Cubist Regression in R

Intro

Cubist is a rule based model that builds regression solutions based on building rules. In this article, we will learn how to use cubist model in r.

Data

For this tutorial, we will use the Boston data set which includes housing data with features of the houses and their prices. We would like to predict the medv column or the medium value.

library(MASS)
data(Boston)

str(Boston)

## 'data.frame':    506 obs. of  14 variables:
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : num  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ black  : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...

Basic CubistRegression Model in R

To create a basic Cubist model in R, we can use the cubist function from the cubist function. We pass the formula of the model medv ~. which means to model medium value by all other predictors. We also pass our data Boston.

library(Cubist)

## Warning: package 'Cubist' was built under R version 4.0.5

## Loading required package: lattice

features = subset(Boston, select=-c(medv))
target = subset(Boston, select=medv)[,1]

model = cubist(features, target)
model

## 
## Call:
## cubist.default(x = features, y = target)
## 
## Number of samples: 506 
## Number of predictors: 13 
## 
## Number of committees: 1 
## Number of rules: 4

Modeling Cubist in R with Caret

We will now see how to model a ridge regression using the Caret package. We will use this library as it provides us with many features for real life modeling. To do this, we use the train method. We pass the same parameters as above, but in addition we pass the method = 'rf' model to tell Caret to use a lasso model.

library(caret)

## Loading required package: ggplot2

set.seed(1)

model <- train(
  medv ~ .,
  data = Boston,
  method = 'cubist'
)
model

## Cubist 
## 
## 506 samples
##  13 predictor
## 
## No pre-processing
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 506, 506, 506, 506, 506, 506, ... 
## Resampling results across tuning parameters:
## 
##   committees  neighbors  RMSE      Rsquared   MAE     
##    1          0          4.906555  0.7379561  2.936537
##    1          5          4.829737  0.7488338  2.837241
##    1          9          4.831213  0.7480432  2.842246
##   10          0          3.529736  0.8513274  2.272161
##   10          5          3.465366  0.8577794  2.207494
##   10          9          3.466467  0.8573427  2.206431
##   20          0          3.425982  0.8594506  2.212515
##   20          5          3.355960  0.8658640  2.143559
##   20          9          3.360982  0.8651655  2.144974
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 20 and neighbors = 5.

Here we can see that caret automatically trained over multiple hyper parameters. We can easily plot those to visualize.

plot(model)

Preprocessing with Caret

One feature that we use from Caret is preprocessing. Often in real life data science we want to run some pre processing before modeling. We will center and scale our data by passing the following to the train method: preProcess = c("center", "scale").

set.seed(1)

model2 <- train(
  medv ~ .,
  data = Boston,
  method = 'cubist',
  preProcess = c("center", "scale")
)
model2

## Cubist 
## 
## 506 samples
##  13 predictor
## 
## Pre-processing: centered (13), scaled (13) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 506, 506, 506, 506, 506, 506, ... 
## Resampling results across tuning parameters:
## 
##   committees  neighbors  RMSE      Rsquared   MAE     
##    1          0          4.904962  0.7390994  2.929891
##    1          5          4.831118  0.7495491  2.833273
##    1          9          4.831585  0.7488174  2.837360
##   10          0          3.543803  0.8504440  2.291523
##   10          5          3.476877  0.8570426  2.217470
##   10          9          3.480213  0.8565179  2.215752
##   20          0          3.457679  0.8569993  2.226730
##   20          5          3.398680  0.8626777  2.152162
##   20          9          3.398507  0.8624353  2.150988
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 20 and neighbors = 9.

Splitting the Data Set

Often when we are modeling, we want to split our data into a train and test set. This way, we can check for overfitting. We can use the createDataPartition method to do this. In this example, we use the target medv to split into an 80/20 split, p = .80.

