# Regularized Greedy Forest in R

This article is originally published at

This blog post is about my newly released RGF package (the blog post consists mainly of the package Vignette). The *RGF* package is a wrapper of the *Regularized Greedy Forest* *python* package, which also includes a *Multi-core implementation (FastRGF)*. Portability from Python to R was made possible using the reticulate package and the installation requires basic knowledge of Python. Except for the Linux Operating System, the installation on Macintosh and Windows might be somehow cumbersome (*on windows the package currently can be used only from within the command prompt*). Detailed installation instructions for all three Operating Systems can be found in the *README.md* file and in the *rgf_python* Github repository.

**UPDATE 26-07-2018**: A Singularity image file is available in case that someone intends to run *RGF* on Ubuntu Linux (locally or in a cloud instance) with all package requirements pre-installed. This allows the user to utilize the *RGF* package without having to spend time on the installation process.

The *Regularized Greedy Forest* algorithm is explained in detail in the paper *Rie Johnson and Tong Zhang, Learning Nonlinear Functions Using Regularized Greedy Forest*. A small synopsis would be *“… the resulting method, which we refer to as regularized greedy forest (RGF), integrates two ideas: one is to include tree-structured regularization into the learning formulation; and the other is to employ the fully-corrective regularized greedy algorithm ….”*.

At the time of writing this blog post (14 - 02 - 2018), there isn’t a corresponding implementation of the algorithm in the R language, so I decided to port the Python package in R taking advantage of the reticulate package. In the next lines, I will explain the functionality of the package and I compare RGF with other similar implementations, such as *ranger* (random forest algorithm) and *xgboost* (gradient boosting algorithm), in terms of time efficiency and error rate improvement.

**The RGF package**

The *RGF* package includes the following R6-classes / functions,

**classes**

RGF_Regressor | RGF_Classifier | FastRGF_Regressor | FastRGF_Classifier |
---|---|---|---|

fit() | fit(() | fit() | fit() |

predict() | predict() | predict() | predict() |

cleanup() | predict_proba() | cleanup() | predict_proba() |

get_params() | cleanup() | get_params() | cleanup() |

score() | get_params() | score() | get_params() |

feature_importances() | score() | score() | |

dump_model() | feature_importances() | ||

dump_model() |

**functions**

**UPDATE 10-05-2018** : Beginning from version **1.0.3** the **dgCMatrix_2scipy_sparse** function was renamed to **TO_scipy_sparse** and now accepts either a *dgCMatrix* or a *dgRMatrix* as input. The appropriate format for the RGF package in case of sparse matrices is the **dgCMatrix** format (*scipy.sparse.csc_matrix*)

TO_scipy_sparse()

RGF_cleanup_temp_files()

mat_2scipy_sparse()

The package documentation includes details and examples for all R6-classes and functions. In the following code chunks, I’ll explain how a user can work with sparse matrices as all RGF algorithms (besides a dense matrix) **require a python sparse matrix as input**.

**Sparse matrices as input**

The RGF package includes two functions (**mat_2scipy_sparse** and **TO_scipy_sparse**) which allow the user to convert from a *matrix* / *sparse matrix* (*dgCMatrix*, *dgRMatrix*) to a *scipy sparse matrix* (*scipy.sparse.csc_matrix*, *scipy.sparse.csr_matrix*),

```
library(nmslibR)
# conversion from a matrix object to a scipy sparse matrix
#----------------------------------------------------------
set.seed(1)
x = matrix(runif(1000), nrow = 100, ncol = 10)
x_sparse = mat_2scipy_sparse(x, format = "sparse_row_matrix")
print(dim(x))
[1] 100 10
print(x_sparse$shape)
(100, 10)
```

```
# conversion from a dgCMatrix object to a scipy sparse matrix
#-------------------------------------------------------------
data = c(1, 0, 2, 0, 0, 3, 4, 5, 6)
# 'dgCMatrix' sparse matrix
#--------------------------
dgcM = Matrix::Matrix(data = data, nrow = 3,
ncol = 3, byrow = TRUE,
sparse = TRUE)
print(dim(dgcM))
[1] 3 3
x_sparse = TO_scipy_sparse(dgcM)
print(x_sparse$shape)
(3, 3)
# 'dgRMatrix' sparse matrix
#--------------------------
dgrM = as(dgcM, "RsparseMatrix")
class(dgrM)
# [1] "dgRMatrix"
# attr(,"package")
# [1] "Matrix"
print(dim(dgrM))
[1] 3 3
res_dgr = TO_scipy_sparse(dgrM)
print(res_dgr$shape)
(3, 3)
```

