Conformal Prediction Equivalence

Interactive demonstration of equivalent formulations for prediction set inclusion

Significance Level \(\alpha\) 0.10
Candidate Score \(V\) 0.00
1. Empirical Cumulative Distribution Function \(\hat{F}_n(v)\)
2. Calibration Scores \(R_i\) and Candidate Score \(V\)
Computed Parameters
Target rank \(k = \lceil(1-\alpha)(n+1)\rceil\) -
Threshold \(R_{(k)}\) -
Target probability \(p = k/n\) -
Indicator fraction \(\frac{1}{n} \sum_{i=1}^n \mathbb{I}(R_i < V)\) -
Formulation Predicates
Order Statistic: \(V \le R_{(k)}\) TRUE
Empirical Quantile: \(V \le \hat{q}(p)\) TRUE
Empirical Counting: \(\frac{1}{n} \sum_{i=1}^n \mathbb{I}(R_i < V) < \frac{k}{n}\) TRUE
Equivalence Verified