Author: Lampros Mouselimis
Date: 2022-09-10

# Regularized Greedy Forest in R

#### Lampros Mouselimis

#### 2022-09-10

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.

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 Vignette (11 - 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()
| predict_proba() |  | predict_proba()
cleanup() | cleanup() | cleanup() | cleanup()
get_params() | get_params() | get_params() | get_params()
score() | score() | score() | score()
feature_importances() | feature_importances() |  |
dump_model() | 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(RGF)

    # 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 (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 data set and presence of multicollinearity ]

For the high-dimensional data (can be downloaded from the following GitHub repository) we’ll use the FastRGF_Regressor rather than the RGF_Regressor (comparison without doing hyper-parameter tuning),

    # download the data from the following 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)       # 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