**Comparison of RGF with ranger and xgboost**

First the data, libraries and cross-validation function will be inputted (the *MLmetrics* library is also required),

```
data(Boston, package = 'KernelKnn')
library(RGF)
library(ranger)
library(xgboost)
# shuffling function for cross-validation folds
#-----------------------------------------------
func_shuffle = function(vec, times = 10) {
for (i in 1:times) {
out = sample(vec, length(vec))
}
out
}
# cross-validation folds [ regression]
#-------------------------------------
regr_folds = function(folds, RESP, stratified = FALSE) {
if (is.factor(RESP)) {
stop(simpleError("this function is meant for regression for classification use the 'class_folds' function"))
}
samp_vec = rep(1/folds, folds)
sort_names = paste0('fold_', 1:folds)
if (stratified == TRUE) {
stratif = cut(RESP, breaks = folds)
clas = lapply(unique(stratif), function(x) which(stratif == x))
len = lapply(clas, function(x) length(x))
prop = lapply(len, function(y) sapply(1:length(samp_vec), function(x) round(y * samp_vec[x])))
repl = unlist(lapply(prop, function(x) sapply(1:length(x), function(y) rep(paste0('fold_', y), x[y]))))
spl = suppressWarnings(split(1:length(RESP), repl))}
else {
prop = lapply(length(RESP), function(y) sapply(1:length(samp_vec), function(x) round(y * samp_vec[x])))
repl = func_shuffle(unlist(lapply(prop, function(x) sapply(1:length(x), function(y) rep(paste0('fold_', y), x[y])))))
spl = suppressWarnings(split(1:length(RESP), repl))
}
spl = spl[sort_names]
if (length(table(unlist(lapply(spl, function(x) length(x))))) > 1) {
warning('the folds are not equally split')
}
if (length(unlist(spl)) != length(RESP)) {
stop(simpleError("the length of the splits are not equal with the length of the response"))
}
spl
}
```

**single threaded ( small data set )**

In the next code chunk, I’ll perform 5-fold cross-validation using the Boston dataset and I’ll compare time execution and error rate for all three algorithms (comparison **without doing hyper-parameter tuning**),

```
NUM_FOLDS = 5
set.seed(1)
FOLDS = regr_folds(folds = NUM_FOLDS, Boston[, 'medv'], stratified = T)
boston_rgf_te = boston_ranger_te = boston_xgb_te = boston_rgf_time = boston_ranger_time = boston_xgb_time = rep(NA, NUM_FOLDS)
for (i in 1:length(FOLDS)) {
cat("fold : ", i, "\n")
samp = unlist(FOLDS[-i])
samp_ = unlist(FOLDS[i])
# RGF
#----
rgf_start = Sys.time()
init_regr = RGF_Regressor$new(l2 = 0.1)
init_regr$fit(x = as.matrix(Boston[samp, -ncol(Boston)]), y = Boston[samp, ncol(Boston)])
pr_te = init_regr$predict(as.matrix(Boston[samp_, -ncol(Boston)]))
rgf_end = Sys.time()
boston_rgf_time[i] = rgf_end - rgf_start
boston_rgf_te[i] = MLmetrics::RMSE(Boston[samp_, 'medv'], pr_te)
# ranger
#-------
ranger_start = Sys.time()
fit = ranger(dependent.variable.name = "medv", data = Boston[samp, ], write.forest = TRUE,
probability = F, num.threads = 1, num.trees = 500, verbose = T,
classification = F, mtry = NULL, min.node.size = 5, keep.inbag = T)
pred_te = predict(fit, data = Boston[samp_, -ncol(Boston)], type = 'se')$predictions
ranger_end = Sys.time()
boston_ranger_time[i] = ranger_end - ranger_start
boston_ranger_te[i] = MLmetrics::RMSE(Boston[samp_, 'medv'], pred_te)
# xgboost
#--------
xgb_start = Sys.time()
dtrain <- xgb.DMatrix(data = as.matrix(Boston[samp, -ncol(Boston)]), label = Boston[samp, ncol(Boston)])
dtest <- xgb.DMatrix(data = as.matrix(Boston[samp_, -ncol(Boston)]), label = Boston[samp_, ncol(Boston)])
watchlist <- list(train = dtrain, test = dtest)
param = list("objective" = "reg:linear", "bst:eta" = 0.05, "max_depth" = 4,
"subsample" = 0.85, "colsample_bytree" = 0.85, "booster" = "gbtree",
"nthread" = 1)
fit = xgb.train(param, dtrain, nround = 500, print_every_n = 100, watchlist = watchlist, early_stopping_rounds = 20,
maximize = FALSE, verbose = 0)
p_te = xgboost:::predict.xgb.Booster(fit, as.matrix(Boston[samp_, -ncol(Boston)]), ntreelimit = fit$best_iteration)
xgb_end = Sys.time()
boston_xgb_time[i] = xgb_end - xgb_start
boston_xgb_te[i] = MLmetrics::RMSE(Boston[samp_, 'medv'], p_te)
}
```

```
fold : 1
fold : 2
fold : 3
fold : 4
fold : 5
```

```
cat("total time rgf 5 fold cross-validation : ", sum(boston_rgf_time), " mean rmse on test data : ", mean(boston_rgf_te), "\n")
cat("total time ranger 5 fold cross-validation : ", sum(boston_ranger_time), " mean rmse on test data : ", mean(boston_ranger_te), "\n")
cat("total time xgb 5 fold cross-validation : ", sum(boston_xgb_time), " mean rmse on test data : ", mean(boston_xgb_te), "\n")
```

```
total time rgf 5 fold cross-validation : 0.7730639 mean rmse on test data : 3.832135
total time ranger 5 fold cross-validation : 3.826846 mean rmse on test data : 4.17419
total time xgb 5 fold cross-validation : 0.4316094 mean rmse on test data : 3.949122
```

