Pith. sign in

REVIEW 3 major objections 4 minor 70 references

Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read For black-box generative models, conformal coverage can be built from sampling alone: the optimal query-stopping rule and the optimal prediction-set rule are both governed by the missing mass, the probability that the correct output has…

desk verdict Novel missing-mass framework for query-based conformal prediction, but the central optimality theorem is false as stated and the method currently rests on a heuristic with only a coverage guarantee. read the letter →

arxiv 2506.05497 v1 pith:TZCWZSNY submitted 2025-06-05 cs.LG cs.AI

Sima Noorani , Shayan Kiyani , George Pappas , Hamed Hassani This is my paper
classification cs.LGcs.AI
keywords conformalpredictionuncertaintyquantificationmissingmassGood-Turingestimationgenerativemodelslargelanguagequeryoraclesets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper works out how to do conformal prediction for generative models when the only access to the model is a query oracle: you can draw samples, but there are no logits, no geometric distances, and no structured label space to threshold. The central claim is that both decisions in such a pipeline — how many times to query each input, and which sampled outputs to place in the prediction set — are governed by a single classical quantity, the missing mass, defined as the probability that the correct output has not appeared among the samples drawn so far. The paper proves that an optimal query policy stops when the rate at which missing mass shrinks falls below a common threshold, and that an optimal prediction set is obtained by thresholding a score in which a special 'Everything Else' label carries the missing mass itself. These two principles are assembled into a finite-sample algorithm with distribution-free coverage guarantees, and on open-ended LLM tasks the algorithm produces far more informative prediction sets — far fewer unnecessary 'Everything Else' fallbacks — than existing conformal language-model methods at the same coverage and query budget. If the argument holds, any black-box generative model with a sampling interface gets principled uncertainty quantification with an explicit test-time query budget.

What carries the argument

The load-bearing object is the missing mass $\theta(x,t) = \Pr[Y \notin Z_t(x) \mid X=x]$, the probability that $t$ independent queries at input $x$ have not produced the true label, together with its discrete derivative $\Delta(x,t) = \theta(x,t+1) - \theta(x,t)$, which is negative and non-decreasing in $t$ — the diminishing-returns property that makes thresholding meaningful. Around it the paper builds three further pieces: the abstract label $\mathrm{EE}$ ('Everything Else') representing $Y \setminus Z(x)$, whose inclusion guarantees coverage but costs informativeness and is penalized by $\lambda$; the conformity score with $S(x,y) = 1 - p(y|x)$ on seen labels and $S(x,\mathrm{EE}) = 2 - p(\mathrm{EE}|x)$ on the unseen remainder; and a Neyman-Pearson benefit-to-cost argument that converts the constrained set-selection problem into this threshold rule. In the finite-sample algorithm, $p(\mathrm{EE}|x)$ is estimated by the Good-Turing singleton count $N_1/t$ and $\Delta$ by the new doubleton estimator $-2N_2/t^2$, with the threshold $\beta^*$ tuned to satisfy the query budget and $q^*$ set by split-conformal calibration.

What would settle it

Construct a synthetic label distribution over, say, 100 labels in which one label has probability strictly below $p(\mathrm{EE}|x)/\lambda$ while the rest are uniform, solve the constrained set-selection problem exactly with a Neyman-Pearson allocation, and compare with the paper's score threshold: the two rules must differ precisely on that rare seen label, showing the claimed optimal structure fails there. A second check is to compute the empirical EE fraction at the budgets used in the paper ($B = 7$ to $40$) and see whether any coverage level produces sets whose composition contradicts the threshold rule.

Watch

Extended reading notes

Core claim

In the population regime where the query oracle matches the true conditional distribution, the paper establishes two structural results. First, with a fixed expected query budget, the expected missing mass $\mathbb{E}_X[\theta(X,T(X))]$ is minimized by a threshold rule on the discrete derivative $\Delta(x,t) = \theta(x,t+1) - \theta(x,t)$: there is a single threshold $\beta^*$ such that the optimal number of queries for input $x$ is the first $t$ where an additional draw stops reducing missing mass enough. Second, with the penalty $\lambda$ on the fallback label sufficiently large, the optimal set map is a threshold on the conformity score $S(x,y) = 1 - p(y|x)$ for sampled labels and $S(x,\mathrm{EE}) = 2 - p(\mathrm{EE}|x)$ for the abstract 'Everything Else' label, where $p(\mathrm{EE}|x)$ is exactly the missing mass; this reduces to the classical thresholding of $1 - p(y|x)$ when nothing is missing. The finite-sample algorithm replaces these population quantities with estimates — the Good-Turing count of singletons $N_1/t$ for the missing mass, and a newly derived doubleton estimator $-2N_2/t^2$ for its derivative — then calibrates the score threshold $q^*$ by split conformal quantiles, which gives distribution-free coverage even when the oracle differs from the truth. Taken together, the two results claim a query-based conformal method that is simultaneously optimal in its use of the query budget, its avoidance of uninformative fallbacks, and its set sizes, for any black-box generative model.

