How can I perform bootstrap to find the confidence interval for a k-nn model in R?

Question

I have a training df with 2 columns like

   a     b
1  1000  20
2  1008  13
...
n  ...   ...

Now, as I am required to find a 95% CI for the estimate of 'b' based on a specific 'a' value, with a 'k' value of my choice and compare the CI result to other specific value of 'k's. My question is how can I perform bootstrap for this with 1000 bootstrap reps as I am required to use a fitted knn model for the training data with kernel = 'gaussian' and k can only be in range 1-20 ? I have found that the best k for this model is k = 5, and had a go for bootstrap but it doesn't work

library(kknn)
library(boot)

boot.kn = function(formula, data, indices)
{
  # Create a bootstrapped version
  d = data[indices,]
  
  # Fit a model for bs
  fit.kn =  fitted(train.kknn(formula,data, kernel= "gaussian", ks = 5))
  
  # Do I even need this complicated block
  target = as.character(fit.kn$terms[[2]])
  rv = my.pred.stats(fit.kn, d[,target])
  return(rv)
}
bs = boot(data=df, statistic=boot.kn, R=1000, formula=b ~ a)
boot.ci(bs,conf=0.95,type="bca")

Please inform me for more info if I'm not clear enough. Thank you.

Answer 1

Here is a way to regress b on a with the k-nearest neighbors algorithm.

First, a data set. This is a subset of the iris data set, keeping the first two columns. One row is removed to later be the new data.

i <- which(iris$Sepal.Length == 5.3)
df1 <- iris[-i, 1:2]
newdata <- iris[i, 1:2]
names(df1) <- c("a", "b")
names(newdata) <- c("a", "b")

Now load the packages to be used and determine the optimal value for k with package kknn.

library(caret)
library(kknn)
library(boot)

fit <- kknn::train.kknn(
  formula = b ~ a,
  data = df1,
  kmax = 15,
  kernel = "gaussian",
  distance = 1
)
k <- fit$best.parameters$k
k
#[1] 9

And bootstrap predictions for the new point a <- 5.3.

boot.kn <- function(data, indices, formula, newdata, k){
  d <- data[indices, ]
  fit <- knnreg(formula, data = d)
  predict(fit, newdata = newdata)
}

set.seed(2021)
R <- 1e4
bs <- boot(df1, boot.kn, R = R, formula = b ~ a, newdata = newdata, k = k)
ci <- boot.ci(bs, level = 0.95, type = "bca")

ci
#BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
#Based on 10000 bootstrap replicates
#
#CALL : 
#boot.ci(boot.out = bs, type = "bca", level = 0.95)
#
#Intervals : 
#Level       BCa          
#95%   ( 3.177,  3.740 )  
#Calculations and Intervals on Original Scale

Plot the results.

old_par <- par(mfrow = c(2, 1),
               oma = c(5, 4, 0, 0) + 0.1,
               mar = c(1, 1, 1, 1) + 0.1)

hist(bs$t, main = "Histogram of bootstrap values")
abline(v = 3.7, col = "red")
abline(v = mean(bs$t), col = "blue")
abline(v = ci$bca[4:5], col = "blue", lty = "dashed")

plot(b ~ a, df1)
points(5.3, 3.7, col = "red", pch = 19)
points(5.3, mean(bs$t), col = "blue", pch = 19)
arrows(x0 = 5.3, y0 = ci$bca[4],
       x1 = 5.3, y1 = ci$bca[5],
       col = "blue", angle = 90, code = 3)

par(old_par)