Explainable ‘AI’ using Gradient Boosted randomized networks Pt2 (the Lasso)

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This post is about LSBoost, an Explainable ‘AI’ algorithm which uses Gradient Boosted randomized networks for pattern recognition. As we’ve discussed it last week LSBoost is a cousin of GFAGBM’s LS_Boost. In LSBoost, more specifically, the so called weak learners from LS_Boost are based on randomized neural networks’ components and variants of Least Squares regression models.

I’ve already presented some promising examples of use of LSBoost based on Ridge Regression weak learners. In mlsauce’s version 0.7.1, the Lasso can also be used as an alternative ingredient to the weak learners. Here is a comparison of the regression coefficients obtained by using mlsauce’s implementation of Ridge regression and the Lasso:

image-title-here

R example: LSBoostRegressor with Ridge regression and the Lasso

The following example is about training set error vs testing set error, as a function of the regularization parameter, both for Ridge regression and Lasso-based weak learners.

Packages and data


# 0 - Packages and data -------------------------------------------------------

library(devtools)
devtools::install_github("thierrymoudiki/mlsauce/R-package")
library(mlsauce)
library(datasets)

print(summary(datasets::mtcars))

X <- as.matrix(datasets::mtcars[, -1])
y <- as.integer(datasets::mtcars[, 1])

n <- dim(X)[1]
p <- dim(X)[2]
set.seed(21341)
train_index <- sample(x = 1:n, size = floor(0.8*n), replace = TRUE)
test_index <- -train_index
X_train <- as.matrix(X[train_index, ])
y_train <- as.double(y[train_index])
X_test <- as.matrix(X[test_index, ])
y_test <- as.double(y[test_index])

LSBoost using Ridge regression


# 1 - Ridge -------------------------------------------------------------------

obj <- mlsauce::LSBoostRegressor() # default h is Ridge
print(obj$get_params())

n_lambdas <- 100
lambdas <- 10**seq(from=-6, to=6, 
                   length.out = n_lambdas)
rmse_matrix <- matrix(NA, nrow = 2, ncol = n_lambdas)
rownames(rmse_matrix) <- c("training rmse", "testing rmse")

for (j in 1:n_lambdas)
{
  obj$set_params(reg_lambda = lambdas[j])
  obj$fit(X_train, y_train)
  rmse_matrix[, j] <- c(sqrt(mean((obj$predict(X_train) - y_train)**2)), 
                        sqrt(mean((obj$predict(X_test) - y_test)**2)))
}

image-title-here

LSBoost using the Lasso


# 2 - Lasso -------------------------------------------------------------------

obj <- mlsauce::LSBoostRegressor(solver = "lasso")
print(obj$get_params())

n_lambdas <- 100
lambdas <- 10**seq(from=-6, to=6, 
                   length.out = n_lambdas)
rmse_matrix2 <- matrix(NA, nrow = 2, ncol = n_lambdas)
rownames(rmse_matrix2) <- c("training rmse", "testing rmse")

for (j in 1:n_lambdas)
{
  obj$set_params(reg_lambda = lambdas[j])
  obj$fit(X_train, y_train)
  rmse_matrix2[, j] <- c(sqrt(mean((obj$predict(X_train) - y_train)**2)), 
                         sqrt(mean((obj$predict(X_test) - y_test)**2)))
}

image-title-here

R session info


> print(session_info())
 Session info ─────────────────────────────────────────────────────────────
 setting  value                       
 version  R version 4.0.2 (2020-06-22)
 os       Ubuntu 16.04.6 LTS          
 system   x86_64, linux-gnu           
 ui       RStudio                     
 language (EN)                        
 collate  C.UTF-8                     
 ctype    C.UTF-8                     
 tz       Etc/UTC                     
 date     2020-07-31                  

 Packages ─────────────────────────────────────────────────────────────────
 package     * version date       lib source                                 
 assertthat    0.2.1   2019-03-21 [1] RSPM (R 4.0.2)                         
 backports     1.1.8   2020-06-17 [1] RSPM (R 4.0.2)                         
 callr         3.4.3   2020-03-28 [1] RSPM (R 4.0.2)                         
 cli           2.0.2   2020-02-28 [1] RSPM (R 4.0.2)                         
 crayon        1.3.4   2017-09-16 [1] RSPM (R 4.0.2)                         
 curl          4.3     2019-12-02 [1] RSPM (R 4.0.2)                         
 desc          1.2.0   2018-05-01 [1] RSPM (R 4.0.2)                         
 devtools    * 2.3.1   2020-07-21 [1] RSPM (R 4.0.2)                         
 digest        0.6.25  2020-02-23 [1] RSPM (R 4.0.2)                         
 ellipsis      0.3.1   2020-05-15 [1] RSPM (R 4.0.2)                         
 fansi         0.4.1   2020-01-08 [1] RSPM (R 4.0.2)                         
 fs            1.4.2   2020-06-30 [1] RSPM (R 4.0.2)                         
 glue          1.4.1   2020-05-13 [1] RSPM (R 4.0.2)                         
 jsonlite      1.7.0   2020-06-25 [1] RSPM (R 4.0.2)                         
 lattice       0.20-41 2020-04-02 [2] CRAN (R 4.0.2)                         
 magrittr      1.5     2014-11-22 [1] RSPM (R 4.0.2)                         
 Matrix        1.2-18  2019-11-27 [2] CRAN (R 4.0.2)                         
 memoise       1.1.0   2017-04-21 [1] RSPM (R 4.0.2)                         
 mlsauce     * 0.7.1   2020-07-31 [1] Github (thierrymoudiki/mlsauce@68e391a)
 pkgbuild      1.1.0   2020-07-13 [1] RSPM (R 4.0.2)                         
 pkgload       1.1.0   2020-05-29 [1] RSPM (R 4.0.2)                         
 prettyunits   1.1.1   2020-01-24 [1] RSPM (R 4.0.2)                         
 processx      3.4.3   2020-07-05 [1] RSPM (R 4.0.2)                         
 ps            1.3.3   2020-05-08 [1] RSPM (R 4.0.2)                         
 R6            2.4.1   2019-11-12 [1] RSPM (R 4.0.2)                         
 rappdirs      0.3.1   2016-03-28 [1] RSPM (R 4.0.2)                         
 Rcpp          1.0.5   2020-07-06 [1] RSPM (R 4.0.2)                         
 remotes       2.2.0   2020-07-21 [1] RSPM (R 4.0.2)                         
 reticulate    1.16    2020-05-27 [1] RSPM (R 4.0.2)                         
 rlang         0.4.7   2020-07-09 [1] RSPM (R 4.0.2)                         
 rprojroot     1.3-2   2018-01-03 [1] RSPM (R 4.0.2)                         
 rstudioapi    0.11    2020-02-07 [1] RSPM (R 4.0.2)                         
 sessioninfo   1.1.1   2018-11-05 [1] RSPM (R 4.0.2)                         
 testthat      2.3.2   2020-03-02 [1] RSPM (R 4.0.2)                         
 usethis     * 1.6.1   2020-04-29 [1] RSPM (R 4.0.2)                         
 withr         2.2.0   2020-04-20 [1] RSPM (R 4.0.2)                         

[1] /home/rstudio-user/R/x86_64-pc-linux-gnu-library/4.0
[2] /opt/R/4.0.2/lib/R/library

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