Load-bearing premise

Everything rests on the rule that places the 'Everything Else' label after all sampled answers being optimal, which the proof needs the penalty weight $\lambda$ to be large enough that every sampled answer is more probable than the missing mass divided by $\lambda$; on real query distributions a sampled answer can be rarer than that fraction, and then the true optimum would rank the unseen remainder ahead of it.

Editorial extensions

If this is right

  • Any black-box generative model that can be sampled — with no logits, token probabilities, or internal scores — can be wrapped in a distribution-free coverage guarantee at any user-chosen level, including levels above the model's own few-shot accuracy.
  • The query budget becomes an explicit, tunable knob: calibrating $\beta^*$ fixes the expected number of queries per input, so coverage, informativeness, and cost are set by the scalars $\alpha$, $\beta^*$, and $\lambda$ independently.
  • At matched coverage and matched query budget, CPQ needs the 'Everything Else' fallback far less often than conformal language modelling baselines: on GSM8K at 95% nominal coverage, about 16% of CPQ sets contain $\mathrm{EE}$, versus roughly 70% for CLM and 61% for SCOPE-Gen.
  • The optimal-score structure extends the classical result that minimal conformal sets threshold $1 - p(y|x)$: in an effectively infinite label space the missing mass enters through a single extra score value assigned to the unseen remainder.
  • A principled stopping rule replaces fixed per-input sample counts: querying continues exactly while an additional draw still reduces the estimated missing mass at a rate above the calibrated threshold.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The doubleton estimator $-2N_2/t^2$ is a cheap, logit-free stopping signal that could transfer to other sampling pipelines — for instance deciding when to stop drawing responses for semantic-entropy or self-consistency checks in LLM systems, where stopping rules are currently heuristic.
  • Because the coverage proof only needs exchangeability of scores and never uses $\pi \equiv p$, the two-module design should tolerate mismatch between the query oracle and the calibration distribution; an explicit synthetic-shift experiment would test how much drift the $\mathrm{EE}$ fallback absorbs.
  • The authors decouple the query policy from the set map and note this only approximates the joint optimum; an ablation that alternates the two optimization stages could quantify how much of the reported informativeness gain comes from the coupling they left out.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper introduces CPQ, a conformal prediction framework for black-box generative models in a query-only setting. It formalizes an optimization problem over a query policy T and a set map f that balances coverage, informativeness, and query budget, with a special fallback label EE representing the unseen remainder of the label space. The paper derives two principles: the optimal query policy is characterized by a threshold on the missing-mass derivative, and the optimal set map is claimed to be a threshold rule on a conformity score involving the missing mass. A finite-sample algorithm is then proposed, using Good–Turing estimators for the missing mass and its derivative, together with split conformal calibration. Experiments on three open-ended LLM tasks compare CPQ with CLM and SCOPE-Gen, reporting lower EE fractions at matched query budgets.

Significance. If the optimality results were correct, this would be a valuable contribution: it would provide the first principled treatment of the coverage–informativeness–query-budget trade-off for generative models, with a clean connection to the classical missing-mass problem. The paper does have credible elements: the split-conformal coverage argument in Theorem 4.1 is standard and appears valid; the Good–Turing-based derivative estimator -2N_2/t^2 is a clean derivation; and the empirical comparison is systematic, with released code. However, the central optimal-mapping theorem, Theorem 3.2, is false as stated, and the finite-sample algorithm inherits the flaw. Since the advertised optimality is the main scientific claim of the paper, the contribution is not established despite the valid coverage guarantee.

