library(tidyverse)

Data is downloaded from here:

https://www.kaggle.com/c/digit-recognizer

kaggle_data <- read_csv("~/Downloads/train.csv")

pixels_gathered <- kaggle_data %>% mutate(instance = row_number()) %>% gather(pixel, value, -label, -instance) %>% extract(pixel, "pixel", "(\d+)", convert = TRUE)

roc_by_pixel <- pixels_gathered %>% filter(instance %% 20 == 0) %>% crossing(compare1 = 0:4, compare2 = 0:4) %>% filter(label == compare1 | label == compare2, compare1 != compare2) %>% group_by(compare1, compare2, pixel, value) %>% summarize(positive = sum(label == compare2), negative = n() - positive) %>% arrange(desc(value)) %>% mutate(tpr = cumsum(positive) / sum(positive), fpr = cumsum(negative) / sum(negative)) %>% filter(n() > 1)

roc_by_pixel %>% summarize(auc = sum(diff(fpr) * (tpr + lag(tpr))[-1]) / 2) %>% arrange(desc(auc)) %>% mutate(row = pixel %/% 28, column = pixel %% 28) %>% ggplot(aes(column, 28 - row, fill = auc)) + geom_tile() + scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = .5) + facet_grid(compare2 ~ compare1) + labs(title = "AUC for distinguishing pairs of MNIST digits by one pixel", subtitle = "Red means pixel is predictive of the row, blue predictive of the column", fill = "AUC") + theme_void()