code for a blog post on Wilson scoring vs. Laplace smoothing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
par(pty='s') | |
par(mfrow=c(1, 2)) | |
ci_lower_bound <- function(pos, n, confidence) { | |
if (n == 0) return(0) | |
z = qnorm(1 - (1 - confidence) / 2) | |
p = pos / n | |
(p + z^2 / (2*n) - z * sqrt((p * (1-p) + z^2 / (4*n)) / n )) / | |
(1 + z^2 / n) | |
} | |
bayes_estimate <- function(pos, n, alpha, beta) { | |
(pos + alpha) / (n + beta) | |
} | |
confidence <- 0.95 | |
alpha <- 1 | |
beta <- 2 | |
colors <- 200 | |
make_plot <- function(range) { # function wrapping start | |
ci = expand.grid(range, range) | |
names(ci) <- c("pos", "neg") | |
ci$score <- apply(ci, 1, function(v) { | |
return(ci_lower_bound(v[1], sum(v), confidence)) | |
}) | |
ci_matrix <- matrix(ci$score, ncol=length(range)) | |
image(range, range, t(ci_matrix), | |
breaks=0:colors/colors, | |
col=colorRampPalette(c("blue", "white", "red"))(colors), | |
xlab="downvotes", | |
ylab="upvotes", | |
main=expression("Wilson 95% interval lower bound")) | |
bayes = expand.grid(range, range) | |
names(bayes) <- c("pos", "neg") | |
bayes$score <- apply(bayes, 1, function(v) { | |
return(bayes_estimate(v[1], sum(v), alpha, beta)) | |
}) | |
bayes_matrix <- matrix(bayes$score, ncol=length(range)) | |
image(range, range, t(bayes_matrix), | |
breaks=0:colors/colors, | |
col=colorRampPalette(c("blue", "white", "red"))(colors), | |
xlab="downvotes", | |
ylab="upvotes", | |
main=expression("Laplace Smoothing," ~ alpha==1 * ", " ~ beta==2)) | |
} # end make_plot function wrapping | |
# plots to by 800x460 | |
make_plot(0:200) # plot1 | |
make_plot(0:10) # plot2 | |
make_plot_2 <- function(down, uprange) { # function wrapping start | |
plot(sapply(uprange, function(x) ci_lower_bound(x, x+down, confidence)) ~ uprange, ylim=c(0,1), ylab="Wilson 95% interval lower bound", xlab=paste("upvotes (against", down, "downvotes)")) | |
plot(sapply(uprange, function(x) bayes_estimate(x, x+down, alpha, beta)) ~ uprange, ylim=c(0,1), ylab=expression("Laplace Smoothing," ~ alpha==1 * ", " ~ beta==2), xlab=paste("upvotes (against", down, "downvotes)")) | |
} # end make_plot_2 function wrapping | |
make_plot_2(10, 0:100) # plot3 | |
# numbers for post | |
209 - 50 | |
118 - 25 | |
209 / (209+50) | |
118 / (118+25) | |
ci_lower_bound(209, 209+50, 0.95) | |
ci_lower_bound(118, 118+25, 0.95) | |
bayes_estimate(209, 209+50, 1, 2) | |
bayes_estimate(118, 118+25, 1, 2) | |
1 - 0 | |
534 - 46 | |
1 / 1 | |
534 / 580 | |
ci_lower_bound(1, 1, 0.95) | |
ci_lower_bound(534, 580, 0.95) | |
bayes_estimate(1, 1, 1, 2) | |
bayes_estimate(534, 580, 1, 2) | |
range <- 0:10 | |
data <- expand.grid(range, range, range, range) | |
names(data) <- c("first_up", "first_down", "second_up", "second_down") | |
compare_ci <- function(v) { | |
first <- ci_lower_bound(v[1], v[1]+v[2], confidence) | |
second <- ci_lower_bound(v[3], v[3]+v[4], confidence) | |
if (first > second) return('first') | |
if (first < second) return('second') | |
return('tie') | |
} | |
compare_bayes <- function(v) { | |
first <- bayes_estimate(v[1], v[1]+v[2], alpha, beta) | |
second <- bayes_estimate(v[3], v[3]+v[4], alpha, beta) | |
if (first > second) return('first') | |
if (first < second) return('second') | |
return('tie') | |
} | |
data$ci <- apply(data[, 1:4], 1, compare_ci) | |
data$bayes <- apply(data[, 1:4], 1, compare_bayes) | |
disagreement <- data[data$ci != data$bayes, ] | |
# You can find problems like this either way... | |
7 - 6 | |
10 - 10 | |
7 / (7+6) | |
10 / 20 | |
ci_lower_bound(7, (7+6), 0.95) | |
ci_lower_bound(10, 20, 0.95) | |
bayes_estimate(7, (7+6), 1, 2) | |
bayes_estimate(10, 20, 1, 2) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment