Pith. sign in

REVIEW 3 major objections 3 minor 31 references

The paper claims that prediction intervals valid conditional on the point prediction itself are achievable with a single isotonic recalibration fit, and that a transductive variant adds exact finite-sample self-calibration without per-candi

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 20:17 UTC pith:QQEILSJR

load-bearing objection SICP is a genuine, lightweight contribution to prediction-conditional coverage; TICP's advertised exact self-calibration is an oracle artifact and should not be accepted as stated. the 3 major comments →

arxiv 2607.16675 v1 pith:QQEILSJR submitted 2026-07-18 stat.ML cs.LGstat.ME

Isotonic Conformal Prediction

Daniel Bensimon , Sean Xiang Yu , Eric D. Kolaczyk , Archer Y. Yang This is my paper
classification stat.ML cs.LGstat.ME MSC 62G0862G1562G20
keywords isotonic conformal predictionself-calibrationprediction-conditional coverageconformal predictionisotonic regressionMondrian conformal predictionfinite-sample guaranteestransductive conformal prediction
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper's aim is to make prediction-conditional uncertainty quantification practical. Standard conformal intervals guarantee coverage on average but can systematically over- or under-cover for specific predicted values; the earlier SC-CP procedure fixes this by conditioning every interval on the calibrated prediction itself, but it must refit its calibration map once per candidate outcome, which is prohibitive for continuous responses. The authors show that isotonic regression's output is a step function with finitely many level sets, so conditioning on the prediction is equivalent to conditioning on which level set the test point belongs to. That lets them run a Mondrian-style conformal quantile within each level set using a single calibration fit. The result is two procedures—split and transductive—that attain finite-sample prediction-conditional coverage, with the transductive variant also giving exact finite-sample self-calibration, at a fraction of SC-CP's runtime.

Core claim

The paper claims two things. Split Isotonic Conformal Prediction obtains finite-sample coverage conditional on the calibrated prediction (Theorem 1) by fitting one isotonic recalibration map and computing the conformal quantile only among calibration points sharing the test point's recalibrated value; its calibrator is exactly self-calibrated on the fitting split and asymptotically on the population (Theorem 2). Transductive Isotonic Conformal Prediction obtains both exact finite-sample self-calibration and prediction-conditional coverage (Theorems 3 and 4) by replacing the global refit with a scalar within-bin mean update. Both procedures need only one isotonic fit, so SC-CP-style guarantee

What carries the argument

The central object is the isotonic recalibration map θ̂ = argmin over nondecreasing functions of Σ(Y_i − θ(f(X_i)))^2, composed with the base model to give f̂ = θ̂ ∘ f. Because θ̂ is a nondecreasing step function, f̂ takes finitely many distinct values and partitions the feature space into level sets; membership in a level set is exactly the event that the calibrated prediction equals a given value. Conditioning on the prediction therefore reduces to conditioning on a Mondrian-style category, and the conformal quantile can be computed from the calibration scores inside that category. The transductive variant's second key object is the local mean μ̂^(y)(X_{n+1}) = (Σ_{i∈I} Y_i + y)/(m+1), the

Load-bearing premise

The load-bearing premise is that at least one held-out calibration point shares the test point's calibrated prediction value; when none does, both procedures fall back to a marginal interval and the prediction-conditional guarantee lapses for that test point.

