--- title: "Precept 5 Solutions" output: html_document: df_print: paged editor_options: chunk_output_type: console --- ### Small training sets and overfitting ```{r echo = F} titanic <- read.csv("titanic.csv") library(ggplot2) library(dplyr) ``` We'll create one training set of size 100, and a validation set of size 500. We'll only use subsets of the training set throught. ```{r} set.seed(0) idx <- sample(1:nrow(titanic)) train.idx <- idx[1:100] valid.idx <- idx[101:600] ``` We will now get our performance data ```{r warning = F} GetTrainValidPerformance <- function(titanic.train, titanic.valid){ fit <- glm(Survived ~ Age + Sex + Pclass, family=binomial, data = titanic.train) pred.train <- predict(fit, newdata = titanic.train, type = "response") > 0.5 pred.valid <- predict(fit, newdata = titanic.valid, type = "response") > 0.5 return(c(mean(pred.train == titanic.train$Survived), mean(pred.valid == titanic.valid$Survived))) } GetTrainValidPerformanceTrSize <- function(train.size, titanic, train.idx, valid.idx){ titanic.valid <- titanic[valid.idx, ] titanic.train <- titanic[train.idx[1:train.size], ] return(GetTrainValidPerformance(titanic.train, titanic.valid)) } sizes <- c(3, 6, 9, 15, 20, 25, 30, 40, 50, 70, 100) perf <- sapply(sizes, FUN = GetTrainValidPerformanceTrSize, titanic, train.idx, valid.idx) ``` First, let's simply add two layers to display the two curves (that's the non-challenge version) ```{r} perf.data <- data.frame(size = sizes, perf.train = perf[1, ], perf.valid = perf[2, ]) ggplot(data = perf.data, mapping = aes(x = sizes)) + geom_smooth(mapping = aes(y = perf.train), method = "loess", color = "red") + geom_smooth(mapping = aes(y = perf.valid), method = "loess", color = "blue") ``` Now, let's do things the tidy data way: ```{r} library(reshape2) perf.data <- data.frame(size = sizes, perf.train = perf[1, ], perf.valid = perf[2, ]) perf.data <- melt(perf.data, 1) perf.data <- perf.data %>% select(size = size, set = variable, performance = value) perf.data$set <- as.character(perf.data$set) perf.data$set[perf.data$set == "perf.train"] <- "train" perf.data$set[perf.data$set == "perf.valid"] <- "valid" ggplot(data = perf.data, mapping = aes(x = size, y = performance, color = set)) + geom_smooth(method = "loess") ```