major comments (3)
  1. [§3.2, Theorem 3.2, Eq. (5)] Theorem 3.2 is false as stated. Consider a single input x with seen labels A and B, p(A)=0.15, p(B)=0.05, p(EE)=0.8, λ=100, and α=0.1. The feasible sets and costs are: {} cost 0, {A} cost 1, {B} cost 1, {A,B} cost 2, {EE} cost 100, {EE,A} cost 101, and {EE,A,B} cost 102; {EE,B} has coverage 0.85 and is infeasible. The optimum is {EE,A}. The score in Eq. (5) gives S(A)=0.85, S(B)=0.95, and S(EE)=1.20, so thresholding yields only {A}, {A,B}, or {A,B,EE}; it can never produce {EE,A}. This example also satisfies the large-λ ordering condition p(B)=0.05 > p(EE)/λ=0.008, so adding that condition to the theorem does not rescue it. Additionally, Appendix A.2 requires 1-p(EE|x)/λ > 1-p(y|x) for every seen label y, equivalently p(y|x)>p(EE|x)/λ, which is not stated in the theorem and need not hold when a seen label has very small probability.
  2. [Appendix A.2, Eq. (7)] The LP relaxation argument is invalid. The Neyman-Pearson reasoning applied to the relaxed problem (7) identifies an optimal fractional solution by benefit-to-cost ratios, but with a single coverage constraint the LP optimum generally requires a fractional final item, and its value can be strictly below the integer optimum. In the counterexample above, the LP selects A and B in full and a fraction 0.875 of EE, giving cost 2+87.5=89.5, which is cheaper than the integer optimum {EE,A} at cost 101 and is not an integer solution. Therefore the claimed equivalence between the relaxed problem (7) and the original integer problem (6) does not follow, and the conclusion that the optimal set map is a threshold rule does not follow.
  3. [Abstract, §4, Algorithm 1] Because Algorithm 1 constructs sets by thresholding the estimated score S with EE scored after every seen label, it cannot realize the optimal set map in the counterexample: including EE forces inclusion of all seen labels with score below the EE score, so it cannot output {EE,A} while excluding B. The paper's central claims of optimality — in the abstract, Section 3, and Section 5 — are therefore unsupported. Theorem 4.1 remains a valid split-conformal coverage guarantee for any score function, but it does not establish that CPQ optimally balances EE usage and set size.
minor comments (4)
  1. [§3.1, Theorem 3.1] The theorem statement writes Δ(x,T*(x)-1), which is undefined when T*(x)=0; the corner case T*(x)=0 when Δ(x,0)≤β* is only discussed in the proof and should be included in the theorem statement.
  2. [§5, §6] There are several typos and inconsistencies: 'open-eneded', 'Datsets', 'out method', and 'compares' should be corrected; the method name is written as both SCOPE-Gen and Scope-Gen.
  3. [§5, Clustering] The clustering section says that cluster frequencies are scaled to form a valid probability distribution over seen and unseen clusters, but the precise scaling procedure is not specified; this is important because the missing-mass estimates and scores depend on these probabilities.
  4. [Table 2] The claim that CPQ is constrained to the lowest average query budget used by the baselines is favorable to CPQ and should be justified or relaxed in the main text; the reader currently has to infer this from the appendix.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the query-policy and set-map principles are derived from the stated optimization, q* is standard split-conformal calibration, and self-citations are contextual.

full rationale

The derivation chain is self-contained. Theorem 3.1 characterizes the budgeted missing-mass allocation problem (2) through the diminishing-returns monotonicity of Δ(x,t) and an exchange argument; no fitted parameter is inserted into the theorem. Theorem 3.2 derives the threshold form of the optimal set map from the paper's own objective (4) via the Neyman-Pearson/LP relaxation, with the score S(x,y) and q* emerging from the benefit-to-cost ordering rather than being assumed. In the finite-sample algorithm, q* is the (1−α)-quantile of calibration scores and Theorem 4.1 is the standard exchangeability argument, so coverage is not forced by estimating missing mass or by tuning β*. The threshold β* is tuned on a separate calibration subset only to satisfy the stated average budget B; this is budget calibration, not a fitted 'prediction' of the reported test metrics. The Good–Turing missing-mass estimator and the derivative estimator −2N2/t2 are derived from classical missing-mass identities, with no target quantity appearing as an input. Self-citations [8,33] provide context and are not load-bearing: the proof of Theorem 3.2 rests on [68,69], not on those self-citations. The reviewer's counterexample concerns the mathematical correctness of Theorem 3.2, which is a separate issue from circularity.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The central theoretical claims rest on standard exchangeability, an idealized oracle assumption, and a hidden ad hoc condition on lambda that is not satisfiable in general. The free parameters are mostly standard calibration thresholds and experimental choices, not fitted constants that secretly encode the answer. EE is the only invented entity and it is a modeling device rather than a physical postulate.

