crisp-package {crisp}

crisp: A package for fitting a model that partitions the covariate space into blocks in a data-adaptive way.

Description

This package is called crisp for "Convex Regression with Interpretable Sharp Partitions", which considers the problem of predicting an outcome variable on the basis of two covariates, using an interpretable yet non-additive model. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. More details are provided in Petersen, A., Simon, N., and Witten, D. (2016). Convex Regression with Interpretable Sharp Partitions. Journal of Machine Learning Research, 17(94): 1-31 <http://jmlr.org/papers/volume17/15-344/15-344.pdf>.

Details

The main functions are: (1)crisp and (2)crispCV. The first function crisp fits CRISP for a sequence of tuning parameters and provides the fits for this entire sequence of tuning parameters. The second function crispCV considers a sequence of tuning parameters and provides the fits, but also returns the optimal tuning parameter, as chosen using K-fold cross-validation.

Examples

## Not run: 
#general example illustrating all functions
#see specific function help pages for details of using each function

#generate data (using a very small 'n' for illustration purposes)
set.seed(1)
data <- sim.data(n = 15, scenario = 2)
#plot the mean model for the scenario from which we generated data
plot(data)

#fit model for a range of tuning parameters, i.e., lambda values
#lambda sequence is chosen automatically if not specified
crisp.out <- crisp(X = data$X, y = data$y)
#or fit model and select lambda using 2-fold cross-validation
#note: use larger 'n.fold' (e.g., 10) in practice
crispCV.out <- crispCV(X = data$X, y = data$y, n.fold = 2)

#summarize all of the fits
summary(crisp.out)
#or just summarize a single fit
#we examine the fit with an index of 25. that is, lambda of
crisp.out$lambda.seq[25]
summary(crisp.out, lambda.index = 25)
#lastly, we can summarize the fit chosen using cross-validation
summary(crispCV.out)
#and also plot the cross-validation error
plot(summary(crispCV.out))
#the lambda chosen by cross-validation is also available using
crispCV.out$lambda.cv

#plot the estimated relationships between two predictors and outcome
#do this for a specific fit
plot(crisp.out, lambda.index = 25)
#or for the fit chosen using cross-validation
plot(crispCV.out)

#we can make predictions for a covariate matrix with new observations
#new.X with 20 observations
new.data <- sim.data(n = 20, scenario = 2)
new.X <- new.data$X
#these will give the same predictions:
yhat1 <- predict(crisp.out, new.X = new.X, lambda.index = crispCV.out$index.cv)
yhat2 <- predict(crispCV.out, new.X = new.X)

## End(Not run)