DEVI {DEBBI}

DEVI

Description

DE optimization for mean-field variational inference. Minimizes the KL divergence (maximizes the ELBO) between $q(theta|lambda)$ and the target posterior $p(theta|data)$ For a tutorial on variational inference check out Galdo, Bahg, & Turner 2020.

Usage

DEVI(LogPostLike, control_params = AlgoParamsDEVI(), ...)

Arguments

LogPostLike

function whose first argument is an n_params-dimensional model parameter vector and returns (scalar) sum of log prior density and log likelihood for the parameter vector.

control_params

control parameters for DE algorithm. see AlgoParamsDEVI function documentation for more details.

...

additional arguments to pass LogPostLike

Value

list contain mean in a n_iters_per_chain by n_chains by 2*n_params_model array and the ELBO of each sample in a n_iters_per_chain by n_chains array.

Examples

# simulate from model
dataExample <- matrix(stats::rnorm(100, c(-1, 1), c(1, 1)), nrow = 50, ncol = 2, byrow = TRUE)
## list parameter names
param_names_example <- c("mu_1", "mu_2")

# log posterior likelihood function = log likelihood + log prior | returns a scalar
LogPostLikeExample <- function(x, data, param_names) {
  out <- 0

  names(x) <- param_names

  # log prior
  out <- out + sum(dnorm(x["mu_1"], 0, sd = 1, log = TRUE))
  out <- out + sum(dnorm(x["mu_2"], 0, sd = 1, log = TRUE))

  # log likelihoods
  out <- out + sum(dnorm(data[, 1], x["mu_1"], sd = 1, log = TRUE))
  out <- out + sum(dnorm(data[, 2], x["mu_2"], sd = 1, log = TRUE))

  return(out)
}

# Get variational approximation
DEVI(
  LogPostLike = LogPostLikeExample,
  control_params = AlgoParamsDEVI(
    n_params = length(param_names_example),
    n_iter = 200,
    n_chains = 12
  ),
  data = dataExample,
  param_names = param_names_example
)