free parameters (5)
  • lambda
    Penalty ratio in the CPQ objective (Section 2). Chosen by hand with lambda >> 1; exact value used in experiments not reported. Affects Theorem 3.2's 'sufficiently large lambda' condition.
  • beta* = grid search on Dcal1
    Query-stopping threshold tuned on calibration split Dcal1 to meet average query budget B (Section 4, Algorithm 1).
  • q* = calibrated quantile on Dcal2
    Conformal threshold for prediction set scores, set as (1-alpha) quantile of calibration scores (Algorithm 1). Standard conformal calibration.
  • entailment_rule = relaxed bidirectional entailment
    Hand-chosen matching function for semantic clustering: one direction entailment, other entailment or neutral (Appendix B.4). Choice affects label space and hence all estimates.
  • budget B = 7, 20, 30, 40 per dataset
    Average query budget per dataset, chosen to reflect intermediate values based on few-shot model accuracy (Section 5).
assumptions (5)
  • standard math Calibration and test points are exchangeable
    Used in Theorem 4.1 for coverage validity, standard split-conformal assumption.
  • domain assumption pi = p in the population analysis
    Section 3 assumes the query oracle is perfect to derive Principles 1 and 2; the finite-sample algorithm relaxes this.
  • standard math X is a continuous random variable
    Used in Theorems 3.1 and 3.2 to enable equal-probability splitting and avoid tie-breaking; LLM prompts are discrete, so this is a gap.
  • ad hoc to paper lambda is sufficiently large so that 1 - p(EE|x)/lambda > 1 - p(y|x) for all seen y
    Appendix A.2 uses this to justify the score transformation. It is not guaranteed and can fail for low-probability seen labels; this is the load-bearing flaw.
  • domain assumption Clustering produces valid semantic equivalence classes
    LLM-based entailment clustering groups generations into labels; if clustering is wrong, coverage statements refer to clusters, not raw strings.
invented entities (1)
  • EE (Everything Else)
    purpose: Abstract fallback label representing all unseen outputs, included in prediction sets to maintain coverage when the true label is not sampled.
    It is a modeling construct, not an empirical entity. Its inclusion is directly measured as EE fraction, but there is no external falsifiable prediction attached to it beyond the conformal coverage property.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models." pith.science (2026). https://pith.science/paper/TZCWZSNY

@misc{pith2026250605497,
  author       = {Pith},
  title        = {Pith review of: Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TZCWZSNY}},
  note         = {Machine review of arXiv:2506.05497}
}
read the original abstract

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification framework, but classical methods focus on regression and classification, relying on geometric distances or softmax scores: tools that presuppose structured outputs. We depart from this paradigm by studying CP in a query only setting, where prediction sets must be constructed solely from finite queries to a black box generative model, introducing a new trade off between coverage, test time query budget, and informativeness. We introduce Conformal Prediction with Query Oracle (CPQ), a framework characterizing the optimal interplay between these objectives. Our finite sample algorithm is built on two core principles: one governs the optimal query policy, and the other defines the optimal mapping from queried samples to prediction sets. Remarkably, both are rooted in the classical missing mass problem in statistics. Specifically, the optimal query policy depends on the rate of decay, or the derivative, of the missing mass, for which we develop a novel estimator. Meanwhile, the optimal mapping hinges on the missing mass itself, which we estimate using Good Turing estimators. We then turn our focus to implementing our method for language models, where outputs are vast, variable, and often under specified. Fine grained experiments on three real world open ended tasks and two LLMs, show CPQ applicability to any black box LLM and highlight: (1) individual contribution of each principle to CPQ performance, and (2) CPQ ability to yield significantly more informative prediction sets than existing conformal methods for language uncertainty quantification.

Figures

Figures reproduced from arXiv: 2506.05497 by the authors.

Figure 1
Figure 1. Missing mass and its discrete derivative for two synthetic distributions over a support of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Performance of the three algorithmic variants (Vanilla, P1, P1+P2 : corresponds to our [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Comparison of the fine-grained variants—vanilla baseline, optimal adaptive querying [PITH_FULL_IMAGE:figures/full_fig_p028_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Empirical comparison of missing mass and its derivative estimators on two synthetic [PITH_FULL_IMAGE:figures/full_fig_p033_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

70 extracted references · 51 canonical work pages

  1. [1]

    A survey on hallucination in large language models: Principles, taxonomy, challenges, and open questions.ACM Transactions on Information Systems, 43(2):1–55, 2025

    Lei Huang, Weijiang Yu, Weitao Ma, Weihong Zhong, Zhangyin Feng, Haotian Wang, Qianglong Chen, Weihua Peng, Xiaocheng Feng, Bing Qin, et al. A survey on hallucination in large language models: Principles, taxonomy, challenges, and open questions.ACM Transactions on Information Systems, 43(2):1–55, 2025