This function will return indexes that contains 80% of the data that we should use for training. We then use the indexes to get our training data from the data set.

set.seed(1)

inTraining <- createDataPartition(Boston$medv, p = .80, list = FALSE)
training <- Boston[inTraining,]
testing  <- Boston[-inTraining,]

We can then fit our model again using only the training data.

set.seed(1)
model3 <- train(
  medv ~ .,
  data = training,
  method = 'cubist',
  preProcess = c("center", "scale")
)
model3

## Cubist 
## 
## 407 samples
##  13 predictor
## 
## Pre-processing: centered (13), scaled (13) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 407, 407, 407, 407, 407, 407, ... 
## Resampling results across tuning parameters:
## 
##   committees  neighbors  RMSE      Rsquared   MAE     
##    1          0          5.105071  0.7204939  3.120618
##    1          5          5.040083  0.7305274  3.033722
##    1          9          5.041142  0.7292094  3.037932
##   10          0          3.861458  0.8192079  2.449168
##   10          5          3.813028  0.8256909  2.389976
##   10          9          3.819712  0.8245150  2.389547
##   20          0          3.698578  0.8331434  2.364653
##   20          5          3.644622  0.8388160  2.292814
##   20          9          3.649504  0.8380138  2.296908
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 20 and neighbors = 5.

Now, we want to check our data on the test set. We can use the subset method to get the features and test target. We then use the predict method passing in our model from above and the test features.

Finally, we calculate the RMSE and r2 to compare to the model above.

test.features = subset(testing, select=-c(medv))
test.target = subset(testing, select=medv)[,1]

predictions = predict(model3, newdata = test.features)

# RMSE
sqrt(mean((test.target - predictions)^2))

## [1] 2.611903

# R2
cor(test.target, predictions) ^ 2

## [1] 0.9223673

Cross Validation

In practice, we don’t normal build our data in on training set. It is common to use a data partitioning strategy like k-fold cross-validation that resamples and splits our data many times. We then train the model on these samples and pick the best model. Caret makes this easy with the trainControl method.

We will use 10-fold cross-validation in this tutorial. To do this we need to pass three parameters method = "cv", number = 10 (for 10-fold). We store this result in a variable.

set.seed(1)
ctrl <- trainControl(
  method = "cv",
  number = 10,
)

Now, we can retrain our model and pass the ctrl response to the trControl parameter. Notice the our call has added trControl = set.seed.

# set.seed(1)
model4 <- train(
  medv ~ .,
  data = training,
  method = 'cubist',
  preProcess = c("center", "scale"),
  trControl = ctrl
)
model4

## Cubist 
## 
## 407 samples
##  13 predictor
## 
## Pre-processing: centered (13), scaled (13) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 367, 366, 367, 366, 365, 367, ... 
## Resampling results across tuning parameters:
## 
##   committees  neighbors  RMSE      Rsquared   MAE     
##    1          0          3.905715  0.8186095  2.626573
##    1          5          3.566908  0.8497957  2.326520
##    1          9          3.662474  0.8417196  2.402689
##   10          0          3.368629  0.8620058  2.342268
##   10          5          3.082114  0.8832821  2.087365
##   10          9          3.146574  0.8783804  2.126777
##   20          0          3.388005  0.8614741  2.345478
##   20          5          3.068712  0.8848840  2.074521
##   20          9          3.142148  0.8793731  2.124737
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 20 and neighbors = 5.

plot(model4)

This results seemed to have improved our accuracy for our training data. Let’s check this on the test data to see the results.

test.features = subset(testing, select=-c(medv))
test.target = subset(testing, select=medv)[,1]

predictions = predict(model4, newdata = test.features)

# RMSE
sqrt(mean((test.target - predictions)^2))

## [1] 2.611903

# R2
cor(test.target, predictions) ^ 2

## [1] 0.9223673

Tuning Hyper Parameters

To tune a cubist model, we can give the model different values of committees and neighbors. Caret will retrain the model using different tuning values and select the best version.

set.seed(1)

tuneGrid <- expand.grid(
   committees = c(5, 10),
   neighbors = c(5, 9)
)

model5 <- train(
  medv ~ .,
  data = training,
  method = 'cubist',
  preProcess = c("center", "scale"),
  trControl = ctrl,
  tuneGrid = tuneGrid
)
model5

## Cubist 
## 
## 407 samples
##  13 predictor
## 
## Pre-processing: centered (13), scaled (13) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 367, 366, 367, 366, 365, 367, ... 
## Resampling results across tuning parameters:
## 
##   committees  neighbors  RMSE      Rsquared   MAE     
##    5          5          3.099071  0.8852719  2.125691
##    5          9          3.149099  0.8809142  2.163837
##   10          5          3.082114  0.8832821  2.087365
##   10          9          3.146574  0.8783804  2.126777
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 10 and neighbors = 5.

Finally, we can again plot the model to see how it performs over different tuning parameters.

plot(model5)