Efficient approximate leave-one-out cross-validation (LOO) using subsampling, so that less costly and more approximate computation is made for all LOO-fold, and more costly and accurate computations are made only for m<N LOO-folds.
loo_subsample(x, ...)# S3 method for `function`
loo_subsample(
x,
...,
data = NULL,
draws = NULL,
observations = 400,
log_p = NULL,
log_g = NULL,
r_eff = 1,
save_psis = FALSE,
cores = getOption("mc.cores", 1),
loo_approximation = "plpd",
loo_approximation_draws = NULL,
estimator = "diff_srs",
llgrad = NULL,
llhess = NULL
)
loo_subsample() returns a named list with class c("psis_loo_ss", "psis_loo", "loo"). This has the same structure as objects returned by
loo() but with the additional slot:
loo_subsampling: 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.
A function. The Methods (by class) section, below, has detailed descriptions of how to specify the inputs.
For loo_subsample.function(), these are the data,
posterior draws, and other arguments to pass to the log-likelihood
function. Note that for some loo_approximations, the draws will be replaced
by the posteriors summary statistics to compute loo approximations. See
argument loo_approximation for details.
The subsample observations to use. The argument can take four (4) types of arguments:
NULL to use all observations. The algorithm then just uses
standard loo() or loo_approximate_posterior().
A single integer to specify the number of observations to be subsampled.
A vector of integers to provide the indices used to subset the data.
These observations need to be subsampled with the same scheme as given by
the estimator argument.
A psis_loo_ss object to use the same observations that were used in a
previous call to loo_subsample().
Should be supplied only if approximate posterior draws are
used. The default (NULL) indicates draws are from "true" posterior (i.e.
using MCMC). If not NULL then they should be specified as described in
loo_approximate_posterior().
Vector of relative effective sample size estimates for the
likelihood (exp(log_lik)) of each observation. This is related to
the relative efficiency of estimating the normalizing term in
self-normalized importance sampling when using posterior draws obtained
with MCMC. If MCMC draws are used and r_eff is not provided then
the reported PSIS effective sample sizes and Monte Carlo error estimates
can be over-optimistic. If the posterior draws are (near) independent then
r_eff=1 can be used. r_eff has to be a scalar (same value is used
for all observations) or a vector with length equal to the number of
observations. The default value is 1. See the relative_eff() helper
functions for help computing r_eff.
Should the "psis" object created internally by
loo_subsample() be saved in the returned object? See loo() for details.
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).
What type of approximation of the loo_i's should be used?
The default is "plpd" (the log predictive density using the posterior expectation).
There are six different methods implemented to approximate loo_i's
(see the references for more details):
"plpd": uses the lpd based on point estimates (i.e., \(p(y_i|\hat{\theta})\)).
"lpd": uses the lpds (i,e., \(p(y_i|y)\)).
"tis": uses truncated importance sampling to approximate PSIS-LOO.
"waic": uses waic (i.e., \(p(y_i|y) - p_{waic}\)).
"waic_grad_marginal": uses waic approximation using first order delta
method and posterior marginal variances to approximate \(p_{waic}\) (ie.
\(p(y_i|\hat{\theta})\)-p_waic_grad_marginal). Requires gradient of
likelihood function.
"waic_grad": uses waic approximation using first order delta method and
posterior covariance to approximate \(p_{waic}\) (ie.
\(p(y_i|\hat{\theta})\)-p_waic_grad). Requires gradient of likelihood
function.
"waic_hess": uses waic approximation using second order delta method and
posterior covariance to approximate \(p_{waic}\) (ie.
\(p(y_i|\hat{\theta})\)-p_waic_grad). Requires gradient and Hessian of
likelihood function.
As point estimates of \(\hat{\theta}\), the posterior expectations of the parameters are used.
The number of posterior draws used when
integrating over the posterior. This is used if loo_approximation is set
to "lpd", "waic", or "tis".
How should elpd_loo, p_loo and looic be estimated?
The default is "diff_srs".
"diff_srs": uses the difference estimator with simple random sampling
without replacement (srs). p_loo is estimated using standard srs.
(Magnusson et al., 2020)
"hh": uses the Hansen-Hurwitz estimator with sampling with replacement
proportional to size, where abs of loo_approximation is used as size.
(Magnusson et al., 2019)
"srs": uses simple random sampling and ordinary estimation.
The gradient of the log-likelihood. This
is only used when loo_approximation is "waic_grad",
"waic_grad_marginal", or "waic_hess". The default is NULL.
The Hessian of the log-likelihood. This is only used
with loo_approximation = "waic_hess". The default is NULL.
loo_subsample(`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.
The loo_subsample() function is an S3 generic and a methods is
currently provided for log-likelihood functions. The implementation works
for both MCMC and for posterior approximations where it is possible to
compute the log density for the approximation.
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.
loo(), psis(), loo_compare()