    2025

  2. [2]

    The dawn after the dark: An empirical study on factuality hallucination in large language models

    Junyi Li, Jie Chen, Ruiyang Ren, Xiaoxue Cheng, Wayne Xin Zhao, Jian-Yun Nie, and Ji-Rong Wen. The dawn after the dark: An empirical study on factuality hallucination in large language models. arXiv preprint arXiv:2401.03205, 2024. 15

    arXiv 2024

  3. [3]

    Sources of hallucination by large language models on inference tasks.arXiv preprint arXiv:2305.14552, 2023

    Nick McKenna, Tianyi Li, Liang Cheng, Mohammad Javad Hosseini, Mark Johnson, and Mark Steedman. Sources of hallucination by large language models on inference tasks.arXiv preprint arXiv:2305.14552, 2023

    arXiv 2023

  4. [4]

    Detecting hallucinations in large language models using semantic entropy.Nature, 630(8017):625–630, 2024

    Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal. Detecting hallucinations in large language models using semantic entropy.Nature, 630(8017):625–630, 2024

    2024

  5. [5]

    Machine-learning applications of algorithmic randomness

    Volodya Vovk, Alexander Gammerman, and Craig Saunders. Machine-learning applications of algorithmic randomness. 1999

    work page 1999

  6. [6]

    Transduction with confidence and credibility

    Craig Saunders, Alex Gammerman, and Volodya Vovk. Transduction with confidence and credibility. 1999

    work page 1999

  7. [7]

    Springer, 2005

    Vladimir Vovk, Alexander Gammerman, and Glenn Shafer.Algorithmic learning in a random world, volume 29. Springer, 2005

    work page 2005

  8. [8]

    Decision theoretic foundations for conformal prediction: Optimal uncertainty quantification for risk-averse agents.arXiv preprint arXiv:2502.02561, 2025

    Shayan Kiyani, George Pappas, Aaron Roth, and Hamed Hassani. Decision theoretic foundations for conformal prediction: Optimal uncertainty quantification for risk-averse agents.arXiv preprint arXiv:2502.02561, 2025

    arXiv 2025

Show all 70 references
  1. [9]

    A tutorial on conformal prediction.Journal of Machine Learning Research, 9(3), 2008

    Glenn Shafer and Vladimir Vovk. A tutorial on conformal prediction.Journal of Machine Learning Research, 9(3), 2008

    2008

  2. [10]

    Conformalized quantile regression

    Yaniv Romano, Evan Patterson, and Emmanuel Candes. Conformalized quantile regression. Advances in neural information processing systems, 32, 2019

    2019

  3. [11]

    Uncertainty sets for image classifiers using conformal prediction.arXiv preprint arXiv:2009.14193, 2020

    Anastasios Angelopoulos, Stephen Bates, Jitendra Malik, and Michael I Jordan. Uncertainty sets for image classifiers using conformal prediction.arXiv preprint arXiv:2009.14193, 2020

    2009 arXiv

  4. [12]

    Distribution-free predictive inference for regression.Journal of the American Statistical Associ- ation, 113(523):1094–1111, 2018

    Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J Tibshirani, and Larry Wasserman. Distribution-free predictive inference for regression.Journal of the American Statistical Associ- ation, 113(523):1094–1111, 2018

    2018

  5. [13]

    Jaakkola, and Regina Barzilay

    Victor Quach, Adam Fisch, Tal Schuster, Adam Yala, Jae Ho Sohn, Tommi S. Jaakkola, and Regina Barzilay. Conformal language modeling, 2024

    2024

  6. [14]

    Conformal generative modeling with improved sample efficiency through sequential greedy filtering, 2025

    Klaus-Rudolf Kladny, Bernhard Schölkopf, and Michael Muehlebach. Conformal generative modeling with improved sample efficiency through sequential greedy filtering, 2025

    2025

  7. [15]

    Good-turing frequency estimation without tears.Journal of quantitative linguistics, 2(3):217–237, 1995

    William A Gale and Geoffrey Sampson. Good-turing frequency estimation without tears.Journal of quantitative linguistics, 2(3):217–237, 1995

    1995

  8. [16]

    Competitive distribution estimation: Why is good-turing good

    Alon Orlitsky and Ananda Theertha Suresh. Competitive distribution estimation: Why is good-turing good. Advances in Neural Information Processing Systems, 28, 2015

    2015

  9. [17]

