Conformal linear regression

LinearRegressionBostonDatav2.R

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+####
+#Conformal prediction for linear regression in classic data set Boston Data
+# Author : Adarsh Vijayaraghavan
+####
+#Start by clearing all variables in the evironment
+rm(list=ls())
+
+#Import conformalInference package. Install instructions at : https://github.com/ryantibs/conformal
+library(conformalInference)
+
+#linear Regression - data setup
+library(MASS)
+#Step 1 - import Boston data to a dataframe variable
+bostonData <- Boston
+summary(bostonData)
+dim(bostonData)
+
+#Partition data set into training and test data
+set.seed(4)
+bostonTrain<-bostonData[samp<-sample(1:nrow(bostonData),floor(0.78*nrow(bostonData))),]
+dim(bostonTrain)
+bostonTest<-bostonData[-samp,]
+dim(bostonTest)
+
+#Simple linear regression for training data set
+lm.fit= lm(medv~lstat, data = bostonTrain)
+#summarize regression data
+summary(lm.fit)
+
+#Step 5
+plot(bostonData$lstat, bostonData$medv)
+abline(lm.fit, lwd=3, col="red")
+
+#Predict confidence interval for test data set
+abcde <- data.frame(lstat = bostonTest$lstat)
+#lm.pred = predict(lm.fit, list(bostonTest$lstat), interval="confidence")
+lm.pred = predict(lm.fit, newdata= abcde, interval="prediction")
+
+#Start conformal preidction
+funs = lm.funs()
+out.conf = conformal.pred(data.matrix(bostonTrain["lstat"]), unlist(bostonTrain["medv"], use.names=FALSE), 
+                          data.matrix(bostonTest["lstat"]), alpha=0.05, 
+                          train.fun = funs$train, predict.fun = funs$predict, verb=TRUE)
+
+#Combine results from the two regressions into a matrix
+#tab = matrix(c(lm.pred[-samp,"lwr"], lm.pred[-samp,"upr"], out.conf$lo, out.conf$up, bostonTest[,'medv']), ncol=5)
+tab = matrix(c(lm.pred[,"lwr"], lm.pred[,"upr"], out.conf$lo, out.conf$up, bostonTest[,'medv']), ncol=5)
+colnames(tab) = c("Clsc_L","Clsc_H", "Con_L", "Con_H", "Obs")
+
+#Convert to dataframe for convenience and add Truth columns
+data.final <- data.frame(tab)
+data.final$Classic_truth = data.final$Clsc_L <= data.final$Obs &  data.final$Obs <= data.final$Clsc_H
+#data.final$Classic_truth = data.final$Clsc_L >= data.final$Obs & data.final$Clsc_H <= data.final$Obs
+data.final$Classic_truth <- as.factor(data.final$Classic_truth)
+data.final$Con_truth = data.final$Con_L <= data.final$Obs & data.final$Con_H >= data.final$Obs
+#data.final$Con_truth = data.final$Con_L >= data.final$Obs & data.final$Con_H <= data.final$Obs
+data.final$Con_truth <- as.factor(data.final$Con_truth)
+
+data.final$Classic_width = abs(data.final$Clsc_L - data.final$Clsc_H)
+data.final$Con_width = abs(data.final$Con_L - data.final$Con_H) 
+
+#Summarize results
+cat("Vanilla linear regression error prediction\n")
+summary(data.final$Classic_truth)
+
+cat("Conformal prediction using linear regression error prediction\n")
+summary(data.final$Con_truth)
+cat("Average width of linear regression prediction interval")
+mean(data.final$Classic_width)
+cat("Average width of CONFORMAL linear regression prediction interval")
+mean(data.final$Con_width)
+data.final
+
+

ReadMe.md

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+This is a small demo in R of Conformal Prediction given in Prof. Glenn Shafer's class in Spring 2018. Compares the prediction regions obtained from simple linear regression with conformal prediction using linear regression. Uses the R package "ConformalInference"