---
title: "Multiclass Calibration"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Multiclass Calibration}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 6,
  fig.height = 4
)
```

```{r setup}
library(probcal)
```

## From two classes to several

The binary calibrators in `probcal` take a vector of scores or probabilities.
The multiclass calibrators take a matrix with one row per observation and one
column per class. The same functions serve both settings: a vector input is
treated as binary, and a matrix input is treated as multiclass. Labels are a
factor or a vector of integer class codes in `1:K`, where `K` is the number of
columns.

A multiclass model usually returns either a matrix of logits or a matrix of
softmax probabilities. Temperature scaling and vector scaling work on logits.
Dirichlet calibration works on probability matrices. The one-vs-rest wrapper
uses the input scale required by its binary base method: scores or probabilities
for Platt scaling, probabilities for beta calibration, isotonic regression, and
histogram binning, and logits for temperature scaling.

## Simulating an overconfident classifier

We simulate true class probabilities for three classes, draw labels from them,
and then sharpen the probabilities to mimic an overconfident model. The
calibration split fits the calibrator and the test split evaluates it.

```{r simulate}
set.seed(2024)
n <- 1200
k <- 3

true_prob <- matrix(stats::runif(n * k), ncol = k)
true_prob <- true_prob / rowSums(true_prob)
labels <- apply(true_prob, 1, function(row) sample.int(k, 1, prob = row))

# An overconfident model: push probabilities toward 0 and 1.
sharpen <- function(p, power = 2.5) {
  q <- p^power
  q / rowSums(q)
}
raw_prob <- sharpen(true_prob)
raw_logits <- log(pmax(raw_prob, 1e-12))

split <- sample(rep(c("calibration", "test"), each = n / 2))
cal <- split == "calibration"
test <- split == "test"
```

## Measuring multiclass calibration

The calibration metrics accept the probability matrix and a `type` argument. The
classwise form averages the binary calibration error over the one-vs-rest
columns. The confidence form looks only at the top-label probability and whether
the predicted class is correct.

```{r metrics-raw}
ece(raw_prob[test, ], labels[test], type = "classwise")
ece(raw_prob[test, ], labels[test], type = "confidence")
mmce(raw_prob[test, ], labels[test])
```

## Temperature scaling on logits

Temperature scaling estimates a single positive scalar. Dividing every logit by
the same value does not change the predicted class, so temperature scaling only
sharpens or softens the probabilities.

```{r temperature}
temp_fit <- cal_temperature(raw_logits[cal, ], labels[cal])
temp_fit

temp_pred <- predict(temp_fit, raw_logits[test, ])
ece(temp_pred, labels[test], type = "classwise")
```

## Dirichlet calibration on probabilities

Dirichlet calibration is the multiclass generalization of beta calibration. It
fits a linear map on the log-probabilities, regularized by an off-diagonal and
intercept penalty whose strength is chosen by cross-validation when `lambda` is
left at its default.

```{r dirichlet}
dir_fit <- cal_dirichlet(raw_prob[cal, ], labels[cal])
dir_pred <- predict(dir_fit, raw_prob[test, ])
ece(dir_pred, labels[test], type = "classwise")
```

## One-vs-rest calibration

The one-vs-rest wrapper lifts any binary calibrator to several classes. It fits
a binary calibrator that separates each class from the rest, applies them column
by column, and renormalizes each row to sum to one.

```{r ovr}
ovr_fit <- cal_ovr(raw_prob[cal, ], labels[cal], method = "isotonic")
ovr_pred <- predict(ovr_fit, raw_prob[test, ])
ece(ovr_pred, labels[test], type = "classwise")
```

## Comparing the calibrators

```{r compare}
data.frame(
  method = c("raw", "temperature", "dirichlet", "one-vs-rest"),
  classwise_ece = c(
    ece(raw_prob[test, ], labels[test], type = "classwise"),
    ece(temp_pred, labels[test], type = "classwise"),
    ece(dir_pred, labels[test], type = "classwise"),
    ece(ovr_pred, labels[test], type = "classwise")
  )
)
```

## Reliability diagram

For a probability matrix the reliability diagram draws one panel per class in
the classwise layout, or a single panel of top-label confidence in the
confidence layout.

```{r diagram, fig.alt="Faceted multiclass reliability diagram showing mean predicted probability on the x-axis and observed event frequency on the y-axis for each class, with a diagonal reference line for perfect calibration."}
reliability_diagram(dir_pred, labels[test], bins = 10, type = "classwise")
```

## Out-of-fold calibration

When calibration data are scarce, `cal_cv()` fits the calibrator with
out-of-fold predictions. It accepts a matrix input and the multiclass methods
`"temperature"`, `"vector"`, `"dirichlet"`, and `"ovr"`.

```{r cv}
cv_fit <- cal_cv(
  raw_prob,
  labels,
  method = "dirichlet",
  folds = 5,
  seed = 1
)
ece(cv_fit$oof_predictions, labels, type = "classwise")
```

## Scope

The multiclass methods cover temperature scaling, vector scaling, Dirichlet
calibration, and one-vs-rest calibration. Bayesian binning, near-isotonic
ensembles, object detection calibration, and regression uncertainty calibration
are future work.