    On the convergence rate of good-turing estimators

    David A McAllester and Robert E Schapire. On the convergence rate of good-turing estimators. In COLT, pages 1–6, 2000

    2000

  10. [18]

    Always good turing: Asymptotically optimal probability estimation.Science, 302(5644):427–431, 2003

    Alon Orlitsky, Narayana P Santhanam, and Junan Zhang. Always good turing: Asymptotically optimal probability estimation.Science, 302(5644):427–431, 2003

    2003

  11. [19]

    Cobb, Anirban Roy, Brian Matejek, Manoj Acharya, Daniel Elenius, Alexander M

    Ramneet Kaur, Colin Samplawski, Adam D. Cobb, Anirban Roy, Brian Matejek, Manoj Acharya, Daniel Elenius, Alexander M. Berenbeim, John A. Pavlik, Nathaniel D. Bastian, and Susmit Jha. Addressing uncertainty in llms to enhance reliability in generative ai, 2024. 16

    2024

  12. [20]

    Conformal prediction sets for deep generative models via reduction to conformal regression

    Hooman Shahrokhi, Devjeet Raj Roy, Yan Yan, Venera Arnaoudova, and Janaradhan Rao Doppa. Conformal prediction sets for deep generative models via reduction to conformal regression. arXiv preprint arXiv:2503.10512, 2025

    2025 arXiv

  13. [21]

    Api is enough: Conformal prediction for large language models without logit-access, 2024

    Jiayuan Su, Jing Luo, Hongwei Wang, and Lu Cheng. Api is enough: Conformal prediction for large language models without logit-access, 2024

    2024

  14. [22]

    Mitigating llm hallucinations via conformal abstention, 2024

    Yasin Abbasi Yadkori, Ilja Kuzborskij, David Stutz, András György, Adam Fisch, Arnaud Doucet, Iuliya Beloshapka, Wei-Hung Weng, Yao-Yuan Yang, Csaba Szepesvári, Ali Taylan Cemgil, and Nenad Tomasev. Mitigating llm hallucinations via conformal abstention, 2024

    2024

  15. [23]

    Learning conformal abstention policies for adaptive risk management in large language and vision-language models, 2025

    Sina Tayebati, Divake Kumar, Nastaran Darabi, Dinithi Jayasuriya, Ranganath Krishnan, and Amit Ranjan Trivedi. Learning conformal abstention policies for adaptive risk management in large language and vision-language models, 2025

    2025

  16. [24]

    To believe or not to believe your llm, 2024

    Yasin Abbasi Yadkori, Ilja Kuzborskij, András György, and Csaba Szepesvári. To believe or not to believe your llm, 2024

    2024

  17. [25]

    Dennis Ulmer, Chrysoula Zerva, and André F. T. Martins. Non-exchangeable conformal language generation with nearest neighbors, 2024

    2024

  18. [26]

    Conformal alignment: Knowing when to trust foundation models with guarantees, 2024

    Yu Gui, Ying Jin, and Zhimei Ren. Conformal alignment: Knowing when to trust foundation models with guarantees, 2024

    2024

  19. [27]

    Conformal prediction with large language models for multi-choice question answering, 2023

    Bhawesh Kumar, Charlie Lu, Gauri Gupta, Anil Palepu, David Bellamy, Ramesh Raskar, and Andrew Beam. Conformal prediction with large language models for multi-choice question answering, 2023

    2023

  20. [28]

    Cherian, Isaac Gibbs, and Emmanuel J

    John J. Cherian, Isaac Gibbs, and Emmanuel J. Candès. Large language model validity via enhanced conformal prediction methods, 2024

    2024

  21. [29]

    Language models with conformal factuality guarantees, 2024

    Christopher Mohri and Tatsunori Hashimoto. Language models with conformal factuality guarantees, 2024

    2024

  22. [30]

    Multi-group uncertainty quantification for long-form text generation, 2024

    Terrance Liu and Zhiwei Steven Wu. Multi-group uncertainty quantification for long-form text generation, 2024

    2024

  23. [31]

    Conformal language model reasoning with coherent factuality

    Maxon Rubin-Toles, Maya Gambhir, Keshav Ramji, Aaron Roth, and Surbhi Goel. Conformal language model reasoning with coherent factuality. InThe Thirteenth International Conference on Learning Representations

  24. [32]

    Least ambiguous set-valued classifiers with bounded error levels.Journal of the American Statistical Association, 114(525):223–234, 2019

    Mauricio Sadinle, Jing Lei, and Larry Wasserman. Least ambiguous set-valued classifiers with bounded error levels.Journal of the American Statistical Association, 114(525):223–234, 2019

