README.md

cppconformal

An implementation of conformal regression with Rcpp.

How to install

library('devtools')
devtools::install_github('gioelece/cppconformal')

How to use

To read the documentation, including this README with well-formatted math, go to https://gioelece.github.io/cppconformal/.

The library exports in R the following functions:

run_linear_conformal_single_grid(X, y, Xhat, grid_side, grid_param)
run_ridge_conformal_single_grid(X, y, Xhat, lambda, grid_side, grid_param)
run_linear_conformal_multi_grid(X, y, Xhat, grid_levels, grid_sides, initial_grid_param)
run_ridge_conformal_multi_grid(X, y, Xhat, lambda, grid_levels, grid_sides, initial_grid_param)

For example, one can call run_linear_conformal(X, Y, Xhat, grid_side, grid_param): X ($n \times p$ matrix) contains the covariates, Y ($n \times d$) is the matrix of the corresponding observed values, and one wants to construct a confidence interval for the response to the covariates Xhat ($n_0 \times p$).

To sample the response space, for the single_grid function family, a uniform grid is created. The limits of the grid for the $i$-th axis are -limit_i to +limit_i where limit_i = grid_param * max(abs(y_i)), with grid_side points for each dimension.

Instead, when using a *_multi_grid function, an initial "coarse" grid is created as before, with parameters initial_grid_param and grid_sides[0]. Then a subgrid of size grid_sides[1] is created to contain all the points (from the previous grid) where the value of $p$ is greater or equal than grid_levels[0], and so on, for all the elements of grid_levels. Note that, in order to use these functions, one needs to have a single Xhat, i.e. $n_0 = 1$.

Let $G = \text{grid_side} ^ d$ be the total number of grid points. The functions return a R list with grid ($G \times d$), containing the sampled points, and p_values ($n_0 \times G$), containing the corresponding p-values for each Xhat. For *_multi_grid functions, only the values referring to the last grid are returned, but the grid history is added as y_grid_parameters.

Remark: the intercept coefficient is not included in the prediction. To have a "typical" linear regression, one needs to add to X a column of ones.

References

Zeni G, Fontana M, Vantini S. Conformal Prediction: a Unified Review of Theory and New Challenges. arXiv:200507972 [cs, econ, stat]. Published online May 16, 2020. Accessed October 26, 2020. http://arxiv.org/abs/2005.07972

Vovk V, Gammerman A, Shafer G. Algorithmic Learning in a Random World. Springer; 2005.

Nouretdinov I, Gammerman J, Fontana M, Rehal D. Multi-level conformal clustering: A distribution-free technique for clustering and anomaly detection. Neurocomputing. 2020;397:279-291. doi:10.1016/j.neucom.2019.07.114