Package 'ASML'

Title:	Algorithm Portfolio Selection with Machine Learning
Description:	A wrapper for machine learning (ML) methods to select among a portfolio of algorithms based on the value of a key performance indicator (KPI). A number of features is used to adjust a model to predict the value of the KPI for each algorithm, then, for a new value of the features the KPI is estimated and the algorithm with the best one is chosen. To learn it can use the regression methods in 'caret' package or a custom function defined by the user. Several graphics available to analyze the results obtained. This library has been used in Ghaddar et al. (2023) <doi:10.1287/ijoc.2022.0090>).
Authors:	Brais González-Rodríguez [aut, cre] , Ignacio Gómez-Casares [aut] , Beatriz Pateiro-López [aut] , Julio González-Díaz [aut] , María Caseiro-Arias [ctb], Antonio Fariña-Elorza [ctb], Manuel Timiraos-López [ctb]
Maintainer:	Brais González-Rodríguez <[email protected]>
License:	GPL-3
Version:	1.0.0
Built:	2025-02-20 09:54:10 UTC
Source:	https://github.com/cran/ASML

Help Index

Predicting the KPI value for the algorithms
Predicting the KPI value for the algorithms
Training models for posterior selection of algorithms
Training models for posterior selection of algorithms
Boxplots
Boxplots
Branching point selection in Polynomial Optimization
Branching point selection in Polynomial Optimization
Figure comparison
Figure Comparison
KPI summary table
KPI table
Machine learning process
Partition and Normalize
Plot
Ranking
Ranking Plot

Predicting the KPI value for the algorithms

Description

For each algorithm, the output (KPI) is predicted using the models trained with AStrain().

Usage

ASpredict(training_object, ...)
ASpredict(training_object, ...)

Arguments

`training_object`	list of class `as_train`.
`...`	other parameters.

Value

A data frame, result of the respective ASpredict method.

Predicting the KPI value for the algorithms

Description

For each algorithm, the output (KPI) is predicted using the models traing with AStrain().

Usage

## S3 method for class 'as_train'
ASpredict(training_object, newdata = NULL, f = NULL, ...)
## S3 method for class 'as_train'
ASpredict(training_object, newdata = NULL, f = NULL, ...)

Arguments

`training_object`	list of class `as_train`.
`newdata`	dataframe with the new data to predict. If not present, predictions are computed using the training data.
`f`	function to use for the predictions. If NULL, `caret`'s function will be used.
`...`	arguments passed to the predict function f when f is not NULL.

Details

The ASpredict() uses the prediction function from caret to compute (for each of the models trained) the predictions for the new data provided by the user. If the user used a custom function in AStrain() (given by parameter f), caret's default prediction function might not work, and the user might have to provide a custom function for ASpredict() as well. Additionally, this custom prediction function allows to pass additional arguments, something that caret's default prediction function does not. The object return by the train function used in AStrain() (caret's or a custom one) is the one passed to the custom f function defined by the user. This f function must return a vector with the predictions.

Value

A data frame with the predictions for each instance (rows), corresponding to each algorithm (columns). In case f is specified, some actions might be needed to get the predictions from the returned value.

Examples

data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
predictions <- ASpredict(training, newdata = data_object$x.test)
qrf_q_predict <- function(modelFit, newdata, what = 0.5, submodels = NULL) {
  out <- predict(modelFit, newdata, what = what)
  if (is.matrix(out))
    out <- out[, 1]
  out
}
custom_predictions <- ASpredict(training, newdata = data_object$x.test, f = "qrf_q_predict",
what = 0.25)
data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
predictions <- ASpredict(training, newdata = data_object$x.test)
qrf_q_predict <- function(modelFit, newdata, what = 0.5, submodels = NULL) {
  out <- predict(modelFit, newdata, what = what)
  if (is.matrix(out))
    out <- out[, 1]
  out
}
custom_predictions <- ASpredict(training, newdata = data_object$x.test, f = "qrf_q_predict",
what = 0.25)

Training models for posterior selection of algorithms

Description

For each algorithm (column) in the data, a model is trained to later predict the output (KPI) for that algorithm (using function ASpredict()).

Usage

AStrain(data_object, ...)
AStrain(data_object, ...)

Arguments

`data_object`	an object.
`...`	other parameters.

Value

A list, result of the respective AStrain method.

Training models for posterior selection of algorithms

Description

For each algorithm (column) in the data, a model is trained to later predict the output (KPI) for that algorithm (using function ASpredict()).

