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title tags authors affiliations date bibliography
origami: A Generalized Framework for Cross-Validation in R
R
statistics
machine learning
cross-validation
name orcid affiliation
Jeremy R. Coyle
0000-0002-9874-6649
1
name orcid affiliation
Nima S. Hejazi
0000-0002-7127-2789
1
name index
Division of Biostatistics, University of California, Berkeley
1
19 June 2017
paper.bib

Summary

Cross-validation is an essential tool for evaluating how any given data analytic procedure extends from a sample to the target population from which the sample is derived. It has seen widespread application in all facets of statistics, perhaps most notably statistical machine learning. When used for model selection, cross-validation has powerful optimality properties [@Vaart:2006bz; @vanderLaan:2007bz].

Cross-validation works by partitioning a sample into complementary subsets, applying a particular data analytic (statistical) routine on a subset (the "training" set), and evaluating the routine of choice on the complementary subset (the "testing" set). This procedure is repeated across multiple partitions of the data, and a variety of different partitioning schemes exist, such as $V$-fold cross-validation and bootstrap cross-validation. origami, a package for the R language for statistical computing [@R], supports many of the existing cross-validation schemes, providing a suite of tools that generalize the application of cross-validation to arbitrary data analytic procedures.


General workflow

The main function in the origami R package is cross_validate. To start off, the user must define folds and a function that operates on each fold. Once these are passed to cross_validate, this function will map the fold-specific function across the folds, combining the results in a reasonable way. Specific details on each each step of this process are given below.

(1) Define folds

The folds object passed to cross_validate is a list of folds. Such lists can be generated using the make_folds function. Each fold consists of a list with a training index vector, a validation index vector, and a fold_index (its order in the list of folds). This function supports a variety of cross-validation schemes including $V$-fold and bootstrap cross-validation, as well as time series methods like "rolling window". See [@vanderLaan:2007bz] for formal definitions of these schemes. make_folds can balance across levels of a variable (stratify_ids), and it can also keep all observations from the same independent unit together (cluster). We invite interested users to consult the documentation of the make_folds function for further details.

(2) Define fold function

The cv_fun argument to cross_validate is a function that will perform some operation on each fold. The first argument to this function must be fold, which will receive an individual fold object to operate on. Additional arguments can be passed to cv_fun using the ... argument to cross_validate. Within this function, the convenience functions training, validation and fold_index can return the various components of a fold object. If training or validation is passed an object, it will index into it in a sensible way. For instance, if it is a vector, it will index the vector directly. If it is a data.frame or matrix, it will index rows. This allows the user to easily partition data into training and validation sets. This fold function must return a named list of results containing whatever fold-specific outputs are generated.

(3) Apply cross-validate

After defining folds, cross_validate can be used to map the cv_fun across the folds using future_lapply. This means that it can be easily parallelized by specifying a parallelization scheme (i.e., a plan). See the future package for further details.

The application of cross_validate generates a list of results. As described above, each call to cv_fun itself returns a list of results, with different elements for each type of result we care about. The main loop generates a list of these individual lists of results (a sort of "meta-list"). This "meta-list" is then inverted such that there is one element per result type (this too is a list of the results for each fold). By default, combine_results is used to combine these results type lists in a sensible manner. How results are combined is determined automatically by examining the data types of the results from the first fold. This can be modified by specifying a list of arguments to .combine_control. See the help for combine_results for more details. In most cases, the defaults should suffice.

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References