| Title: | Game Theory-Based Influence Measures |
|---|---|
| Description: | Understanding how features influence a specific response variable becomes crucial in classification problems, with applications ranging from medical diagnosis to customer behavior analysis. This packages provides tools to compute such an influence measure grounded on game theory concepts. In particular, the influence measures presented in Davila-Pena, Saavedra-Nieves, and Casas-Méndez (2024) <doi:10.48550/arXiv.2408.02481> can be obtained. |
| Authors: | Laura Davila-Pena [aut, cre]
|
| Maintainer: | Laura Davila-Pena <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.0 |
| Built: | 2024-10-08 03:30:50 UTC |
| Source: | CRAN |
This dataset contains data on car crash fatalities after transforming the original
categorical variables of the dataset cars_original into binary variables. Details
about such transformations are available in Davila-Pena et al. (2024).
(Section 6.1, Table 5).
data(cars_binary)data(cars_binary)
A dataframe with 17565 rows (representing individuals) and 12 columns, one corresponding to the index number
(first column, X), one to the binary response (last column, deceased), and the remaining 10 representing the following binary features:
dvcatBinary variable indicating whether the vehicle, at the moment of the accident, was traveling at a speed higher than 55 km/h (1) or not (0).
airbagBinary variable indicating whether the vehicle had an airbag system (1) or not (0).
seatbeltBinary variable indicating whether the person involved was wearing a seat belt (1) or not (0).
frontalBinary variable indicating whether the vehicle crash was frontal (1) or nonfrontal (0).
sexBinary variable indicating the sex of the person involved: 1 for male and 0 for female.
abcatBinary variable indicating airbag activation: 1 if one or more airbags in the vehicle were activated (even if not deployed) and 0 if none were deployed (either due to malfunction or being disabled).
occRoleBinary variable indicating whether the person involved was the driver (1) or a passenger (0) of the vehicle.
deployBinary variable indicating whether the airbag functioned correctly (1) or was unavailable or not functioning (0).
ageOFoccBinary variable indicating whether the person was 30 years old or less (1) or over 30 years old (0).
ageBinary variable indicating whether the vehicle was 10 years old or more (1) or less than 10 years old (0).
Generated data for illustrative purposes, see: Davila-Pena, L., Saavedra-Nieves, A., & Casas-Méndez, B. (2024). On the influence of dependent features in classification problems: a game-theoretic perspective. arXiv preprint. doi:10.48550/arXiv.2408.02481.
data(cars_binary) head(cars_binary)data(cars_binary) head(cars_binary)
This dataset contains data on car crash fatalities.
data(cars_original)data(cars_original)
A dataframe with 17565 rows (representing individuals) and 16 columns, one corresponding to the index number
(first column, X) and the remaining ones corresponding to different variables. For details, please refer
to the source below.
This dataset contains data on car crash fatalities from the nassCDS dataset via the "DAAG" R package (doi:10.32614/CRAN.package.DAAG) from Maindonald & Braun (2021).
Maindonald, J. H. & Braun W. J. (2021). Data analysis and graphics using R. An example-based approach (3rd edition). Cambridge University Press, Cambridge. The DAAG package was created to support this text. https://CRAN.R-project.org/package=DAAG (R package version 1.25.6.)
data(cars_original) head(cars_original)data(cars_original) head(cars_original)
The checking function checks whether a given pair (Xdata.i.ell, Yell.i)
is present in the dataset (Xdata, Ydata) and returns the corresponding indices, if any.
checking(Xdata, Ydata, Xdata.i.ell, Yell.i)checking(Xdata, Ydata, Xdata.i.ell, Yell.i)
Xdata |
Matrix. A dataset where rows represent observations and columns represent features. |
Ydata |
Vector. The response variable associated with each row in |
Xdata.i.ell |
Vector. A vector of feature values, potentially representing a row of |
Yell.i |
Integer. The specific response value to check. |
A vector of indices where the match occurs.
# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 Xdata.i.ell <- c(1,2,0,1) # obviously, considering `Xdata` is binary, this cannot be present. Yell.i <- 1 checking(Xdata, Ydata, Xdata.i.ell, Yell.i) Xdata.i.ell <- c(1,1,0,1) Yell.i <- 0 checking(Xdata, Ydata, Xdata.i.ell, Yell.i)# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 Xdata.i.ell <- c(1,2,0,1) # obviously, considering `Xdata` is binary, this cannot be present. Yell.i <- 1 checking(Xdata, Ydata, Xdata.i.ell, Yell.i) Xdata.i.ell <- c(1,1,0,1) Yell.i <- 0 checking(Xdata, Ydata, Xdata.i.ell, Yell.i)
The IM_dep function calculates the influence measure of equation (2) in Davila-Pena et al. (2024).
The features are grouped into unions based on the index vector.
IM_dep(Xdata, Ydata, index)IM_dep(Xdata, Ydata, index)
Xdata |
Matrix. A dataset where rows represent observations and columns represent features. |
Ydata |
Vector. The response variable associated with each row in |
index |
Vector. A grouping vector that assigns each feature in |
The IM_dep function calculates the weighted average of the number of times a change in
the value of a feature associated to a specific union influences the response value.
A vector of influences for each feature.
Davila-Pena, L., Saavedra-Nieves, A., & Casas-Méndez, B. (2024). On the influence of dependent features in classification problems: a game-theoretic perspective. arXiv preprint. doi:10.48550/arXiv.2408.02481.
# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 # Scenario 1: IM_dep(Xdata,Ydata,index = c(1,2,3,4)) # Scenario 9: IM_dep(Xdata,Ydata,index = c(1,2,1,2))# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 # Scenario 1: IM_dep(Xdata,Ydata,index = c(1,2,3,4)) # Scenario 9: IM_dep(Xdata,Ydata,index = c(1,2,1,2))
The IM_nodep function calculates the influence measure of equation (2) in Davila-Pena et al. (2024)
when the partition set is P={{1},{2},{3},{4}}, which is equivalent to the influence measure in Datta et al. (2015).
IM_nodep(Xdata, Ydata)IM_nodep(Xdata, Ydata)
Xdata |
Matrix. A dataset where rows represent observations and columns represent features. |
Ydata |
Vector. The response variable associated with each row in |
The IM_nodep function calculates the weighted average of the number of times a change in
the value of a feature influences the response value.
A vector of influences for each feature.
Datta, A., Datta, A., Procaccia, A., & Zick, Y. (2015). Influence in classification via cooperative game theory. Proceedings of the Twenty–fourth International Joint Conference on Artificial Intelligence, 511–517. https://www.ijcai.org/Proceedings/15/Papers/078.pdf.
Davila-Pena, L., Saavedra-Nieves, A., & Casas-Méndez, B. (2024). On the influence of dependent features in classification problems: a game-theoretic perspective. arXiv preprint. doi:10.48550/arXiv.2408.02481.
# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 # Scenario 1: IM_nodep(Xdata,Ydata)# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 # Scenario 1: IM_nodep(Xdata,Ydata)
The Mell function computes equation (1) in page 9 of Davila-Pena et al. (2024)
when the dependency is positive and features are binary. It filters rows from Xdata and Ydata based on specific conditions
of features' dependency as defined by index. It selects rows where the values
of features within the same union, except for those in union ell, coincide.
Mell(Xdata, Ydata, index, ell)Mell(Xdata, Ydata, index, ell)
Xdata |
Matrix. A dataset where rows represent observations and columns represent features. |
Ydata |
Vector. The response variable associated with each row in |
index |
Vector. A grouping vector that assigns each feature in |
ell |
Integer. The index of the union to exclude from the comparison. |
The Mell function iterates through each row of Xdata and compares the values of features
within predefined unions (determined by index). For each union, excluding the one specified
by ell, the function checks if all feature values in that union coincide.
If this condition is satisfied for all unions except ell, the row is selected.
A list containing the following components:
A subset of Xdata that meets the specified group conditions.
The corresponding values from Ydata for the selected rows in Xdata.ell.
The number of selected rows that meet the group condition.
Davila-Pena, L., Saavedra-Nieves, A., & Casas-Méndez, B. (2024). On the influence of dependent features in classification problems: a game-theoretic perspective. arXiv preprint. doi:10.48550/arXiv.2408.02481.
# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 # Scenario 1: Mell(Xdata = Xdata, Ydata = Ydata, index = c(1,2,3,4), ell = 3) # Scenario 9: Mell(Xdata = Xdata, Ydata = Ydata, index = c(1,2,1,2), ell = 2)# Example usage from Example 5.2 in Davila-Pena et al. (2024): library(CoopGame) n.user <- 16 Xdata <- createBitMatrix(4)[,-5] Xdata <- rbind(c(0,0,0,0),Xdata) Ydata <- rep(0,n.user) Ydata[1+c(10,11,13,14,15)] <- 1 # Scenario 1: Mell(Xdata = Xdata, Ydata = Ydata, index = c(1,2,3,4), ell = 3) # Scenario 9: Mell(Xdata = Xdata, Ydata = Ydata, index = c(1,2,1,2), ell = 2)
This function trains three different classifiers—Random Forest (RF), Support Vector Machine (SVM), and Logistic Regression (LR)—on the input dataset and returns their predictions.
predictions(Xdata, Ydata)predictions(Xdata, Ydata)
Xdata |
Matrix. A dataset where rows represent observations and columns represent features. |
Ydata |
Vector. The actual response variable associated with each row in |
The function utilizes the RWeka package to build three different classifiers: Random Forest (RF), Support Vector Machine (SVM), and Logistic Regression (LR). It then predicts the response variable for the input data using each of these models.
A list containing predictions from the three models:
predictionRFPredictions from the Random Forest (RF) model.
predictionSVMPredictions from the Support Vector Machine (SVM) model.
predictionLRPredictions from the Logistic Regression (LR) model.
Davila-Pena, L., Saavedra-Nieves, A., & Casas-Méndez, B. (2024). On the influence of dependent features in classification problems: a game-theoretic perspective. arXiv preprint. doi:10.48550/arXiv.2408.02481.
# Example usage: X <- matrix(rnorm(100), ncol=5) Y <- sample(0:1, 20, replace=TRUE) predictions(X, Y)# Example usage: X <- matrix(rnorm(100), ncol=5) Y <- sample(0:1, 20, replace=TRUE) predictions(X, Y)
This dataset contains data on musical tastes in Spotify considering only
the 15 most listened-to artists from the dataset spotify_original.
Details about such artists are available in Davila-Pena et al. (2024)
(Section 6.2, Table 11).
data(spotify_15)data(spotify_15)
A dataframe with 1226 rows (users) and 16 columns, one corresponding to the index number
(first column, X) and the remaining 15 corresponding to different artists.
Item-item collaborative filtering with binary or unitary data, https://medium.com/radon-dev/item-item-collaborative-filtering-with-binary-or-unary-data-e8f0b465b2c3. Accessed: 02 October 2024
data(spotify_15) head(spotify_15)data(spotify_15) head(spotify_15)
This dataset contains data on musical tastes in Spotify considering only
the 75 most listened-to artists from the dataset spotify_original.
Details about such artists are available in Davila-Pena et al. (2024)
(Section 6.2, Table 11).
data(spotify_75)data(spotify_75)
A dataframe with 1226 rows (users) and 76 columns, one corresponding to the index number
(first column, X) and the remaining 75 corresponding to different artists.
Item-item collaborative filtering with binary or unitary data, https://medium.com/radon-dev/item-item-collaborative-filtering-with-binary-or-unary-data-e8f0b465b2c3. Accessed: 02 October 2024
data(spotify_75) head(spotify_75)data(spotify_75) head(spotify_75)
This dataset contains data on musical tastes in Spotify from the last.fm dataset. It informs
about which users have listened to which artists. Refer to the source for details.
data(spotify_original)data(spotify_original)
A dataframe with 1226 rows (users) and 286 columns, one corresponding to the index number
(first column, X) and the remaining 285 corresponding to different artists.
Item-item collaborative filtering with binary or unitary data, https://medium.com/radon-dev/item-item-collaborative-filtering-with-binary-or-unary-data-e8f0b465b2c3. Accessed: 02 October 2024
data(spotify_original) head(spotify_original)data(spotify_original) head(spotify_original)