Usage

## S3 method for class 'as_data'
AStrain(data_object, method = NULL, parallel = FALSE, f = NULL, ...)
## S3 method for class 'as_data'
AStrain(data_object, method = NULL, parallel = FALSE, f = NULL, ...)

Arguments

`data_object`	object of class `as_data`.
`method`	name of the model to be used. The user can choose from any of the models provided by `caret`. See http://topepo.github.io/caret/train-models-by-tag.html for more information about the models supported.
`parallel`	boolean to control whether to parallelise the training or not (paralellization is handled by library snow).
`f`	function we want to use to train the models. If NULL, `caret`'s function will be used.
`...`	arguments passed to the caret train function.

Value

A list is returned of class as_train containing the trained models, one for each of the algorithms.

Examples

data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
custom_function <- function(x, y) {
  glm.fit(x, y)
}
custom_training <- AStrain(data_object, f = "custom_function")
data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
custom_function <- function(x, y) {
  glm.fit(x, y)
}
custom_training <- AStrain(data_object, f = "custom_function")

Boxplots

Description

Generates boxplots for an object.

Usage

boxplots(data_object, ...)
boxplots(data_object, ...)

Arguments

`data_object`	an object.
`...`	other parameters.

Value

A ggplot object, result of the respective boxplots method.

Boxplots

Description

Represents a boxplot for each of the algorithms to compare their performance according to the response variable (KPI). When available, it also includes a box plot for the "ML" algorithm generated from the predictions.

Usage

## S3 method for class 'as_data'
boxplots(
  data_object,
  main = "Boxplot Comparison",
  labels = NULL,
  test = TRUE,
  predictions = NULL,
  by_families = FALSE,
  color_list = NULL,
  ml_color = NULL,
  ordered_option_names = NULL,
  xlab = "Strategy",
  ylab = "KPI",
  ...
)
## S3 method for class 'as_data'
boxplots(
  data_object,
  main = "Boxplot Comparison",
  labels = NULL,
  test = TRUE,
  predictions = NULL,
  by_families = FALSE,
  color_list = NULL,
  ml_color = NULL,
  ordered_option_names = NULL,
  xlab = "Strategy",
  ylab = "KPI",
  ...
)

Arguments

`data_object`	object of class `as_data`.
`main`	an overall title for the plot.
`labels`	character vector with the labels for each of the algorithms. If NULL, the y names of the `data_object` names will be used.
`test`	flag that indicates whether the function should use test data or training data.
`predictions`	a data frame with the predicted KPI for each algorithm (columns) and for each instance (rows). If NULL, the plot won't include a ML column.
`by_families`	boolean indicating whether the function should represent data by families or not. The family information must be included in the `data_object` parameter.
`color_list`	list with the colors for the plots. If NULL, or insufficient number of colors, the colors will be generated automatically.
`ml_color`	color por the ML boxplot. If NULL, it will be generated automatically.
`ordered_option_names`	vector with the name of the columns of `data_object` y variable in the correct order.
`xlab`	a label for the x axis.
`ylab`	a label for the y axis.
`...`	other parameters.

Value

A ggplot object representing the boxplots of instance-normalized KPI for each algorithm across instances.

Examples

data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
boxplots(data, predictions = predict_test)
data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
boxplots(data, predictions = predict_test)

Branching point selection in Polynomial Optimization

Description

Data from Ghaddar et al. (2023) used to select among several branching criteria for an RLT-based algorithm. Includes features for the instances and KPI values for the different branching criteria for executions lasting 1 hour.

Usage

branching
branching

Format

A list with x (features) and y (KPIs) data.frames.

Source

Ghaddar, B., Gómez-Casares, I., González-Díaz, J., González-Rodríguez, B., Pateiro-López, B., & Rodríguez-Ballesteros, S. (2023). Learning for Spatial Branching: An Algorithm Selection Approach. INFORMS Journal on Computing.

Branching point selection in Polynomial Optimization

Description

Usage

branchingsmall
branchingsmall

Format

A list with x (features) and y (KPIs) data.frames.

Source

Figure comparison

Description

Generates figure comparison plot for an object.

Usage

figure_comparison(data_object, ...)
figure_comparison(data_object, ...)

Arguments

`data_object`	an object
`...`	other parameters

Value

A ggplot object, result of the respective figure_comparison method.

Figure Comparison

Description

Represents a bar plot with the percentage of times each algorithm is selected by ML compared with the optimal selection (according to the response variable or KPI).