What would settle it

Run either algorithm on data where the isotonic calibrator produces many singleton level sets (or where test points frequently land in empty level sets), and measure coverage only on test points whose level set is empty in the calibration split. The fallback to a marginal interval will yield coverage below the nominal level on that stratum, showing that the finite-sample conditional guarantee requires the non-empty level-set condition.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Prediction-conditional coverage is achievable at split-conformal cost: SICP's per-test-point work is only a within-level-set quantile, so latency-sensitive applications can get conditional validity.
  • Exact finite-sample self-calibration is decoupled from candidate-wise refitting: TICP recovers SC-CP's dual guarantee with a single isotonic fit plus an inner loop over candidate labels.
  • Calibration before interval construction isolates aleatoric variability from model bias, so interval width reflects genuine outcome uncertainty rather than systematic miscalibration; experiments show narrower intervals at matched coverage when the base model is miscalibrated.
  • Because level sets are learned rather than fixed in advance, the method yields group-conditional coverage as a by-product when a sensitive attribute is correlated with the calibrated prediction, as observed in the healthcare-utilization and bike-sharing experiments.
  • The guarantees inherit split-sample trade-offs: partitioning the calibration data into D1 and D2 reduces the effective sample size for each stage, and SICP's asymptotic self-calibration requires continuity and strict monotonicity of the true calibration curve.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the framework suggests a general recipe—any recalibrator that outputs finitely many distinct values (e.g., histogram binning or tree-based models) could be substituted for isotonic regression and would inherit the same prediction-conditional coverage argument, provided level sets are populated.
  • Editorial inference: the m=0 fallback means the guarantee is conditional on the level set being non-empty; in settings where calibrated predictions are near-continuous or data are sparse, the practical value depends on how often level sets contain enough calibration points, a quantity the paper does not quantify.
  • Editorial inference: a natural testable extension is an adaptive grid for candidate labels in TICP; because the local mean update is scalar, one could replace a uniform grid with a bisection or root-finding scheme to locate interval endpoints without enumerating K labels, potentially removing the factor K.
  • Editorial inference: the self-calibration identity in Theorem 3 holds for any symmetric within-bin statistic, not only the mean; using a median or quantile-based local center would trade exact mean calibration for robustness to heavy tails while preserving the exchangeability argument.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper proposes Isotonic Conformal Prediction (ICP), a framework for obtaining prediction-conditional coverage and self-calibration at lower computational cost than Self-Calibrating Conformal Prediction (SC-CP). Two procedures are introduced: Split Isotonic Conformal Prediction (SICP), which fits a single isotonic calibrator on one split and applies split conformal prediction within the level sets of the resulting step function; and Transductive Isotonic Conformal Prediction (TICP), which replaces fixed residuals by a transductive local mean that includes the candidate outcome and claims exact finite-sample self-calibration and prediction-conditional coverage. The paper reports synthetic and real-data experiments showing coverage comparable to SC-CP with large runtime gains, and reports zero calibration error for TICP.

Significance. The motivation is timely and important: prediction-conditional coverage is a practically relevant relaxation of the impossible full conditional coverage, and reducing the computational burden of SC-CP is a worthwhile goal. SICP's prediction-conditional coverage theorem appears valid and its computational advantage over SC-CP is real. If the TICP claims were supported, the paper would make a substantial contribution. However, as stated, the exact finite-sample guarantees for TICP are established only for an oracle object that depends on the true test outcome, not for any prediction that the method outputs. This affects the central advertised advantage of TICP and the interpretation of the calibration-error results. The SICP contribution remains sound, but the paper's headline claims about TICP need substantial revision.

