regressionPairs: Regression model for pairs of algorithms
In llama: Leveraging Learning to Automatically Manage Algorithms

Description Usage Arguments Details Value Author(s) See Also Examples

Builds regression models for each pair of algorithms that predict the performance difference based on the features of the problem and optionally features of the algorithms. The sum over all pairs that involve a particular algorithm is aggregated as the score of the algorithm.

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regressionPairs(regressor = NULL, data = NULL,
    pre = function(x, y=NULL) { list(features=x) }, combine = NULL,
    save.models = NA, use.weights = TRUE)

`regressor`	the regression function to use. Must accept a formula of the values to predict and a data frame with features. Return value should be a structure that can be given to `predict` along with new data. See examples.
`data`	the data to use with training and test sets. The structure returned by one of the partitioning functions.
`pre`	a function to preprocess the data. Currently only `normalize`. Optional. Does nothing by default.
`combine`	the function used to combine the predictions of the individual regression models for stacking. Default `NULL`. See details.
`save.models`	Whether to serialize and save the models trained during evaluation of the model. If not `NA`, will be used as a prefix for the file name.
`use.weights`	Whether to use instance weights if supported. Default `TRUE`.

regressionPairs takes the training and test sets in data and processes it using pre (if supplied). If no algorithm features are provided, regressor is called to induce a regression model for each pair of algorithms to predict the performance difference between them. When algorithm features are present, regressor is called to induce one regression model for all pairs of algorithms to predict the performance difference between them. If combine is not supplied, the best overall algorithm is determined by summing the performance differences over all pairs for each algorithm and ranking them by this sum. The algorithm with the largest value is chosen. If it is supplied, it is assumed to be an mlr classifier. This classifier is passed the original features and the predictions for each pair of algorithms. combine option is currently not supported with algorithm features. If the classifier supports weights and use.weights is TRUE, the performance difference between the best and the worst algorithm is passed as weight.

The aggregated score for each algorithm quantifies how much better it is than the other algorithms, where bigger values are better. Positive numbers denote that the respective algorithm usually exhibits better performance than most of the other algorithms, while negative numbers denote that it is usually worse.

The evaluation across the training and test sets will be parallelized automatically if a suitable backend for parallel computation is loaded. The parallelMap level is "llama.fold".

Training this model can take a very long time. Given n algorithms, choose(n, 2) * n models are trained and evaluated. This is significantly slower than the other approaches that train a single model or one for each algorithm. Even with algorithmic features present, when only a single model is trained, the process still takes a long time due to the amount of data.

If all predictions of an underlying machine learning model are NA, the prediction will be NA for the algorithm and -Inf for the score if the performance value is to be maximised, Inf otherwise.

If save.models is not NA, the models trained during evaluation are serialized into files. Each file contains a list with members model (the mlr model), train.data (the mlr task with the training data), and test.data (the data frame with the test data used to make predictions). The file name starts with save.models, followed by the ID of the machine learning model, followed by "combined" if the model combines predictions of other models, followed by the number of the fold. Each model for each fold is saved in a different file.

`predictions`	a data frame with the predictions for each instance and test set. The columns of the data frame are the instance ID columns (as determined by `input`), the algorithm, the score of the algorithm, and the iteration (e.g. the number of the fold for cross-validation). More than one prediction may be made for each instance and iteration. The score corresponds to how much better performance the algorithm delivers compared to the other algorithms in the portfolio. If stacking is used, each prediction is simply the best algorithm with a score of 1.
`predictor`	a function that encapsulates the classifier learned on the entire data set. Can be called with data for the same features with the same feature names as the training data to obtain predictions in the same format as the `predictions` member.
`models`	the models for each pair of algorithms trained on the entire data set. This is meant for debugging/inspection purposes and does not include any models used to combine predictions of individual models.

Lars Kotthoff

classify, classifyPairs, cluster, regression

if(Sys.getenv("RUN_EXPENSIVE") == "true") {
data(satsolvers)
folds = cvFolds(satsolvers)

model = regressionPairs(regressor=makeLearner("regr.lm"), data=folds)
# the total number of successes
sum(successes(folds, model))
# predictions on the entire data set
model$predictor(satsolvers$data[satsolvers$features])

# combine predictions using J48 induced classifier
model = regressionPairs(regressor=makeLearner("regr.lm"), data=folds,
    combine=makeLearner("classif.J48"))
}