Usage

## S3 method for class 'as_data'
figure_comparison(
  data_object,
  ties = "different_data_points",
  main = "Option Comparison",
  labels = NULL,
  mllabel = NULL,
  test = TRUE,
  predictions,
  by_families = FALSE,
  stacked = TRUE,
  color_list = NULL,
  legend = TRUE,
  ordered_option_names = NULL,
  xlab = "Criteria",
  ylab = "Instances (%)",
  ...
)
## S3 method for class 'as_data'
figure_comparison(
  data_object,
  ties = "different_data_points",
  main = "Option Comparison",
  labels = NULL,
  mllabel = NULL,
  test = TRUE,
  predictions,
  by_families = FALSE,
  stacked = TRUE,
  color_list = NULL,
  legend = TRUE,
  ordered_option_names = NULL,
  xlab = "Criteria",
  ylab = "Instances (%)",
  ...
)

Arguments

`data_object`	object of class `as_data`.
`ties`	How to deal with ties. Must be one of: "different_data_points": Tied algorithms in the optimal selection are all counted as different data points (increasing the total number of x values and therefore giving all of the tied algorithms the same weight). "ml_if_optimal": For tied algorithms, the one selected by ML is chosen if it corresponds to the optimal one. Otherwise, the same as in option `different_data_points` is done. "ml_selection": For tied algorithms, the one prefered by the ML is chosen.
`main`	an overall title for the plot.
`labels`	character vector with the labels for each of the algorithms. If NULL, the y names of the `data_object` names will be used.
`mllabel`	character vector with the labels for the Optimal and ML bars. If NULL, default names will be used.
`test`	flag that indicates whether the function should use test data or training data.
`predictions`	a data frame with the predicted KPI for each algorithm (columns) and for each instance (rows).
`by_families`	boolean indicating whether the function should represent data by families or not. The family information must be included in the `data_object` parameter.
`stacked`	boolean to choose between bar plot and stacked bar plot.
`color_list`	list with the colors for the plots. If NULL, or insufficient number of colors, the colors will be generated automatically.
`legend`	boolean to activate or deactivate the legend in the plot.
`ordered_option_names`	vector with the name of the columns of data_object y variable in the correct order.
`xlab`	a label for the x axis.
`ylab`	a label for the y axis.
`...`	other parameters.

Value

A ggplot object representing the bar plot with the percentage of times each algorithm is selected by ML compared with the optimal selection (according to the response variable or KPI).

Examples

data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
figure_comparison(data, predictions = predict_test)
data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
figure_comparison(data, predictions = predict_test)

KPI summary table

Description

Generates a summary table with the values of the KPI.

Function that generates a summary table of the KPI values. Optimal is the value of the KPI when choosing the best option for each instance. It's the best that we could do with respect to that KPI. Best is the value of the KPI for the best option overall according to the KPI. ML is the value of the KPI choosing for each instance the option selected by the learning.

Usage

KPI_summary_table(data_object, ...)

## S3 method for class 'as_data'
KPI_summary_table(
  data_object,
  predictions = NULL,
  test = TRUE,
  normalized = FALSE,
  ...
)
KPI_summary_table(data_object, ...)

## S3 method for class 'as_data'
KPI_summary_table(
  data_object,
  predictions = NULL,
  test = TRUE,
  normalized = FALSE,
  ...
)

Arguments

`data_object`	an object of class `as_data`.
`...`	other parameters.
`predictions`	a data frame with the predicted KPI for each algorithm (columns) and for each instance (rows). If NULL, the table won't include a ML column.
`test`	flag that indicates whether the function should use test data or training data.
`normalized`	whether to use the original values of the KPI or the normalized ones used for the learning.

Value

A table, result of the respective KPI_summary_table method.

A table with the statistics of the pace.

Examples

data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
predictions <- ASpredict(training, newdata = data_object$x.test)
KPI_summary_table(data_object, predictions = predictions)
data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
predictions <- ASpredict(training, newdata = data_object$x.test)
KPI_summary_table(data_object, predictions = predictions)

KPI table

Description

Generates a table with the values of the KPI.

Function that generates a table with the values of the KPI.

Usage

KPI_table(data_object, ...)

## S3 method for class 'as_data'
KPI_table(data_object, predictions = NULL, test = TRUE, ...)
KPI_table(data_object, ...)

## S3 method for class 'as_data'
KPI_table(data_object, predictions = NULL, test = TRUE, ...)

Arguments

`data_object`	an object of class `as_data`.
`...`	other parameters.
`predictions`	a data frame with the predicted KPI for each algorithm (columns) and for each instance (rows). If NULL, the table won't include a ML column.
`test`	flag that indicates whether the function should use test data or training data.