major comments (3)
  1. [Section 3.2.1, Theorem 3] The theorem defines mu_hat(X_{n+1}) = mu_hat^(Y_{n+1})(X_{n+1}), i.e. the within-bin mean computed with the true outcome included. This quantity is not a function of the covariates and calibration data alone; it cannot be evaluated before Y_{n+1} is observed. Algorithm 2 outputs only a prediction interval and never defines a point predictor, so the self-calibration guarantee E[Y_{n+1}|mu_hat(X_{n+1})] = mu_hat(X_{n+1}) does not attach to any object the method actually delivers. The only computable fixed point of Eq. (4) is the within-bin mean (1/m) sum_{i in I} Y_i, and for exchangeable data E[Y_{n+1} | (1/m)sum Y_i] need not equal that mean. Therefore Theorem 3 is an algebraic identity for an oracle mean, not a property of a deployable predictor. Consequently, the zero calibration error reported for TICP in Tables 2–11 and the abstract's claim that TICP attains exact finite-sample self-
  2. [Section 3.2.1, Theorem 4] The same oracle issue arises for the coverage guarantee. The theorem conditions on mu_hat^(Y_{n+1})(X_{n+1}), which depends on the unknown test outcome. Thus the 'prediction-conditional coverage' established in Theorem 4 is not conditional on any prediction that is a function of X_{n+1} and the training data. The interval produced by Algorithm 2 is not shown to satisfy coverage conditional on any computable point prediction. This undermines the comparison with SC-CP, whose guarantees are stated for its output prediction. The proof of Theorem 4 is internally correct for the conditioning variable used, but that variable is not available at prediction time.
  3. [Section 3.1 and 3.2, m = 0 cases] Theorems 1, 3, and 4 do not state any lower bound on m = |I(X_{n+1})|, but the text and algorithms specify a fallback to a marginal split-conformal interval when m = 0. The proofs effectively cover only the trivial case where S = {n+1} and the conformal quantile is infinite under the algorithm's definition (R ∪ {∞}); the actual fallback procedure is not analyzed in the theorem statements. Section 6 acknowledges the limitation, but the theorem statements and algorithm descriptions need to be reconciled. This is a presentation/consistency issue rather than a fundamental one for the populated-strata guarantees.
minor comments (3)
  1. [Throughout] There are several typographical errors: 'Prediciton' in the introduction, 'T ransductive' in Section 3.2 heading, 'under that fall under that fall' in Section 3, 'A rigourous framework' in Section 2.2, and 'Conferance' in the references. The references for Zadrozny and Elkan and Guo et al. lack years and complete venue information.
  2. [Algorithm 1 and 2] Algorithm 1 line 6 computes q as Quantile(1-α, R ∪ {∞}); when R is empty this returns ∞, so the algorithm returns the whole output space, not the marginal split-conformal interval described in Section 3.1. The same issue appears in Algorithm 2 when m = 0. The fallback described in the text is not implemented by the pseudocode.
  3. [Section 4 and 5] The calibration error definition is not stated precisely. For TICP the reported zero values are attributed to the algebraic identity in Theorem 3, but since Theorem 3 concerns an oracle object, the table entries are not measuring a property of any output prediction. Please clarify the metric and the object to which it is applied.

Circularity Check

3 steps flagged

TICP's exact finite-sample self-calibration and prediction-conditional coverage are defined in terms of the true outcome, making the guarantees algebraic identities rather than properties of a computable predictor.

specific steps
  1. self definitional [Section 3.2.1, Theorem 3 and Eq. (4)]
    "Define ˆµ(Xn+1) = ˆµ(Yn+1)(Xn+1). Then E[Y n+1 |ˆµ(Xn+1)] = ˆµ(Xn+1) a.s."

    The object being calibrated is the within-bin mean that includes the true outcome Y_{n+1}. For any finite bin, the sum of deviations from the bin mean is identically zero, which is exactly the algebraic identity used in the proof. Thus the theorem states a property of the outcome's own group average, not a property of a fitted or usable predictor. Algorithm 2 never outputs such a point prediction, so the exact finite-sample self-calibration claim is true by definition rather than by estimation.

  2. self definitional [Section 3.2.1, Theorem 4]
    "P Yn+1 ∈ bC(X n+1) ˆµ(Yn+1)(Xn+1) ≥1−α."

    The conditioning statistic ˆµ^(Yn+1)(Xn+1) is a function of the unknown test outcome. Thus the coverage guarantee is not conditional on a prediction available before observing Y_{n+1}; it does not match objective (ii) in Eq. (2), which conditions on ˆf(Xn+1). The interval's validity conditional on this outcome-dependent oracle is a conformal exchangeability artifact, centered on the same outcome-dependent mean, rather than a property of a computable prediction. The claimed finite-sample prediction-conditional validity is therefore a statement about an oracle, not about a deployable interval.

