mlsanityData to 14 Oct 2026

Conformalized Deep Splines for Optimal and Efficient Prediction Sets

arXiv 2311.00774 ↗First posted 1 Nov 2023cs.LGcited by 5

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Abstract (arXiv)

Uncertainty estimation is critical in high-stakes machine learning applications. One effective way to estimate uncertainty is conformal prediction, which can provide predictive inference with statistical coverage guarantees. We present a new conformal regression method, Spline Prediction Intervals via Conformal Estimation (SPICE), that estimates the conditional density using neural-network-parameterized splines. We prove universal approximation and optimality results for SPICE, which are empirically validated by our experiments. SPICE is compatible with two different efficient-to-compute conformal scores, one oracle-optimal for marginal coverage (SPICE-ND) and the other asymptotically optimal for conditional coverage (SPICE-HPD). Results on benchmark datasets demonstrate SPICE-ND models achieve the smallest average prediction set sizes, including average size reductions of nearly 50% for some datasets compared to the next best baseline. SPICE-HPD models achieve the best conditional coverage compared to baselines. The SPICE implementation is made available.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 22 of its 54 references that are in the map. First posted on arXiv 1 Nov 2023.

Builds on

22 of 54 references.

References · 22

  1. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
  2. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  3. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 819
  4. 2021A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantificationcited by 792
  5. 2019Conformalized Quantile Regressioncited by 629
  6. 2020Classification with Valid and Adaptive Coveragecited by 396
  7. 2016Least Ambiguous Set-Valued Classifiers with Bounded Error Levelscited by 272
  8. 2017Machine Learning for Survival Analysis: A Surveycited by 112
  9. 2019Distributional conformal predictioncited by 105
  10. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 89
  11. 2013A Conformal Prediction Approach to Explore Functional Datacited by 86
  12. 2021Conformal Prediction using Conditional Histogramscited by 77
10 more
  1. 2020CD-split and HPD-split: efficient conformal regions in high dimensionscited by 76
  2. 2022Selection by Prediction with Conformal p-valuescited by 69
  3. 2019Flexible distribution-free conditional predictive bands using density estimatorscited by 64
  4. 2022Probabilistic Conformal Prediction Using Conditional Random Samplescited by 47
  5. 2019Cubic-Spline Flowscited by 35
  6. 2017Converting High-Dimensional Regression to High-Dimensional Conditional Density Estimationcited by 34
  7. 2022Bayesian Optimization with Conformal Prediction Setscited by 28
  8. 2021Bayes-optimal prediction with frequentist coverage controlcited by 20
  9. 2020A three layer neural network can represent any multivariate functioncited by 10
  10. 2021Deconvolutional Density Network: Modeling Free-Form Conditional Distributionscited by 3

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Cited by year

Citing papers per year: 2024: 2; 2025: 3.

5 papers.

  1. 2024Probabilistic Conformal Prediction with Approximate Conditional Validitycited by 23
  2. 2024Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filteringcited by 10
  3. 2025Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertaintycited by 2
  4. 2025Neural Optimal Transport Meets Multivariate Conformal Predictioncited by 2
  5. 2025Context-Aware Multi-Turn Visual-Textual Reasoning in LVLMs via Dynamic Memory and Adaptive Visual Guidancecited by 1