Split moment matching for efficient approximate leave-one-out cross-validation (LOO)

Source: R/split_moment_matching.R

A function that computes the split moment matching importance sampling loo. Takes in the moment matching total transformation, transforms only half of the draws, and computes a single elpd using multiple importance sampling.

loo_moment_match_split(
  x,
  upars,
  cov,
  total_shift,
  total_scaling,
  total_mapping,
  i,
  log_prob_upars,
  log_lik_i_upars,
  r_eff_i,
  cores,
  is_method,
  ...
)

Arguments

x

A fitted model object.

upars

A matrix containing the model parameters in unconstrained space where they can have any real value.

cov

Logical; Indicate whether to match the covariance matrix of the samples or not. If FALSE, only the mean and marginal variances are matched.

total_shift

A vector representing the total shift made by the moment matching algorithm.

total_scaling

A vector representing the total scaling of marginal variance made by the moment matching algorithm.

total_mapping

A vector representing the total covariance transformation made by the moment matching algorithm.

i

Observation index.

log_prob_upars

A function that takes arguments x and upars and returns a matrix of log-posterior density values of the unconstrained posterior draws passed via upars.

log_lik_i_upars

A function that takes arguments x, upars, and i and returns a vector of log-likeliood draws of the ith observation based on the unconstrained posterior draws passed via upars.

r_eff_i

MCMC relative effective sample size of the i'th log likelihood draws.

cores

The number of cores to use for parallelization. This defaults to the option mc.cores which can be set for an entire R session by options(mc.cores = NUMBER). The old option loo.cores is now deprecated but will be given precedence over mc.cores until loo.cores is removed in a future release. As of version 2.0.0 the default is now 1 core if mc.cores is not set, but we recommend using as many (or close to as many) cores as possible.

  • Note for Windows 10 users: it is strongly recommended to avoid using the .Rprofile file to set mc.cores (using the cores argument or setting mc.cores interactively or in a script is fine).

is_method

The importance sampling method to use. The following methods are implemented:

  • "psis": Pareto-Smoothed Importance Sampling (PSIS). Default method.

  • "tis": Truncated Importance Sampling (TIS) with truncation at sqrt(S), where S is the number of posterior draws.

  • "sis": Standard Importance Sampling (SIS).

...

Further arguments passed to the custom functions documented above.

Value

A list containing the updated log-importance weights and log-likelihood values. Also returns the updated MCMC effective sample size and the integrand-specific log-importance weights.

References

Paananen, T., Piironen, J., Buerkner, P.-C., Vehtari, A. (2021). Implicitly adaptive importance sampling. Statistics and Computing, 31, 16. doi:10.1007/s11222-020-09982-2. arXiv preprint arXiv:1906.08850.