Jackknife(+) Predictive Intervals for Bayesian Models • conformalbayes

conformalbayes provides functions to construct finite-sample calibrated predictive intervals for Bayesian models, following the approach in Barber et al. (2021). These intervals are calculated efficiently using importance sampling for the leave-one-out residuals. By default, the intervals will also reflect the relative uncertainty in the Bayesian model, using the locally-weighted conformal methods of Lei et al. (2018).

Installation

You can install the development version of conformalbayes with:

# install.packages("devtools")
devtools::install_github("CoryMcCartan/conformalbayes")

Example

library(rstanarm)
library(conformalbayes)
data("Loblolly")

fit_idx = sample(nrow(Loblolly), 50)
d_fit = Loblolly[fit_idx, ]
d_test = Loblolly[-fit_idx, ]

# fit a simple linear regression
m = stan_glm(height ~ sqrt(age), data=d_fit,
    chains=1, control=list(adapt_delta=0.999), refresh=0)

# prepare conformal predictions
m = loo_conformal(m)

# make predictive intervals
pred_ci = predictive_interval(m, newdata=d_test, prob=0.9)
print(head(pred_ci))
#>             5%       95%
#> 1  -0.15888597  5.600095
#> 29 25.43314599 30.988491
#> 57 48.67648127 54.182655
#> 2  -0.09561987  5.447242
#> 30 25.42970114 30.938488
#> 72 58.01173186 63.596592

# are we covering?
mean(pred_ci[, "5%"] <= d_test$height &
         d_test$height <= pred_ci[, "95%"])
#> [1] 0.9117647

Citations

Barber, R. F., Candes, E. J., Ramdas, A., & Tibshirani, R. J. (2021). Predictive inference with the jackknife+. The Annals of Statistics, 49(1), 486-507.

Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018). Distribution-free predictive inference for regression. Journal of the American Statistical Association, 113(523), 1094-1111.