    2019

  25. [33]

    Length optimization in conformal prediction

    Shayan Kiyani, George J Pappas, and Hamed Hassani. Length optimization in conformal prediction. Advances in Neural Information Processing Systems, 37:99519–99563, 2024

    2024

  26. [34]

    Le, Ed H

    Mirac Suzgun, Nathan Scales, Nathanael Schärli, Sebastian Gehrmann, Yi Tay, Hyung Won Chung, Aakanksha Chowdhery, Quoc V. Le, Ed H. Chi, Denny Zhou, and Jason Wei. Challenging big-bench tasks and whether chain-of-thought can solve them, 2022

    2022

  27. [35]

    The llama 3 herd of models, 2024

    AI@Meta. The llama 3 herd of models, 2024. 17

    2024

  28. [36]

    Training verifiers to solve math word problems, 2021

    Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, Christopher Hesse, and John Schulman. Training verifiers to solve math word problems, 2021

    2021

  29. [37]

    Mixtral of experts, 2024

    Mistral AI. Mixtral of experts, 2024

    2024

  30. [38]

    Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation, 2023

    Lorenz Kuhn, Yarin Gal, and Sebastian Farquhar. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation, 2023

    2023

  31. [39]

    Determination of sample sizes for setting tolerance limits.The Annals of Mathematical Statistics, 12(1):91–96, 1941

    Samuel S Wilks. Determination of sample sizes for setting tolerance limits.The Annals of Mathematical Statistics, 12(1):91–96, 1941

    1941

  32. [40]

    Henry Scheffé and John W. Tukey. Non-parametric estimation. i. validation of order statistics. Annals of Mathematical Statistics, 16(2):187–192, jun 1945

    1945

  33. [41]

    Saunders, A

    C. Saunders, A. Gammerman, and V. Vovk. Transduction with confidence and credibility. In Proceedings of the 16th International Joint Conference on Artificial Intelligence - Volume 2, IJCAI’99, page 722–726, San Francisco, CA, USA, 1999. Morgan Kaufmann Publishers Inc

    1999

  34. [42]

    Yaniv Romano, Matteo Sesia, and Emmanuel J. Candès. Classification with valid and adaptive coverage, 2020

    2020

  35. [43]

    Conformal prediction with neural networks

    Harris Papadopoulos, Volodya Vovk, and Alex Gammerman. Conformal prediction with neural networks. In19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007), volume 2, pages 388–395, 2007

    2007

  36. [44]

    Inductive confidence machines for regression

    Harris Papadopoulos, Kostas Proedrou, Volodya Vovk, and Alex Gammerman. Inductive confidence machines for regression. In Tapio Elomaa, Heikki Mannila, and Hannu Toivonen, editors, Machine Learning: ECML 2002, pages 345–356, Berlin, Heidelberg, 2002. Springer Berlin Heidelberg

    2002

  37. [45]

    Tibshirani, and Larry Wasserman

    Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J. Tibshirani, and Larry Wasserman. Distribution-free predictive inference for regression, 2017

    2017

  38. [46]

    Yaniv Romano, Evan Patterson, and Emmanuel J. Candès. Conformalized quantile regression, 2019

    2019

  39. [47]

    Sima Noorani, Orlando Romero, Nicolo Dal Fabbro, Hamed Hassani, and George J. Pappas. Conformal risk minimization with variance reduction, 2025

    2025

  40. [48]

    Learning optimal conformal classifiers, 2022

    David Stutz, Krishnamurthy, Dvijotham, Ali Taylan Cemgil, and Arnaud Doucet. Learning optimal conformal classifiers, 2022

    2022

  41. [49]

    Uncertainty estimation and quantification for llms: A simple supervised approach, 2024

    Linyu Liu, Yu Pan, Xiaocheng Li, and Guanting Chen. Uncertainty estimation and quantification for llms: A simple supervised approach, 2024

    2024

  42. [50]

    Semantically diverse language generation for uncertainty estimation in language models, 2024

    Lukas Aichberger, Kajetan Schweighofer, Mykyta Ielanskyi, and Sepp Hochreiter. Semantically diverse language generation for uncertainty estimation in language models, 2024

    2024

  43. [51]

    Shifting attention to relevance: Towards the predictive uncertainty quantification of free-form large language models, 2024

    Jinhao Duan, Hao Cheng, Shiqi Wang, Alex Zavalny, Chenan Wang, Renjing Xu, Bhavya Kailkhura, and Kaidi Xu. Shifting attention to relevance: Towards the predictive uncertainty quantification of free-form large language models, 2024. 18

