Interpretable Conformal Prediction (CP)

• Interpretable CP is a framework that transforms point predictions into statistically valid sets using quantifiable uncertainty measures and human-readable outputs.
• Prototype-based methods like CONFINE extract nearest training samples from latent spaces to provide concrete, example-driven explanations for classification.
• Smoothing techniques such as SCD-split merge disjoint prediction intervals to enhance interpretability while maintaining strict coverage guarantees.

Interpretable conformal prediction (CP) encompasses a suite of post hoc and end-to-end frameworks for quantifying predictive uncertainty in machine learning models while yielding human-interpretable outputs. These methods produce statistically valid prediction sets rather than single-point estimates and augment prediction transparency via prototype selection, set structure simplification, or formula-based explanations. Recent advances include example-based prototype conformity for neural nets (Huang et al., 1 Jun 2024), interval smoothing to merge disconnected set components (Zheng et al., 26 Sep 2025), and differentiable logic-based scoring for temporal inference (Li et al., 29 Sep 2025). This entry surveys core principles, technical mechanisms, and empirical results underpinning interpretable CP approaches.

1. Conformal Prediction: Statistical Validity and Set Outputs

Conformal prediction is a model-agnostic framework that transforms point predictions into sets $C_\alpha(x)\subset\mathcal{Y}$ with coverage guarantees: for miscoverage level $\alpha\in(0,1)$ and data sequence $(X_i,Y_i)$ assumed exchangeable, it holds that

$$P\left\{Y_{n+1}\in C_\alpha(X_{n+1})\right\} \geq 1-\alpha .$$

For classification, a stronger property is class-conditional coverage: $$P\{Y\in C_\alpha(X)\mid Y=y\} \geq 1-\alpha ,\qquad \forall y\in\mathcal{Y} .$$ Prediction sets are constructed by (i) choosing a nonconformity score $s(x,y)$ quantifying label atypicality, (ii) computing scores on a calibration set, and (iii) thresholding by empirical quantiles or $p$-values. The generic inductive CP $p$-value for candidate label $y$ is

$$p(y\mid x) = \frac{1}{m+1}\left|\left\{i: s_i\geq s(x,y)\right\}\right| ,$$

leading to $C_\alpha(x) = \{y: p(y\mid x) > \alpha\}$ (Huang et al., 1 Jun 2024).

2. Prototype-Based Interpretability in Neural Networks (CONFINE Method)

The CONFINE framework (Huang et al., 1 Jun 2024) adapts conformal prediction to pre-trained neural networks via prototype-based explanations. For input $x$ and label $y$:

• Extract embedding $u = f_\ell(x)$ from a chosen layer $\ell$.
• For $y$, identify the $k$ training samples with label $y$ (same-class prototypes) and the $k$ with label $\neq y$ (different-class prototypes) nearest to $u$ in cosine distance.
• Compute the nonconformity score as

$$s(u,y) = A_k(B, u, y) = \frac{\frac{1}{k}\sum_{i=1}^k \mathrm{CosDist}(u, u_i)[y_i = y]}{\frac{1}{k}\sum_{j=1}^k \mathrm{CosDist}(u, u_j)[y_j\neq y]}$$

where $$\mathrm{CosDist}(u,v)=1 - \frac{u\cdot v}{\|u\|\|v\|}$$.

This ratio expresses how much closer $x$'s latent features are to the same-class cluster than to the different-class cluster. CONFINE outputs example-based explanations: the specific $k$ prototypes dictating each $s(u,y)$. These prototypes offer interpretable evidence for inclusion/exclusion of labels in $C_\alpha(x)$, summarizing the algorithm’s reasoning.

3. Interval and Set Structure Simplification: SCD-split Methodology

In regression or structured output settings, conformal prediction often yields prediction sets with multiple disjoint intervals, which can hamper interpretability. The SCD-split method (Zheng et al., 26 Sep 2025) addresses this by smoothing the underlying estimated conditional density $\hat f(y\mid x)$ before set formation:

• A Gaussian kernel $\phi_\sigma$ is applied: $$\tilde f(y\mid x) = (\phi_\sigma * \hat f(\cdot\mid x))(y)$$.
• Calibration quantile thresholding forms

$$C_{\rm SCD}(x) = \left\{ y : \tilde f(y\mid x) \geq t^S \right\}$$

with $t^S$ the appropriate quantile from calibration.

Smoothing provably reduces the number of connected components in $C_{\rm SCD}(x)$ (i.e., merges intervals), without sacrificing marginal coverage. The crucial tuning parameter $\sigma$ is chosen to match a task-specified target for interval count versus total length, balancing efficiency with interpretable simplicity in set structure.

4. End-to-End Differentiable CP for Signal Temporal Logic Inference

For temporal logic rule induction, conformal prediction with interpretable nonconformity is implemented in a differentiable architecture (TLICP) (Li et al., 29 Sep 2025). STL networks output real-valued robustness scores $\pi_\theta(X)$ for each signal $X$; the nonconformity score is defined via margin-based piecewise constants: $$E_\pi(X, Y) = \begin{cases} 0, & Y\, r \geq m \ 1, & -m < Y\, r < m \ M, & Y\, r \leq -m \end{cases}$$ where $Y\in\{\pm 1\}$ is the true label, $r = \pi_\theta(X)$, $m$ is the margin, and $M \gg 1$ is a penalty constant.

The training objective is a single $p$-value–based loss that promotes both coverage and set minimality: $$\mathcal{L}_{\mathrm{cp}} = \frac{1}{|B_{\mathrm{test}|}} \sum_{(X,Y)\in B_{\mathrm{test}}} [p_\theta(X;-Y) - p_\theta(X;Y)]$$ Post-training, classical inductive CP using these robustness-based scores yields sets $C_\theta(X)$ with guaranteed coverage. This approach directly connects rule-learning accuracy and CP efficiency within STL.

5. Efficiency and Interpretability Metrics

To quantify set quality beyond marginal coverage, CONFINE introduces "correct efficiency": $$\mathrm{CorrectEfficiency}(\{\Gamma_i\}) = \frac{|\{i: \Gamma_i = \{y_i\}\}|}{N}$$ measuring the proportion of test examples where the prediction set is singleton and exactly equals the true label (Huang et al., 1 Jun 2024). Higher correct efficiency indicates compact, precise sets with strong interpretability.

In SCD-split, the interpretability surrogate is the number of connected components (maximal intervals) in $C(x)$ (Zheng et al., 26 Sep 2025). Smoothing provably never increases and often strictly decreases this measure. A plausible implication is that practitioners can control the complexity of predictive intervals, improving human comprehensibility in applications—especially critical in domains such as healthcare and time-series logics.

6. Theoretical Guarantees

All above approaches inherit the canonical CP property: under exchangeability, marginal coverage $P\{Y\in C(X)\}\geq 1-\alpha$ is strictly retained (Huang et al., 1 Jun 2024, Zheng et al., 26 Sep 2025, Li et al., 29 Sep 2025). For CONFINE, class-conditional validity is supported via class-wise calibration (Huang et al., 1 Jun 2024). SCD-split’s smoothing does not degrade coverage and also provides strict component-count reductions under appropriate density conditions. The piecewise scoring in TLICP remains unit-invariant and leverages calibration order statistics for exact guarantees post-training.

7. Empirical Performance and Use Cases

CONFINE was evaluated on medical sensor, medical image, standard vision, and NLP datasets. Notable outcomes include up to +3.6% accuracy boost and up to +3.3% improved correct efficiency relative to baseline classifiers and prior CP methods. Prediction sets consistently achieved or exceeded the $1-\alpha$ coverage curve, and prototype explanations were delivered for every test instance (Huang et al., 1 Jun 2024).

SCD-split exhibited interpretable interval reduction across synthetic and real-world tasks, closely tracking specified interval counts and maintaining coverage and length metrics consistently (Zheng et al., 26 Sep 2025).

TLICP outperformed baselines and regularized CP variants in both uncertainty reduction and misclassification rates for time-series STL tasks. Singleton prediction sets persisted for low $\alpha$ settings, and learned logical predicates reflected tighter, more confident rules (Li et al., 29 Sep 2025).

Each method preserves formal uncertainty quantification while producing explanations or sets compatible with human analysis—enabling usage in high-stakes environments requiring both statistical validity and interpretability.