SMARTboost

R version of SMARTboost.jl via the JuliaConnectoR package (requires Julia to be installed).

SMARTboost (Smooth Additive Regression Trees) is described in the paper SMARTboost learning for tabular data. The Julia package is available at https://github.com/PaoloGiordani/SMARTboost.jl

Currently support only L2 loss, but extensions are planned.

Inputs features must be vectors or matrices (while the Julia version also accepts DataFrame).

Troubleshooting: if any output is NaN, switch to T="Float64", i.e. param = SMARTparam( ..., T="Float64") in the Example below. The default Float32 cuts computing time in half and is quite robust in Julia, but for reasons I don't understand it can give NaN when output is translated to R. (Suggestions welcome!).

Installation

1. Ensure Julia is installed. Julia can be downloaded from (https://julialang.org/downloads/)
2. Ensure that the Julia executable is in the system search PATH or that the JULIA_BINDIR environment variable is set to the bin directory of the Julia installation. For example: To find the path of the Julia executable, locate the file julia.exe or run 'Sys.BINDIR' from the Julia command line. Then, in R, start your script with

R> Sys.setenv(JULIA_BINDIR = "path_of_julia_executable")

3. Install JuliaConnectoR, available from the official R repository and from https://github.com/stefan-m-lenz/JuliaConnectoR, e.g.

R> install.packages("JuliaConnectoR")

4. Install the Julia packages Distributed and SMARTboost. Enter the Pkg REPL by pressing ] from the Julia REPL. Then

Pkg> add Distributed
Pkg> add "https://github.com/PaoloGiordani/SMARTboost.jl"

Use

R> SMARTboost = juliaImport("SMARTboost")

You may receive the warning message: "Some names could not be expressed in the native encoding..." This is due to some Greek characters, which R may not recognize. In future versions, I plan to eliminate the problem by staying with US-ASCII encoding. For now, this means that, for some R users, over-riding some defaults in SMARTparam may not be possible.

Set the desired number of workers for parallelization (optional)

R> juliaEval('
R>           number_workers  = 4  # desired number of workers, e.g. 4
R>           using Distributed
R>           nprocs()<number_workers ? addprocs( number_workers - nprocs()  ) : addprocs(0)
R>           @everywhere using SMARTboost
R>           ')

Selected Parameters (incomplete list, see SMARTparam Documentation for more).

• loss [:L2] currently only :L2 is supported, but extensions are planned
• depth [4] tree depth. If not default, then typically cross-validated in SMARTfit.
• lambda [0.2] learning rate
• loglikdivide [1.0] with panel data, SMARTloglikdivide() can be used to set this parameter
• overlap [0] number of overlaps. Typically overlap = h-1, where y(t) = Y(t+h)-Y(t)
• nfold [5] n in n-fold cv. Set nfold = 1 for a single validation set, the last sharevalidation share of the sample.
• verbose [:Off] verbosity "On" or "Off"
• T [Float32] Float32 is faster than Float64. If NaN output is produced (e.g. if true R2 is 1.0), switching to Flot64 should fix the problem.
• randomizecv [FALSE] default is purged-cv (see paper); a time series or panel structure is automatically detected (see SMARTdata)
• subsamplesharevs [1.0] row subs-sampling; if <1.0, only a randomly drawn (at each iteration) share of the sample is used in determining ι (which feature),μ,τ.
• subsampleshare_columns [1.0] column sub-sampling

Example1 with n = 1_000

Example1 with n = 1_000_000

Example1

# install.packages("JuliaConnectoR")    # If needed, install JuliaConnectoR. https://github.com/stefan-m-lenz/JuliaConnectoR

# User's options

path_julia_binaries = "I:\\Software\\Julia-1.4.2\\bin"   # string, location of Julia binaries (see ReadMe -> Installation)

# Some options for SMARTboost
cvdepth   = FALSE    # false to use the default depth (3), true to cv
nfold     = 1        # nfold cv. 1 faster, default 5 is slower, but more accurate.

