# Discrete Boosting Logistic Regression Training dblr_train fits a dblr (discrete boosting logistic regression) model. methods ```r dblr_train(train_x, train_y, category_cols = NULL, metric = "auc", subsample = 1, eta = 0.1, colsample = 1, cv_nfold = 5, cv_nrounds = 1000, cv_early_stops = 25, lambda = 1, alpha = 0, scale_pos_weight = 1, verbose = FALSE, seed = 123456L) ``` ## Arguments - `train_x`: A data.frame of training variables, which can include NA as well - `train_y`: A vector of 0 and 1 to represent labels of training samples - `category_cols`: A vector of column names to indicate which columns are categorical. Default: NULL means all columns are continuous - `metric`: Which metric to use, can be either auc or logloss. Default: auc - `subsample`: Subsample ratio from the trainnig samples in each iteration. Default: 1.0 - `eta`: Controls the rate of learning. eta should be between 0 and 1. Default: 0.1 - `colsample`: Subsample ratio from all available variables/columns. Default: 1.0 - `cv_nfold`: Number of folds used for cross-validation. Default: 5 - `cv_nrounds`: Number of iterations used for cross-validation. Default: 1000 - `cv_early_stops`: Cross-validation would be stopped if there is no improvement after cv_early_stops iterations. Default: 25 - `lambda`: Control L2 regularization term. Default: 1.0 - `alpha`: Control L1 regularization term. Default: 0.0 - `scale_pos_weight`: Useful when training metric is set to auc for imbalanced training data - `verbose`: Default: FALSE. If TRUE, the cross-validation process would be showed - `seed`: Random seed for the sampling. Default: 123456 ## Returns Returns an object of S3 class dblr, which contains two attributes, i.e., continuous_bins and categorical_bins. ## Details As one of the generalized linear models, traditional logistic regression on continuous variables implies that there is a monotonic relation between each predictor and the predicted probability. Bining or discretizing the continuous variables would be helpful when non-monotonic relation exists. In general, it is challenging to find the optimal binning for continuous variables. Too many bins may cause over-fitting and too few bins may not reveal the non-monotinc relation as much as possible. Thus, we propose to use a boosting decision trees to construct a discrete logistic regressions aiming at an automated binning process with good performance. Our algorithm is to construct a sequence of gradient boosting decision trees with at most 1 variable in each tree. Aggregating all decision trees with the same variable would result in the corresponding bins and the coefficients. And by aggregating all trees without variables we would get the intercept. The model is defined as: $$ Pr(y=1|\bm{x}_i)= \frac 1{1+{\exp (- \sum_{j=1}^{m}{g(\bm{x}_{i,j})}- b)}}, $$ where $g(\bm{x}_{i,j})$ denotes the coefficient of the bin which $\bm{x}_{i,j}$ falls into and $b$ denotes the intercept. Both coefficients and intercept are consolidated from boosting trees. More specifically, $$ g(\bm{x}_{i,j})=\sum_{k=1}^{K} f_k(\bm{x}_{i,j})\cdot I(\textrm{tree } k \textrm{ splits on variable } j), $$ $$ b=\sum_{k=1}^{K} f_k\cdot I(\textrm{tree } k \textrm{ does not split on any variable}), $$ where $K$ is the total number of trees and $f_k$ is the output value for tree $k$. In this package, we use xgboost package to training the underlying gradient boosting trees. ## Examples ```r # use iris data for example dat <- iris # create two categorical variables dat$Petal.Width <- as.factor((iris$Petal.Width<=0.2)*1+(iris$Petal.Width>1.0)*2) dat$Sepal.Length <- (iris$Sepal.Length<=3.0)*2+(iris$Sepal.Length>6.0)*1.25 # create the response variable dat$Species <- as.numeric(dat$Species=='versicolor') set.seed(123) # random sampling index <- sample(1:150,100,replace = FALSE) # train the dblr model using the training data dblr_fit <- dblr_train(train_x=dat[index,c(1:4)], train_y=dat[index,5],category_cols = c('Petal.Width','Sepal.Length'), metric = 'logloss',subsample = 0.5,eta = 0.05,colsample = 1.0, lambda = 1.0,cv_early_stops = 10,verbose=FALSE) # make predictions on testing data pred_dblr <- predict(dblr_fit,newdata = dat[-index,],type = 'response') dblr_auc <- Metrics::auc(actual = dat[-index,'Species'],predicted = pred_dblr) dblr_logloss <- Metrics::logLoss(actual = dat[-index,'Species'],predicted = pred_dblr) cat('test auc for dblr model:',dblr_auc,'\n') cat('test logloss for dblr model:',dblr_logloss,'\n') glm_fit <- glm(data=dat[index,],formula =Species~. ,family = binomial) pred_glm <- predict(glm_fit,newdata = dat[-index,],type='response') glm_auc <- Metrics::auc(actual = dat[-index,'Species'],predicted = pred_glm) glm_logloss <- Metrics::logLoss(actual = dat[-index,'Species'],predicted = pred_glm) cat('test auc for glm model:',glm_auc,'\n') cat('test logloss for glm model:',glm_logloss,'\n') ```

dblr_train function