  3. other [Section 5.1, footnote 2 / Figure 2 caption]
    "Transductive Isotonic CP achieves zero calibration error by construction2 ... 2 The first-order conditions of the isotonic regression objective imply E[Y|f (X)] = f (X) on the augmented calibration set; see Theorem 4.1 of van der Laan and Alaa (2024)."

    The zero calibration error reported for TICP in Tables 2–11 is acknowledged to be 'by construction'. It is therefore not an empirical validation of a model's calibration; it is an algebraic consequence of the oracle construction used in the method. Presenting this forced value as evidence of exact self-calibration is a fitted-input-called-prediction pattern: the construction itself guarantees the zero, so the reported calibration error carries no independent empirical support.

full rationale

SICP's Theorem 1 is a legitimate finite-sample coverage result derived from exchangeability of the calibration and test points within a level set; that portion is not circular. The circularity is concentrated in TICP, the paper's headline method for recovering both objectives exactly. Theorem 3 defines its 'prediction' as the within-bin mean including the true test outcome, so the self-calibration equation is an algebraic identity (the average residual is zero by construction) rather than a property of a computable predictor. Theorem 4 conditions on the same outcome-dependent oracle, so the claimed prediction-conditional coverage is not conditional on a prediction a user could know. The experiments further present zero calibration error for TICP, which the paper itself admits is 'by construction'. These are not mere omissions: the central advertised advantage of TICP—exact finite-sample self-calibration at low computational cost—reduces to the definition of the oracle statistic. The score reflects that this is a partial but serious circularity: one of the two proposed procedures (SICP) is non-circular, but the stronger claims of the other procedure (TICP) are by-construction identities. No self-citation chains or imported uniqueness theorems are involved.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The methods introduce no fitted free parameters; the finite-sample guarantees follow from exchangeability and the step-function structure of isotonic regression. The only stated regularity assumptions (compact support, strict monotone calibration curve) are for the asymptotic result. TICP's 'exact self-calibration' is a direct consequence of the exchangeability property of within-group means, not of any fitted constant.

free parameters (2)
  • α (miscoverage level)
    User-specified nominal level (0.1 in experiments). Not fitted; the coverage guarantees hold for any α∈(0,1).
  • K (grid size for discretizing continuous Y)
    User-chosen discretization for TICP's inner loop. Affects computational cost and interval resolution; not a fitted constant.
axioms (5)
  • domain assumption Exchangeability of the n+1 data points (standard split conformal assumption).
    Used in Theorems 1, 3, 4 to justify conditional exchangeability of the level-set subcollection. If violated (e.g., time series drift), the finite-sample guarantees fail.
  • domain assumption Assumption 1: i.i.d. draws, E[Y^2]<∞, compact support of base predictions f(X).
    Needed only for Theorem 2 (asymptotic self-calibration of SICP), via uniform consistency of isotonic regression.
  • domain assumption Assumption 2: true calibration function θ0(s)=E[Y|f(X)=s] is continuous and strictly increasing.
    Needed for the uniform convergence of the isotonic estimator in Theorem 2. If flat regions exist, the boundary convergence rate can degrade.
  • standard math Isotonic regression is uniformly consistent under Assumptions 1-2 (Robertson et al., 1988).
    Imported classical result used in the proof of Theorem 2.
  • standard math For any exchangeable random variables Z_1,...,Z_N, E[Z_i | (1/N)∑Z_j] = (1/N)∑Z_j.
    Implicit in the proof of Theorem 3; the within-group mean is the self-calibrated predictor by exchangeability.

pith-pipeline@v1.3.0-alltime-deepseek · 17903 in / 26253 out tokens · 238138 ms · 2026-08-01T20:17:17.562872+00:00 · methodology

