in some cases. In practice, it is
# advised to set p0_av as a slightly overestimated guess of p0, or perform
# cross-validation using function `set_cv'.

vb_g <- locus(Y = Y, X = X, p0_av = p0, link = "identity",
              list_hyper = list_hyper_g, user_seed = seed)

# With covariates
#
list_hyper_g_z <- set_hyper(d, p, lambda = 1, nu = 1, a = 1, b = 4*d-1,
                            eta = 1, kappa = apply(Y, 2, var),
                            link = "identity", q = q, phi = 1, xi = 1)

vb_g_z <- locus(Y = Y, X = X, p0_av = p0, Z = Z, link = "identity",
                list_hyper = list_hyper_g_z, user_seed = seed)

## Binary responses
##
list_hyper_logit <- set_hyper(d, p, lambda = 1, nu = 1, a = 1, b = 4*d-1,
                              eta = NULL, kappa = NULL, link = "logit",
                              q = q, phi = 1, xi = 1)

vb_logit <- locus(Y = Y_bin, X = X, p0_av = p0, Z = Z, link = "logit",
                  list_hyper = list_hyper_logit, user_seed = seed)

list_hyper_probit <- set_hyper(d, p, lambda = 1, nu = 1, a = 1, b = 4*d-1,
                               eta = NULL, kappa = NULL, link = "probit",
                               q = q, phi = 1, xi = 1)

vb_probit <- locus(Y = Y_bin, X = X, p0_av = p0, Z = Z, link = "probit",
                   list_hyper = list_hyper_probit, user_seed = seed)


## Mix of continuous and binary responses
##
Y_mix <- cbind(Y, Y_bin)
ind_bin <- (d+1):(2*d)

list_hyper_mix <- set_hyper(2*d, p, lambda = 1, nu = 1, a = 1, b = 8*d-1,
                            eta = 1, kappa = apply(Y, 2, var), link = "mix",
                            ind_bin = ind_bin, q = q, phi = 1, xi = 1)

vb_mix <- locus(Y = Y_mix, X = X, p0_av = p0, Z = Z, link = "mix",
                ind_bin = ind_bin, list_hyper = list_hyper_mix,
                user_seed = seed)

hruffieux/locus documentation built on Jan. 10, 2024, 10:07 p.m.