# options to generate data. y = sum of four additive nonlinear functions + Gaussian noise(0,stde^2)
n      = 1000
p      = 4
stde   = 1.0

n_test= 100000

f_1 = function(x,b)  x*b
f_2 = function(x,b)  sin(x*b)
f_3 = function(x,b)  b*x^3
f_4 = function(x,b)  b/(1.0 + (exp(4.0*x))) - 0.5*b

b1  = 1.5
b2  = 2.0
b3  = 0.5
b4  = 2.0

# Optionally, set number_workers below
# End user's options  #

library(JuliaConnectoR)
Sys.setenv(JULIA_BINDIR = path_julia_binaries)

SMARTboost = juliaImport("SMARTboost")

# Set the desired number of workers for parallelization   
juliaEval('
          number_workers  = 4  # desired number of workers, e.g. 4
          using Distributed
          nprocs()<number_workers ? addprocs( number_workers - nprocs()  ) : addprocs(0)
          @everywhere using SMARTboost
          ')

# generate data
x      = matrix(rnorm(n*p),nrow = n,ncol = p)
x_test = matrix(rnorm(n_test*p),nrow = n,ncol = p)
f      = f_1(x[,1],b1)+f_2(x[,2],b2)+f_3(x[,3],b3)+f_4(x[,4],b4)
f_test = f_1(x_test[,1],b1)+f_2(x_test[,2],b2)+f_3(x_test[,3],b3)+f_4(x[,4],b4)
y      = f + rnorm(n)*stde

# set up SMARTparam and SMARTdata, then fit and predit
param  = SMARTboost$SMARTparam( nfold = nfold,verbose = "Off", T="Float32" )  # switch to T="Float64" is output is NaN
data   = SMARTboost$SMARTdata(y,x,param)

if (cvdepth==FALSE){
  output = SMARTboost$SMARTfit(data,param)                # default depth
} else {
  output = SMARTboost$SMARTfit(data,param,paramfield="depth",cv_grid=c(1,2,3,4,5),stopwhenlossup=TRUE)  # starts at depth = 1, stops as soon as loss increases
}

# Display some output and plot loss vs iteration

ntrees = output$ntrees
"number of trees "; ntrees
"best_cv_value   "; output$bestvalue

plot(1:ntrees,output$meanloss[1:ntrees], type = 'l',main = "loss vs iteration",col = "blue",)

# forecast
yf     = SMARTboost$SMARTpredict(x_test,output$SMARTtrees)  # predict
RMSE  = sqrt(sum((yf - f_test)^2)/n_test)   
"RMSE "; RMSE

# feature importance, partial dependence plots and marginal effects
tuple  = SMARTboost$SMARTrelevance(output$SMARTtrees,data)

list   = juliaGet(tuple)
fnames = list[1]               # names of features
fi     = list[2]               # feature importance vector
fnames_sorted = list[3]        # names, sorted from most to least important
fi_sorted     = list[4]        # importance, sorted from largest to smallest
sortedindx    = list[5]        # sorted indexes, from largest to smallest importance

# partial dependence plot. Notice that when changing feature i, all other features are fixed at their unconditional mean.
tuple = SMARTboost$SMARTpartialplot(data,output$SMARTtrees,c(1,2,3,4),npoints=1000) # the third input is the J-dimensional vector of features for which to compute partial dependence

list = juliaGet(tuple)
q    = list[1]    # values at which partial dependence is computed, (plot on x-axis) (npoints,J)
pdp  = list[2]    # partial dependence (plot on y-axis), (npoints, J)

# marginal effects
tuple = SMARTboost$SMARTmarginaleffect(data,output$SMARTtrees,c(1,2,3,4),npoints=1000)

# To compute marginal effect at one point x0 rather than over a grid, set npoints = 1 and other_xs = x0 (a p vector, p the number of features), e.g.
# tuple = SMARTboost$SMARTmarginaleffect(data,output$SMARTtrees,c(1,2,3,4),other_xs=x0,npoints=1)


# plot partial dependence
#![](figures/Example1.png)

Example2 (CV and priors for panel data, Global Equity data example)

# install.packages("JuliaConnectoR")    # If needed, install JuliaConnectoR. https://github.com/stefan-m-lenz/JuliaConnectoR

# User's options

path_julia_binaries = "I:\\Software\\Julia-1.4.2\\bin"   # string, location of Julia binaries (see ReadMe -> Installation)

# Some options for SMARTboost
cvdepth   = FALSE    # false to use the default depth (3), true to cv
nfold     = 5        # nfold cv. 1 faster, default 5 is slower, but more accurate.