0 comments
read the original abstract

A point prediction that is well calibrated on average can still be systematically biased conditional on its own value, undermining its use in downstream decision-making. We consider two objectives for reliable uncertainty quantification: self-calibration, requiring a point prediction to be unbiased conditional on its own value, and prediction-conditional validity, requiring a prediction interval to attain nominal coverage conditional on the prediction. Self-Calibrating Conformal Prediction (SC-CP) attains both objectives exactly in finite samples, but requires refitting its calibrator for every candidate outcome, which is computationally prohibitive for continuous outcomes. We propose Isotonic Conformal Prediction (ICP), a framework that decouples calibration from prediction-set construction by fitting a single isotonic recalibration map and constructing prediction intervals within strata of similar recalibrated predictions. Within this framework we develop two procedures. Split Isotonic Conformal Prediction (SICP) attains prediction-conditional validity in finite samples and self-calibration asymptotically, at the computational cost of split conformal prediction. Transductive Isotonic Conformal Prediction (TICP) attains both objectives exactly in finite samples through a per-test-point inner loop that avoids refitting the isotonic calibrator. On synthetic heteroscedastic regression problems and a real-world healthcare-utilization dataset, both procedures match the coverage of SC-CP at substantially lower computational cost.

Figures

Figures reproduced from arXiv: 2607.16675 by Archer Y. Yang, Daniel Bensimon, Eric D. Kolaczyk, Sean Xiang Yu.

Figure 1
Figure 1. Figure 1: Runtime by dimension d and κ, on a logarithmic scale. Each value is the wall-clock time to fit the calibrator once and construct prediction intervals for 1000 test points, averaged over replications. SC-CP refits its calibrator for every candidate label; both isotonic procedures fit once. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Prediction intervals and calibrated predictions for MEPS-21 in Setting 1 and Setting 2. Top: poorly calibrated base model. Bottom: well calibrated base model. The black step function denotes the calibrated prediction, and the shaded region denotes the conformal prediction interval. cannot adapt across groups with differing outcome variability. Both self-calibrating methods reduce this imbalance, bringing t… view at source ↗
Figure 3
Figure 3. Figure 3: Prediction intervals and calibrated predictions for the Bike dataset under two calibration settings. The dashed gray line denotes the identity map, corresponding to no calibration. The black step function denotes the calibrated prediction, the red points denote pointwise calibrated predictions, and the shaded region denotes the conformal prediction interval. B.2 Concrete Dataset [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 4
Figure 4. Figure 4: Prediction intervals and calibrated predictions for the Concrete dataset under two calibration settings. The dashed gray line denotes the identity map, corresponding to no calibration. The black step function denotes the calibrated prediction, the red points denote pointwise calibrated predictions, and the shaded region denotes the conformal prediction interval. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Prediction intervals and calibrated predictions for the Bio dataset under two calibration settings. The dashed gray line denotes the identity map, corresponding to no calibration. The black step function denotes the calibrated prediction, the red points denote pointwise calibrated predictions, and the shaded region denotes the conformal prediction interval. B.4 STAR Dataset [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 6
Figure 6. Figure 6: Prediction intervals and calibrated predictions for the STAR dataset under two calibration settings. The dashed gray line denotes the identity map, corresponding to no calibration. The black step function denotes the calibrated prediction, the red points denote pointwise calibrated predictions, and the shaded region denotes the conformal prediction interval. 26 [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 8 canonical work pages · 4 internal anchors

  1. [1]

    1988 , publisher=

    Order restricted statistical inference , author=. 1988 , publisher=

    1988

  2. [2]

    Technical Report , year=

    Mondrian confidence machine , author=. Technical Report , year=

  3. [3]

    Information and Inference: A Journal of the IMA , volume=

    The limits of distribution-free conditional predictive inference , author=. Information and Inference: A Journal of the IMA , volume=. 2021 , publisher=

    2021

  4. [4]

