Package 'ASML'

Create DALEX explainers for multiple ASML-trained models

Description

This function simplifies the use of DALEX with models trained using AStrain from ASML. It automatically creates DALEX explainers for all trained models (one per algorithm in the portfolio), allowing users to easily apply DALEX functions to analyze model performance, evaluate feature importance, and generate partial dependence plots (PDPs), among other analyses.

Usage

ASexplainer(training, data, y, labels = NULL, ...)

Arguments

training	An object of class as_train containing models trained with AStrain.
data	A data.frame or matrix with predictor variables. Must not include the target columns.
y	A matrix or data.frame containing the target variables. Each column corresponds to the output for the model at the same position in training.
labels	Optional character vector of labels for the explainers. If NULL, names(training) are used. Must have the same length as training.
...	Additional arguments passed to DALEX::explain.

Value

A named list of DALEX explainer objects, one per trained model. Names are taken from labels or names(training).

References

Biecek, P. (2018). DALEX: Explainers for Complex Predictive Models in R. Journal of Machine Learning Research, 19(84), 1–5. http://jmlr.org/papers/v19/18-416.html

Examples

## Not run: 
library(ASML)
library(DALEX)
data(branching)
features <- branching$x
KPI <- branching$y
lab_rules <- c("max", "sum", "dual", "range", "eig-VI", "eig-CMI")

# Preprocess data
data_obj <- partition_and_normalize(
  features,
  KPI,
  family_column = 1,
  split_by_family = TRUE,
  better_smaller = TRUE
)

# Train models
training <- AStrain(data_obj, method = "rf", parallel = TRUE)

# Create explainers
out <- ASexplainer(
  training,
  data = data_obj$x.test,
  y = data_obj$y.test,
  labels = lab_rules,
  verbose = FALSE
)

# Model performance
mp_regr_rf <- lapply(out, DALEX::model_performance)
do.call(plot, unname(mp_regr_rf))
do.call(plot, c(unname(mp_regr_rf), list(geom = "boxplot")))

# Variable importance
vi_regr_rf <- lapply(out, DALEX::model_parts)
do.call(plot, c(unname(vi_regr_rf), list(max_vars = 5)))

# Partial dependence plots
pdp_regr_rf <- lapply(out, DALEX::model_profile, variable = "degree", type = "partial")
do.call(plot, unname(pdp_regr_rf))

## End(Not run)

---

Predicting the KPI value for the algorithms

Description

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

Usage

## 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)

---

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, ...)

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)
# Partition and normalize the data
data_object <- partition_and_normalize(branchingsmall$x, branchingsmall$y, test_size = 0.3,
family_column = 1, split_by_family = TRUE)

# Example: training a regression decision tree
# with cross-validation control and basic hyperparameter tuning
train_control <- caret::trainControl(method = "cv", number = 5)
tune_grid <- expand.grid(cp = c(0.01, 0.05, 0.1))
training <- AStrain(
  data_object,
  method = "rpart",
  trControl = train_control,
  tuneGrid = tune_grid
)

# Example: training with glm and similar with custom function
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

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",
  ...
)

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)

---

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

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

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 10 minutes.

Usage

branchingsmall

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.

---

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 (%)",
  ...
)

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 preferred 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)

---

KPI summary table

Description

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

## 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.
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.
...	other parameters.

Value

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)

---

KPI table

Description

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

Usage

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

Arguments

data_object	an object of class as_data.
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.
...	other parameters.

Value

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)

---

Machine learning process

Description

Function that processes 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
)

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, adittional 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 whether 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")

---

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
)

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, adittional 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 whether 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)

---

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,
  ...
)

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 for 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)

---

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 = "",
  ...
)

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)

---

Automatic selection of the most suitable storage format for sparse matrices on GPUs

Description

Data from Pichel and Pateiro-López (2018), which contains information on 8111 sparse matrices. Each matrix is described by a set of nine structural features, and the performance of the single-precision SpMV kernel was measured under three storage formats: compressed row storage (CSR), ELLPACK (ELL), and hybrid (HYB). For each matrix and format, performance is expressed as the average GFLOPS (billions of floating-point operations per second), over 1000 SpMV operations.

Usage

SpMVformat

Format

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

Source

Pichel, J. C., & Pateiro-López, B. (2018). A new approach for sparse matrix classification based on deep learning techniques. In 2018 IEEE International Conference on Cluster Computing (CLUSTER) (pp. 46–54).

---