**5 threads ( high dimensional dataset and presence of multicollinearity )**

For the high-dimensional data (can be downloaded from my Github repository) I’ll use the *FastRGF_Regressor* rather than the RGF_Regressor (comparison **without doing hyper-parameter tuning**),

```
# download the data from my Github repository (tested on a Linux OS)
system("wget https://raw.githubusercontent.com/mlampros/DataSets/master/africa_soil_train_data.zip")
# load the data in the R session
train_dat = read.table(unz("africa_soil_train_data.zip", "train.csv"), nrows = 1157, header = T, quote = "\"", sep = ",")
# c("Ca", "P", "pH", "SOC", "Sand") : response variables
# exclude response-variables and factor variable
x = train_dat[, -c(1, which(colnames(train_dat) %in% c("Ca", "P", "pH", "SOC", "Sand", "Depth")))]
# take (randomly) the first of the responses for train
y = train_dat[, "Ca"]
# dataset for ranger
tmp_rg_dat = cbind(Ca = y, x)
# cross-validation folds
set.seed(2)
FOLDS = regr_folds(folds = NUM_FOLDS, y, stratified = T)
highdim_rgf_te = highdim_ranger_te = highdim_xgb_te = highdim_rgf_time = highdim_ranger_time = highdim_xgb_time = rep(NA, NUM_FOLDS)
for (i in 1:length(FOLDS)) {
cat("fold : ", i, "\n")
new_samp = unlist(FOLDS[-i])
new_samp_ = unlist(FOLDS[i])
# RGF
#----
rgf_start = Sys.time()
init_regr = FastRGF_Regressor$new(n_jobs = 5, l2 = 0.1) # I added 'l2' regularization
init_regr$fit(x = as.matrix(x[new_samp, ]), y = y[new_samp])
pr_te = init_regr$predict(as.matrix(x[new_samp_, ]))
rgf_end = Sys.time()
highdim_rgf_time[i] = rgf_end - rgf_start
highdim_rgf_te[i] = MLmetrics::RMSE(y[new_samp_], pr_te)
# ranger
#-------
ranger_start = Sys.time()
fit = ranger(dependent.variable.name = "Ca", data = tmp_rg_dat[new_samp, ],
write.forest = TRUE, probability = F, num.threads = 5, num.trees = 500,
verbose = T, classification = F, mtry = NULL, min.node.size = 5,
keep.inbag = T)
pred_te = predict(fit, data = x[new_samp_, ], type = 'se')$predictions
ranger_end = Sys.time()
highdim_ranger_time[i] = ranger_end - ranger_start
highdim_ranger_te[i] = MLmetrics::RMSE(y[new_samp_], pred_te)
# xgboost
#--------
xgb_start = Sys.time()
dtrain <- xgb.DMatrix(data = as.matrix(x[new_samp, ]), label = y[new_samp])
dtest <- xgb.DMatrix(data = as.matrix(x[new_samp_, ]), label = y[new_samp_])
watchlist <- list(train = dtrain, test = dtest)
param = list("objective" = "reg:linear", "bst:eta" = 0.05, "max_depth" = 6,
"subsample" = 0.85, "colsample_bytree" = 0.85, "booster" = "gbtree",
"nthread" = 5) # "lambda" = 0.1 does not improve RMSE
fit = xgb.train(param, dtrain, nround = 500, print_every_n = 100, watchlist = watchlist,
early_stopping_rounds = 20, maximize = FALSE, verbose = 0)
p_te = xgboost:::predict.xgb.Booster(fit, as.matrix(x[new_samp_, ]), ntreelimit = fit$best_iteration)
xgb_end = Sys.time()
highdim_xgb_time[i] = xgb_end - xgb_start
highdim_xgb_te[i] = MLmetrics::RMSE(y[new_samp_], p_te)
}
```

```
fold : 1
fold : 2
fold : 3
fold : 4
fold : 5
```

```
cat("total time rgf 5 fold cross-validation : ", sum(highdim_rgf_time), " mean rmse on test data : ", mean(highdim_rgf_te), "\n")
cat("total time ranger 5 fold cross-validation : ", sum(highdim_ranger_time), " mean rmse on test data : ", mean(highdim_ranger_te), "\n")
cat("total time xgb 5 fold cross-validation : ", sum(highdim_xgb_time), " mean rmse on test data : ", mean(highdim_xgb_te), "\n")
```

```
total time rgf 5 fold cross-validation : 92.31971 mean rmse on test data : 0.5155166
total time ranger 5 fold cross-validation : 27.32866 mean rmse on test data : 0.5394164
total time xgb 5 fold cross-validation : 30.48834 mean rmse on test data : 0.5453544
```

The *README.md* file of the *RGF* package includes the SystemRequirements and installation instructions.

An updated version of the RGF package can be found in my Github repository and to report bugs/issues please use the following link, https://github.com/mlampros/RGF/issues.

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