    The Annals of Statistics , volume=

    Conformal prediction beyond exchangeability , author=. The Annals of Statistics , volume=. 2023 , publisher=

    2023

  5. [5]

    Advances in neural information processing systems , volume=

    Conformal prediction under covariate shift , author=. Advances in neural information processing systems , volume=

  6. [6]

    Inductive Confidence Machines for Regression

    Papadopoulos, Harris and Proedrou, Kostas and Vovk, Volodya and Gammerman, Alex. Inductive Confidence Machines for Regression. Machine Learning: ECML 2002. 2002

    2002

  7. [7]

    Self-Calibrating Conformal Prediction

    van der Laan, Lars and Alaa, Ahmed M. , year = 2024, month = oct, number =. Self-. doi:10.48550/arXiv.2402.07307 , urldate =. arXiv , keywords =:2402.07307 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2402.07307 2024

  8. [8]

    doi:10.1007/b106715 , abstract =

    Algorithmic. doi:10.1007/b106715 , abstract =

    doi:10.1007/b106715

  9. [9]

    Distribution-Free

    Lei, Jing and Wasserman, Larry , year = 2014, month = jan, journal =. Distribution-Free. doi:10.1111/rssb.12021 , urldate =

    doi:10.1111/rssb.12021 2014

  10. [10]

    and Cand

    Gibbs, Isaac and Cherian, John J. and Cand. Conformal. doi:10.48550/arXiv.2305.12616 , urldate =. arXiv , keywords =:2305.12616 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2305.12616

  11. [11]

    Conformal Prediction with Local Weights: Randomization Enables Local Guarantees , shorttitle =

    Hore, Rohan and Barber, Rina Foygel , year = 2024, month = oct, number =. Conformal Prediction with Local Weights: Randomization Enables Local Guarantees , shorttitle =. doi:10.48550/arXiv.2310.07850 , urldate =. arXiv , keywords =:2310.07850 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2310.07850 2024

  12. [12]

    and Wasserman, Larry , year = 2017, month = mar, number =

    Lei, Jing and G'Sell, Max and Rinaldo, Alessandro and Tibshirani, Ryan J. and Wasserman, Larry , year = 2017, month = mar, number =. Distribution-. doi:10.48550/arXiv.1604.04173 , urldate =. arXiv , keywords =:1604.04173 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1604.04173 2017

  13. [13]

    Regression

    Koenker, Roger and Bassett, Gilbert , year = 1978, month = jan, journal =. Regression. doi:10.2307/1913643 , urldate =. 1913643 , eprinttype =

    doi:10.2307/1913643 1978

  14. [14]

    Causal isotonic calibration for heterogeneous treatment effects

    Causal Isotonic Calibration for Heterogeneous Treatment Effects , author =. doi:10.48550/arXiv.2302.14011 , urldate =. arXiv , keywords =:2302.14011 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2302.14011

  15. [15]

    Distribution-free calibration guarantees for histogram binning without sample splitting

    Distribution-Free Calibration Guarantees for Histogram Binning without Sample Splitting , author =. doi:10.48550/arXiv.2105.04656 , urldate =. arXiv , keywords =:2105.04656 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2105.04656

  16. [16]

    Barlow, R. E. and Brunk, H. D. , year = 1972, journal =. The. doi:10.2307/2284712 , urldate =. 2284712 , eprinttype =

    work page doi:10.2307/2284712 1972

  17. [17]

    , editor =

    Lichtenstein, Sarah and Fischhoff, Baruch and Phillips, Lawrence D. , editor =. Calibration of. Decision. doi:10.1007/978-94-010-1276-8_19 , urldate =

    work page doi:10.1007/978-94-010-1276-8_19

  18. [18]

    Obtaining Calibrated Probability Estimates from Decision Trees and Naive

    Zadrozny, Bianca and Elkan, Charles , journal =. Obtaining Calibrated Probability Estimates from Decision Trees and Naive

  19. [19]