Value

A table, result of the respective KPI_table method.

A table with the statistics of the pace.

Examples

data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
predictions <- ASpredict(training, newdata = data_object$x.test)
KPI_table(data_object, predictions = predictions)
data(branchingsmall)
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)
training <- AStrain(data_object, method = "glm")
predictions <- ASpredict(training, newdata = data_object$x.test)
KPI_table(data_object, predictions = predictions)

Machine learning process

Description

Function that proceses input data, trains the machine learning models, makes a prediction and plots the results.

Usage

ml(
  x,
  y,
  x.test = NULL,
  y.test = NULL,
  family_column = NULL,
  split_by_family = FALSE,
  predict = TRUE,
  test_size = 0.25,
  better_smaller = TRUE,
  method = "ranger",
  test = TRUE,
  color_list = NULL
)
ml(
  x,
  y,
  x.test = NULL,
  y.test = NULL,
  family_column = NULL,
  split_by_family = FALSE,
  predict = TRUE,
  test_size = 0.25,
  better_smaller = TRUE,
  method = "ranger",
  test = TRUE,
  color_list = NULL
)

Arguments

`x`	dataframe with the instances (rows) and its features (columns). It may also include a column with the family data.
`y`	dataframe with the instances (rows) and the corresponding output (KPI) for each algorithm (columns).
`x.test`	dataframe with the test features. It may also include a column with the family data. If NULL, the algorithm will split x into training and test sets.
`y.test`	dataframe with the test outputs. If NULL, the algorithm will split y into training and test sets.
`family_column`	column number of x where each instance family is indicated. If given, aditional options for the training and set test splitting and the graphics are enabled.
`split_by_family`	boolean indicating if we want to split sets keeping family proportions in case x.test and y.test are NULL. This option requires that option `family_column` is different from NULL
`predict`	boolean indicating if predictions will be made or not. If FALSE plots will use training data only and no ML column will be displayed.
`test_size`	float with the segmentation proportion for the test dataframe. It must be a value between 0 and 1.
`better_smaller`	boolean that indicates wether the output (KPI) is better if smaller (TRUE) or larger (FALSE).
`method`	name of the model to be used. The user can choose from any of the models provided by `caret`. See http://topepo.github.io/caret/train-models-by-tag.html for more information about the models supported.
`test`	boolean indicating whether the predictions will be made with the test set or the training set.
`color_list`	list with the colors for the plots. If NULL or insufficient number of colors, the colors will be generated automatically.

Value

A list with the data and plots generated, including:

data_obj An as_data object with the processed data from partition_and_normalize() function.
training An as_train object with the trainings from the AStrain() function.
predictions A data frame with the predictions from the ASpredict() function, if the predict param is TRUE.
table A table with the summary of the output data.
boxplot, ranking_plot, figure_comparison, optml_figure_comparison and optmlall_figure_comparison with the corresponding plots.

Examples


data(branchingsmall)
machine_learning <- ml(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE, method = "glm")

data(branchingsmall)
machine_learning <- ml(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE, method = "glm")

Partition and Normalize

Description

Function that processes the input data splitting it into training and test sets and normalizes the outputs depending on the best instance performance. The user can bypass the partition into training and test set by passing the parameters x.test and y.test.

Usage

partition_and_normalize(
  x,
  y,
  x.test = NULL,
  y.test = NULL,
  family_column = NULL,
  split_by_family = FALSE,
  test_size = 0.3,
  better_smaller = TRUE
)
partition_and_normalize(
  x,
  y,
  x.test = NULL,
  y.test = NULL,
  family_column = NULL,
  split_by_family = FALSE,
  test_size = 0.3,
  better_smaller = TRUE
)

Arguments

`x`	dataframe with the instances (rows) and its features (columns). It may also include a column with the family data.
`y`	dataframe with the instances (rows) and the corresponding output (KPI) for each algorithm (columns).
`x.test`	dataframe with the test features. It may also include a column with the family data. If NULL the algorithm will split x into training and test sets.
`y.test`	dataframe with the test outputs. If NULL the algorithm will y into training and test sets.
`family_column`	column number of x where each instance family is indicated. If given, aditional options for the training and set test splitting and the graphics are enabled.
`split_by_family`	boolean indicating if we want to split sets keeping family proportions in case x.test and y.test are NULL. This option requires that option `family_column` is different from NULL.
`test_size`	float with the segmentation proportion for the test dataframe. It must be a value between 0 and 1. Only needed when `x.test` and `y.test` are NULL.
`better_smaller`	boolean that indicates wether the output (KPI) is better if smaller (TRUE) or larger (FALSE).