    2024

  44. [52]

    Self-consistency improves chain of thought reasoning in language models, 2023

    Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models, 2023

    2023

  45. [53]

    Potsawee Manakul, Adian Liusie, and Mark J. F. Gales. Selfcheckgpt: Zero-resource black-box hallucination detection for generative large language models, 2023

    2023

  46. [54]

    Concentration inequalities for the missing mass and for histogram rule error.J

    David McAllester and Luis Ortiz. Concentration inequalities for the missing mass and for histogram rule error.J. Mach. Learn. Res., 4(null):895–911, December 2003

    2003

  47. [55]

    On the concentration of the missing mass, 2012

    Daniel Berend and Aryeh Kontorovich. On the concentration of the missing mass, 2012

    2012

  48. [56]

    Ohannessian

    Anna Ben-Hamou, Stéphane Boucheron, and Mesrob I. Ohannessian. Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications. Bernoulli, 23(1), February 2017

    2017

  49. [57]

    Concentration and tail bounds for missing mass

    Prafulla Chandra and Andrew Thangaraj. Concentration and tail bounds for missing mass. pages 1862–1866, 07 2019

    2019

  50. [58]

    I. J. GOOD. The population frequencies of species and the estimation of population parameters. Biometrika, 40(3-4):237–264, 12 1953

    1953

  51. [59]

    Optimal probability estimation with applications to prediction and classification

    Jayadev Acharya, Ashkan Jafarpour, Alon Orlitsky, and Ananda Theertha Suresh. Optimal probability estimation with applications to prediction and classification. In Shai Shalev-Shwartz and Ingo Steinwart, editors,Proceedings of the 26th Annual Conference on Learning Theory, vol...

    2013

  52. [60]

    Competitive distribution estimation: Why is good-turing good

    Alon Orlitsky and Ananda Theertha Suresh. Competitive distribution estimation: Why is good-turing good. In C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 28. Curran Associates, Inc., 2015

    2015

  53. [61]

    The power of absolute discounting: all-dimensional distribution estimation

    Moein Falahatgar, Mesrob I Ohannessian, Alon Orlitsky, and Venkatadheeraj Pichapati. The power of absolute discounting: all-dimensional distribution estimation. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors,Advances in ...

    2017

  54. [62]

    Ohannessian

    Elchanan Mossel and Mesrob I. Ohannessian. On the impossibility of learning the missing mass. Entropy, 21(1), 2019

    2019

  55. [63]

    Competitive distribution estimation, 2015

    Alon Orlitsky and Ananda Theertha Suresh. Competitive distribution estimation, 2015

    2015

  56. [64]

    Mean-squared accuracy of good-turing estimator

    Maciej Skorski. Mean-squared accuracy of good-turing estimator. In2021 IEEE International Symposium on Information Theory (ISIT), pages 2846–2851, 2021

    2021

  57. [65]

    McAllester and Robert E

    David A. McAllester and Robert E. Schapire. On the convergence rate of good-turing estimators. In Proceedings of the Thirteenth Annual Conference on Computational Learning Theory, COLT ’00, page 1–6, San Francisco, CA, USA, 2000. Morgan Kaufmann Publishers Inc

    2000

  58. [66]

    Improved tail bounds for missing mass and confidence intervals for good-turing estimator

    Prafulla Chandra, Aditya Pradeep, and Andrew Thangaraj. Improved tail bounds for missing mass and confidence intervals for good-turing estimator. In 2019 National Conference on Communications (NCC), pages 1–6, 2019. 19

    2019

  59. [67]

    I. J. GOOD and G. H. TOULMIN. The number of new species, and the increase in population coverage, when a sample is increased.Biometrika, 43(1-2):45–63, 06 1956

    1956

  60. [68]

    Jerzy Neyman and Egon Sharpe Pearson. Ix. on the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 231(694-706):289–337, 1933

    1933

  61. [69]

    John Wiley & Sons, 1969

    David G Luenberger.Optimization by vector space methods. John Wiley & Sons, 1969

    1969

  62. [70]

    Lecture 11: The good–turing estimate

    Ellis Weng and Andrew Owens. Lecture 11: The good–turing estimate. https://www.cs. cornell.edu/courses/cs6740/2010sp/guides/lec11.pdf, 2010. CS6740: Advanced Lan- guage Technologies, Cornell University. March 4, 2010. 20 Table of Contents A Proofs 22 A.1 Proof of Theorem 3.1 ....

    2010

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.