The paper studies half-lightlike submanifolds in Lorentzian manifolds with specific distributions.
problem Characterizing half-lightlike submanifolds in Lorentzian manifolds with conformal co-screen distributions.
method Using Cartan's formula, the authors classify half-lightlike submanifolds of Lorentzian space forms with constant screen principal curvatures.
result Screen homothetic half-lightlike submanifolds of a Lorentzian space form with a conformal co-screen distribution are locally lightlike triple product manifolds.
The concept of quasi generalized CR-lightlike was first introduced by the authors in [18]. In this paper, we focus on ascreen and co-screen quasi generalized CR-lightlike submanifolds of indefinite nearly μ-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi generalized CR-lightlike submanifold…
Defines conformal submersion with horizontal distribution and provides necessary conditions for its existence.
problem Existence and conditions for conformal submersion with horizontal distribution.
method Definition and analysis of conformal submersion with horizontal distribution, dual connections, and necessary conditions.
result Necessary and sufficient conditions for conformal submersion with horizontal distribution and geodesics.
Two new methods improve efficiency of conformal predictive systems.
problem Efficiency of conformal predictive systems in regression problems.
method Split conformal predictive systems and cross-conformal predictive systems.
result Cross-conformal predictive systems are more efficient but not guaranteed valid.
Combining Bayesian deep learning and split conformal prediction affects out-of-distribution coverage.
problem Improving out-of-distribution coverage in multiclass image classification.
method Combining Bayesian deep learning with split conformal prediction methods.
result Combining methods can reduce out-of-distribution coverage in some cases.
New method generates molecular conformations efficiently.
problem Generating accurate molecular conformations efficiently.
method Variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions.
result VonMisesNet generates conformations orders of magnitude faster than existing methods.
COP improves online conformal prediction by incorporating data patterns, leading to tighter prediction sets.
problem Overly conservative prediction sets in online conformal prediction methods when data distribution shifts.
method Conformal Optimistic Prediction (COP) incorporating estimated cumulative distribution function of non-conformity scores.
result COP produces tighter prediction sets with valid coverage guarantees, outperforming other methods.
Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then character…
The paper develops distribution-free methods for ordinal classification.
problem Constructing valid prediction sets for ordinal classification problems.
method Leveraging conformal prediction and multiple testing with FWER control.
result The proposed methods achieve satisfactory levels of marginal and class-specific conditional coverages.
New method improves predictive systems with better theoretical guarantees.
problem Constructing predictive systems with out-of-sample calibration guarantees.
method Residual Distribution Predictive Systems (RDPs) that nest conformal predictive systems and offer flexibility.
result Empirically, RDPs perform competitively with conformal predictive systems and can be implemented with various regression methods.
Affine and conformal submersions with horizontal distribution are studied in statistical manifolds.
problem Characterizing submersions and geodesics in statistical manifolds.
method Introducing conformal submersions with horizontal distribution and proving conditions for statistical manifold properties.
result Necessary and sufficient conditions for submersions and geodesics in statistical manifolds.
Exact distribution of split conformal prediction coverage found.
problem Determining the reliability of prediction sets in batch mode.
method Analysis of exchangeable data to find universal distribution of empirical coverage.
result Exact distribution of empirical coverage is universal and determined by nominal miscoverage level and calibration sample size.
Method constructs uniformly valid prediction sets across multiple distributions.
problem Uniformly valid prediction sets across multiple distributions.
method Max-p aggregation scheme and optimization programs.
result Optimal and efficient prediction sets for multiple distributions.
Novel conformal methods test out-of-distribution data with labeled outliers.
problem Testing whether new data comes from the same distribution as a reference.
method Integrative conformal p-values re-weight standard p-values using dependent side information.
result The methods outperform standard conformal p-values in simulations and applications.
Improves full conformal prediction for stochastic non-conformity measures.
problem Inability of existing conditions to guarantee full conformal prediction validity under stochastic settings.
method Introduces a new sufficient condition: Conditional Independence & Permutation Invariance in Distribution.
result Corrects the insufficient condition and provides a new sufficient condition for full conformal prediction validity.
This paper improves conformal prediction for robust interval estimation under distribution shifts.
problem Robustness of conformal prediction under distribution shifts.
method Modeling distribution shifts using Levy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations.
result Constructs robust conformal prediction intervals that remain valid under distribution shifts.
Paper develops new conformal prediction methods for sum or average of unknown labels.
problem Uncertainty quantification in joint distributions of random variables.
method Introduces novel conformal prediction methods for sum or average of unknown labels.
result Validates the proposed method for sum or average of unknown labels under permutation invariant assumptions.
New methods for distributed CP improve reliability in healthcare.
problem Post-hoc calibration of models in safety-critical domains.
method Quantile-based and histogram-based distributed conformal prediction via message passing.
result Improved reliability and coverage guarantees in decentralized settings.