# Optionally, set number_workers below
# end user's options

library(JuliaConnectoR)
Sys.setenv(JULIA_BINDIR = path_julia_binaries)

SMARTboost = juliaImport("SMARTboost")

# Set the desired number of workers for parallelization   
juliaEval('
          number_workers  = 4  # desired number of workers, e.g. 4
          using Distributed
          nprocs()<number_workers ? addprocs( number_workers - nprocs()  ) : addprocs(0)
          @everywhere using SMARTboost
          ')

df = read.csv('examples/data/GlobalEquityReturns.csv')

# prepare data; sorting dataframe by date is required by block-CV.
df = df[order(df$date, decreasing = FALSE),]

# compute loglikdivide (this is a panel, where positive average cross-correlation will result in lld > 1)
lld = SMARTboost$SMARTloglikdivide(data$excessret,data$date,overlap=0)
"loglikdivide "; lld

# We now include lld in param, replacing the default value of 1
param   = SMARTboost$SMARTparam(loglikdivide = lld,overlap=0)     

# SMARTdata() in R requires vectors or matrices (the Julia version also accepts DataFrames)
# Notice the input df$date. In a panel, this ensures that block-cv is done correctly.
data   = SMARTboost$SMARTdata(df$excessret,as.matrix(df[,4:8]),param,df$date,fnames=names(df)[4:8])  # fnames is optional; if omitted, features will be named features1,features2,...

# alternative
#x = df[, c('logCAPE', 'momentum', 'vol3m', 'vol12m')]; data   = SMARTboost$SMARTdata(df$excessret,as.matrix(x),param,df$date,fnames=c('logCAPE', 'momentum', 'vol3m', 'vol12m'))  

if (cvdepth==FALSE){
  output = SMARTboost$SMARTfit(data,param)                # default depth
} else {
  output = SMARTboost$SMARTfit(data,param,paramfield='depth',cv_grid=c(1,2,3,4),stopwhenlossup=TRUE)  # starts at depth = 1, stops as soon as loss increases
}

# See Example1 for forecasting, variable importance, partial dependence, marginal effects

How to do a train-validation-test split in SMARTboost. Notice that the default is to re-fit the model (with the cross-validated tuning parameters) on the entire data (train+validation), as is done in n-fold CV, even if nfold = 1. If you wish to skip this step (for speed or for comparison with other methods), set nofullsample = TRUE in SMARTfit. When nfold = 1, the default is to use the last 30% of the data as validation test ('approximately' 30% in some cases because of purged validation). To change this default, set e.g. sharevalidation = 0.2 for the last 20% of the sample, or sharevalidation = 1000 for the last 1000 observations. Setting sharevalidation to an integer switches the default to nfold = 1.

Some suggestions for speeding up SMARTboost.

Example of approximate computing time for 100 trees, depth = 4, using 8 workers on an AMD EPYC 7542, dgp linear. (dgp is linear. 100 trees are sufficient in most applications.)

n x p	Minutes for 100 trees
100k x 10	1.7'
1m x 10	17'
10m x 10	170'
100k x 100	9'
1m x 100	85'
10m x 100	850'

SMARTboost runs much faster (particularly with large n) with 4-8 cores than with one, after the initial one-off cost. If you are running on few cores, consider limiting depth <= 3.

With large n:

• Use a single validation sample instead of the default 5-fold cv (param$nfold=1). Additionally, in SMARTfit, set nofullsample = TRUE further reduces computing time by roughly 60% (at the cost of a modest efficiency loss.) nofullsample = TRUE is also required if you want to have a train-validation-test split, so that the model is only fit on the train set (the default will use a validation test to CV, and then re-train on the train+validation at the optimum parameter values).
• Computing time increases rapidly with param$depth in smooth trees. If you cv tree depth, start at a low value and stop as soon as there is no sizable improvement (set stopwhenlossup = TRUE in SMARTfit). With 8 workers, as a rule of thumb, computing times double if depth <- depth + 1.
• set stderulestop = 0.05 or 0.1 to stop iterations when the loss is no longer decreasing sizably (at a cost of a small loss in performance.)
• row and column subs-sampling are supported.