Full Conformal Prediction Visualizer

Interactive demonstration of evaluating a single test point $Y_{n+1}$ across the domain.

Training Size ($n$) -
Test Input ($x_{n+1}$) -
Significance ($\alpha$) 0.10
Prediction Interval -
Trial y-value ($y_{trial}$) 0.00
Error value ($\alpha$) 0.10
p = 0.000
ACCEPTED

Mathematical Foundation

Unlike Split Conformal Prediction, Full Conformal Prediction (also known as Transductive Conformal Prediction) does not require data splitting. It achieves valid coverage by refitting the entire model for every possible trial value $y \in \mathbb{R}$ at the test point $X_{n+1}$.

For a given trial value $y$, we construct an augmented dataset of size $n+1$: $$ \mathcal{D}^{y} = \{(X_1, Y_1), \dots, (X_n, Y_n), (X_{n+1}, y)\} $$

We train the model (here, Kernel Ridge Regression) on $\mathcal{D}^{y}$ and compute the absolute residuals for all $n+1$ points: $$ R_i^y = |Y_i - \hat{f}^y(X_i)|, \quad \text{for } i = 1, \dots, n+1 $$

Because the augmented dataset is exchangeable, the test residual $R_{n+1}^y$ is equally likely to rank anywhere among the $n+1$ residuals. The empirical p-value is the proportion of residuals at least as large as the test residual: $$ p(y) = \frac{1}{n+1} \sum_{i=1}^{n+1} \mathbb{I}\left(R_i^y \ge R_{n+1}^y\right) $$

The prediction interval $C(X_{n+1})$ includes all $y$ where $p(y) > \alpha$. The plot above visualizes this process dynamically for a grid of trial values.