    Calibration of

    Bella, Antonio and Ferri, C. Calibration of

  20. [20]

    , date =

    Guo, Chuan and Pleiss, Geoff and Sun, Yu and Weinberger, Kilian Q. , date =. On. Proceedings of the 34th

  21. [21]

    Information and Inference: A Journal of the IMA , volume =

    The Limits of Distribution-Free Conditional Predictive Inference , author =. Information and Inference: A Journal of the IMA , volume =. doi:10.1093/imaiai/iaaa017 , urldate =

    doi:10.1093/imaiai/iaaa017

  22. [22]

    and Cohen, Steven B

    Cohen, Joel W. and Cohen, Steven B. and Banthin, Jessica S. , year = 2009, month = jul, journal =. The Medical Expenditure Panel Survey: A National Information Resource to Support Healthcare Cost Research and Inform Policy and Practice , shorttitle =. doi:10.1097/MLR.0b013e3181a23e3a , abstract =

    work page doi:10.1097/mlr.0b013e3181a23e3a 2009

  23. [23]

    and Barber, Rina Foygel and Bates, Stephen , year = 2026, month = mar, number =

    Angelopoulos, Anastasios N. and Barber, Rina Foygel and Bates, Stephen , year = 2026, month = mar, number =. Theoretical. doi:10.48550/arXiv.2411.11824 , urldate =. arXiv , keywords =:2411.11824 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2411.11824 2026

  24. [24]

    Advances in Neural Information Processing Systems , volume =

    Conformalized Quantile Regression , author =. Advances in Neural Information Processing Systems , volume =. 2019 , publisher =

    2019

  25. [25]

    Vovk, Vladimir and Petej, Ivan , year = 2014, month = jun, number =. Venn-. doi:10.48550/arXiv.1211.0025 , urldate =. arXiv , keywords =:1211.0025 , primaryclass =

    Pith/arXiv arXiv doi:10.48550/arxiv.1211.0025 2014

  26. [26]

    Nature Protocols , pages =

    Facilitating Structure-Based Drug Discovery with an Artificial Intelligence-Driven Virtual Screening Platform , author =. Nature Protocols , pages =. doi:10.1038/s41596-026-01389-z , urldate =

    work page doi:10.1038/s41596-026-01389-z

  27. [27]

    Nature Reviews Drug Discovery , volume =

    Applications of Machine Learning in Drug Discovery and Development , author =. Nature Reviews Drug Discovery , volume =. doi:10.1038/s41573-019-0024-5 , urldate =

    doi:10.1038/s41573-019-0024-5

  28. [28]

    , year = 2019, month = jan, journal =

    Topol, Eric J. , year = 2019, month = jan, journal =. High-Performance Medicine: The Convergence of Human and Artificial Intelligence , shorttitle =. doi:10.1038/s41591-018-0300-7 , urldate =

    doi:10.1038/s41591-018-0300-7 2019

  29. [29]

    Nature , volume =

    Large Language Models Encode Clinical Knowledge , author =. Nature , volume =. doi:10.1038/s41586-023-06291-2 , urldate =

    doi:10.1038/s41586-023-06291-2

  30. [30]

    Distribution-free binary classification: prediction sets, confidence intervals and calibration

    Gupta, Chirag and Podkopaev, Aleksandr and Ramdas, Aaditya , year = 2022, month = feb, number =. Distribution-Free Binary Classification: Prediction Sets, Confidence Intervals and Calibration , shorttitle =. doi:10.48550/arXiv.2006.10564 , urldate =. arXiv , keywords =:2006.10564 , primaryclass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2006.10564 2022

  31. [31]

    , year = 2007, month = apr, journal =

    Gneiting, Tilmann and Balabdaoui, Fadoua and Raftery, Adrian E. , year = 2007, month = apr, journal =. Probabilistic. doi:10.1111/j.1467-9868.2007.00587.x , urldate =

    arXiv 2007