R script for "Practical Prelude to Machine Learning for Sport"

kdpeterson_SPSR.r

# Clear workspace
rm(list = ls())

# Load package
install.packages("mlf")
library(mlf)



# Simulated data: Figure 1A
cor_simulate <- function(y, r) {
  x<-rnorm(length(y))
  y.res<-residuals(lm(x~y))
  r * sd(y.res) * y + y.res * sd(y) * sqrt(1-r^2)}

set.seed(133) # Reproducibility
y2<-rnorm(45, sd=10)
r<-0.40 # Desired correlation
data<-data.frame(x=as.vector(sapply(r, function(r) cor_simulate(y2, r))),y=rep(y2,length(r)))

plot(data$x,data$y,pch = 16,xaxt="n",yaxt="n",ann=F)
abline(lm(data$y~data$x),col="red")



# Simulated data: Figure 1B
set.seed(6) # Reproducibility
x<-c(-20:20)
y<-(x**2+rnorm(41,0,60))

plot(y~x,pch=16,xaxt="n",yaxt="n",ann=F)
abline(lm(y~x),col="red")



# Correlational derivatives Figure 1A
round(stats::cor(data$x,data$y),2) # (Double-check)
round(mlf::distcorr(data$x,data$y),2) # (should be simialr to Pearson r)
round(mlf::mic(data$x,data$y),2)



# Correlational derivatives Figure 1B
round(stats::cor(x,y),2) 
round(mlf::distcorr(x,y),2) 
round(mlf::mic(x,y),2) 
round(mlf::boot(x,y,mlf::mic),2) # Confidence intervals



# Simulated binomial distribution
dist1 <- c(1,1,1,1,1,1,1,1,1,0) # 90/10
dist2 <- c(1,1,1,1,1,1,0,0,0,0) # 60/40

round(mlf::entropy(dist1,2),2)
round(mlf::entropy(dist2,2),2)



##### Computational "sieve" to detect meaningful variables #####
data("mtcars") # Load sample data set
predictors<-data.frame(mic=NA,variable=NA) # Create empty data frame
for(i in 2:length(mtcars)){
  # Let's say we want to predict mpg
  # Fill each row with pairwise MIC and corresponding variable name
  predictors[i,]<-cbind(mlf::mic(mtcars$mpg,mtcars[i]),colnames(mtcars[i]))}

predictors$mic<-as.numeric(predictors$mic)
predictors<-predictors[order(-predictors$mic),] # Sort by MIC
head(predictors)