loo_approximate_posterior: Efficient approximate leave-one-out cross-validation (LOO) for posterior approximations

Description

Efficient approximate leave-one-out cross-validation (LOO) for posterior approximations

Usage

loo_approximate_posterior(x, log_p, log_g, ...)
# S3 method for array
loo_approximate_posterior(
  x,
  log_p,
  log_g,
  ...,
  save_psis = FALSE,
  cores = getOption("mc.cores", 1)
)
# S3 method for matrix
loo_approximate_posterior(
  x,
  log_p,
  log_g,
  ...,
  save_psis = FALSE,
  cores = getOption("mc.cores", 1)
)
# S3 method for `function`
loo_approximate_posterior(
  x,
  ...,
  data = NULL,
  draws = NULL,
  log_p = NULL,
  log_g = NULL,
  save_psis = FALSE,
  cores = getOption("mc.cores", 1)
)

Value

The loo_approximate_posterior() methods return a named list with class c("psis_loo_ap", "psis_loo", "loo"). It has the same structure as the objects returned by loo() but with the additional slot:

posterior_approximation: A list with two vectors, log_p and log_g of the same length containing the posterior density and the approximation density for the individual draws.

Arguments

x

A log-likelihood array, matrix, or function. The Methods (by class) section, below, has detailed descriptions of how to specify the inputs for each method.

log_p

The log-posterior (target) evaluated at S samples from the proposal distribution (g). A vector of length S.

log_g

The log-density (proposal) evaluated at S samples from the proposal distribution (g). A vector of length S.

save_psis

Should the "psis" object created internally by loo_approximate_posterior() be saved in the returned object? See loo() for details.

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).

data, draws, ...

For the loo_approximate_posterior.function() method, these are the data, posterior draws, and other arguments to pass to the log-likelihood function. See the Methods (by class) section below for details on how to specify these arguments.

Methods (by class)

loo_approximate_posterior(array): An \(I\) by \(C\) by \(N\) array, where \(I\) is the number of MCMC iterations per chain, \(C\) is the number of chains, and \(N\) is the number of data points.
loo_approximate_posterior(matrix): An \(S\) by \(N\) matrix, where \(S\) is the size of the posterior sample (with all chains merged) and \(N\) is the number of data points.
loo_approximate_posterior(`function`): A function f() that takes arguments data_i and draws and returns a vector containing the log-likelihood for a single observation i evaluated at each posterior draw. The function should be written such that, for each observation i in 1:N, evaluating
```
f(data_i = data[i,, drop=FALSE], draws = draws)
```
results in a vector of length S (size of posterior sample). The log-likelihood function can also have additional arguments but data_i and draws are required.

If using the function method then the arguments data and draws must also be specified in the call to loo():
- data: A data frame or matrix containing the data (e.g. observed outcome and predictors) needed to compute the pointwise log-likelihood. For each observation i, the ith row of data will be passed to the data_i argument of the log-likelihood function.
- draws: An object containing the posterior draws for any parameters needed to compute the pointwise log-likelihood. Unlike data, which is indexed by observation, for each observation the entire object draws will be passed to the draws argument of the log-likelihood function.
- The ... can be used if your log-likelihood function takes additional arguments. These arguments are used like the draws argument in that they are recycled for each observation.

Details

The loo_approximate_posterior() function is an S3 generic and methods are provided for 3-D pointwise log-likelihood arrays, pointwise log-likelihood matrices, and log-likelihood functions. The implementation works for posterior approximations where it is possible to compute the log density for the posterior approximation.

References

Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2019). Leave-One-Out Cross-Validation for Large Data. In Thirty-sixth International Conference on Machine Learning, PMLR 97:4244-4253.

Magnusson, M., Riis Andersen, M., Jonasson, J. and Vehtari, A. (2020). Leave-One-Out Cross-Validation for Model Comparison in Large Data. In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 108:341-351.