Value

A list is returned of class as_data containing:

x.train A data frame with the training features.
y.train A data frame with the training output.
x.test A data frame with the test features.
y.test A data frame with the test output.
y.train.original A vector with the original training output (without normalizing).
y.test.original A vector with the original test output (without normalizing).
families.train A data frame with the families of the training data.
families.test A data frame with the families of the test data.

Examples

data(branching)
data_obj <- partition_and_normalize(branching$x, branching$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)

data(branching)
data_obj <- partition_and_normalize(branching$x, branching$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)

Plot

Description

For an object of class as_data, function that makes several plots, including the following: a boxplot, a ranking plot and comparisons between the different options.

Usage

## S3 method for class 'as_data'
plot(
  x,
  labels = NULL,
  test = TRUE,
  predictions = NULL,
  by_families = FALSE,
  stacked = TRUE,
  legend = TRUE,
  color_list = NULL,
  ml_color = NULL,
  path = NULL,
  ...
)
## S3 method for class 'as_data'
plot(
  x,
  labels = NULL,
  test = TRUE,
  predictions = NULL,
  by_families = FALSE,
  stacked = TRUE,
  legend = TRUE,
  color_list = NULL,
  ml_color = NULL,
  path = NULL,
  ...
)

Arguments

`x`	object of class `as_data`.
`labels`	character vector with the labels for each of the algorithms. If NULL, the y names of the `data_object` names will be used.
`test`	flag that indicates whether the function should use test data or training data.
`predictions`	a data frame with the predicted KPI for each algorithm (columns) and for each instance (rows). If NULL, the plot won't include a ML column.
`by_families`	boolean indicating whether the function should represent data by families or not. The family information must be included in the `data_object` parameter.
`stacked`	boolean to choose between bar plot and stacked bar plot.
`legend`	boolean to activate or deactivate the legend in the plot.
`color_list`	list with the colors for the plots. If NULL, or insufficient number of colors, the colors will be generated automatically.
`ml_color`	color por the ML boxplot. If NULL, it will be generated automatically.
`path`	path where plots will be saved. If NULL they won't be saved.
`...`	other parameters.

Value

A list with boxplot, ranking, fig_comp, optml_fig_comp and optmlall_fig_comp plots.

Examples


data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
plot(data, predictions = predict_test)

data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
plot(data, predictions = predict_test)

Ranking

Description

Generates ranking plot for an object.

Usage

ranking(data_object, ...)
ranking(data_object, ...)

Arguments

`data_object`	an object
`...`	other parameters

Value

A ggplot object, result of the respective ranking method.

Ranking Plot

Description

After ranking the algorithms for each instance, represents for each of the algorithms, a bar with the percentage of times it was in each of the ranking positions. The number inside is the mean value of the normalized response variable (KPI) for the problems for which the algorithm was in that ranking position. The option predictions allows to control if the "ML" algorithm is added to the plot.

Usage

## S3 method for class 'as_data'
ranking(
  data_object,
  main = "Ranking",
  labels = NULL,
  test = TRUE,
  predictions = NULL,
  by_families = FALSE,
  ordered_option_names = NULL,
  xlab = "",
  ylab = "",
  ...
)
## S3 method for class 'as_data'
ranking(
  data_object,
  main = "Ranking",
  labels = NULL,
  test = TRUE,
  predictions = NULL,
  by_families = FALSE,
  ordered_option_names = NULL,
  xlab = "",
  ylab = "",
  ...
)

Arguments

`data_object`	object of class `as_data`.
`main`	an overall title for the plot.
`labels`	character vector with the labels for each of the algorithms. If NULL, the y names of the `data_object` names will be used.
`test`	flag that indicates whether the function should use test data or training data.
`predictions`	a data frame with the predicted KPI for each algorithm (columns) and for each instance (rows). If NULL, the plot won't include a ML column.
`by_families`	boolean indicating whether the function should represent data by families or not. The family information must be included in the `data_object` parameter.
`ordered_option_names`	vector with the name of the columns of data_object y variable in the correct order.
`xlab`	a label for the x axis.
`ylab`	a label for the y axis.
`...`	other parameters.

Value

A ggplot object representing the ranking of algorithms based on the instance-normalized KPI.

Examples

data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
ranking(data, predictions = predict_test)
data(branchingsmall)
data <- partition_and_normalize(branchingsmall$x, branchingsmall$y)
training <- AStrain(data, method = "glm")
predict_test <- ASpredict(training, newdata = data$x.test)
ranking(data, predictions = predict_test)