New method calibrates uncertainty estimates for image classifiers without labeled data.
problem Uncertainty estimates for modern classifiers are unreliable without labeled calibration data.
method Calibrates uncertainty estimates using unlabeled examples for distribution shifts.
result Proposes a method that provides excellent uncertainty estimates under natural distribution shifts.
New classification of conformal structures with maximal G2 symmetry.
problem Classifying conformal structures with maximal G2 symmetry. method Complete local classification of homogeneous 4D split-conformal structures.
result Established a complete local classification of conformal structures with maximal G2 symmetry. Conformal Test Martingales can be 'blind' to significant changes in data distribution.
problem The converse of exchangeability does not hold, leading to potential blindness of CTMs.
method Explicit construction of A-cryptic change-point using bivariate Gaussian distributions. result CTMs can be perfectly cryptic to a significant change in marginal means.
Extend CPS to non-exchangeable settings with observation-specific permutation weights
problem Calibrated predictive bands under distributional shifts
method Encoding distributional shifts through observation-specific permutation weights
result Shift-aware predictive systems remain valid
Study evaluates conformal prediction methods for safety in vision models under shifts and long-tailed data.
problem Safety guarantees of conformal prediction methods under distribution shifts and long-tailed data.
method Empirical evaluation of post-hoc and training-based conformal prediction methods on large-scale datasets and models.
result Performance of conformal prediction methods degrades significantly under distribution shifts and long-tailed data.
Split conformal prediction provides finite-sample guarantees for black-box models without distributional assumptions.
problem Weak performance guarantees for modern predictive models under minimal assumptions.
method Develops finite-sample guarantees for split conformal prediction, a method that uses nested prediction sets and order statistics.
result The coverage of prediction sets based on order statistics stochastically dominates the Beta distribution.
For a generic distribution of rank two on a manifold M of dimension five, we introduce the notion of a generalized contact form. To such a form we associate a generalized Reeb field and a partial connection. From these data, we explicitly constructed a pseudo--Riemannian metric on M of split signature. We prove tha…
COMA combines prediction sets from multiple models for online, adaptive prediction.
problem Combining multiple prediction models with uncertainty guarantees.
method Online model aggregation using weighted voting of conformal prediction sets.
result COMA retains coverage guarantees under negative correlation assumptions.
Adaptive method for prediction sets under changing data distributions.
problem Forming prediction sets in an online setting with varying data distributions.
method Adaptive conformal inference that re-estimates the distribution shift parameter over time.
result Adaptive method achieves desired coverage frequency over long-time intervals.
CIR method constructs efficient prediction intervals with guaranteed coverage.
problem Efficiently constructing near-minimal prediction intervals with guaranteed coverage.
method Conditional Interquantile Regression (CIR) and CIR+ (enhanced version).
result Optimal balance between predictive accuracy and computational efficiency.
Extends conformal prediction for controlling expected risk of monotone loss functions.
problem Controlling expected risk of monotone loss functions.
method Generalizes split conformal prediction with coverage guarantee, extending to distribution shift, quantile risk, multiple, adversarial, and expectations of U-statistics.
result Tight up to an O(1/n) factor, with worked examples in computer vision and natural language processing. Paper proves conformal prediction works for any data distribution.
problem Quantifying risk in AI systems with non-exchangeable data.
method Developed a method to extend conformal prediction to any data distribution.
result Valid conformal prediction guarantees for any data distribution.
New method optimizes prediction set volume in conformal prediction.
problem Achieving volume optimality in conformal prediction without sacrificing coverage guarantees.
method Dynamic programming algorithm for finding near-optimal volume unions of k-intervals.
result Efficient algorithm finds unions of k-intervals with near-optimal volume for any distribution.
Study improves conformal prediction for EEG classification in healthcare, enhancing coverage.
problem Uncertainty quantification in clinical predictions, especially in distribution-shifted settings.
method Personalized calibration strategies to improve coverage of prediction sets.
result Coverage improved by over 20 percentage points with comparable prediction set sizes.
Conformal prediction offers distribution-free inference for complex models.
problem Traditional predictive inference methods are limited by assumptions about data distributions and model details.
method Conformal prediction uses symmetry assumptions and treats learning algorithms as black boxes.
result Conformal prediction provides exact finite-sample guarantees, even under limited assumptions.
ResCP uses reservoir computing to create efficient, scalable time series prediction intervals.
problem Building distribution-free prediction intervals for time series data with small sample sizes and changing distributions.
method Reservoir Conformal Prediction (ResCP) leverages reservoir computing to dynamically reweight conformity scores based on similarity among reservoir states.
result ResCP achieves asymptotic conditional coverage and is effective across diverse forecasting tasks.
A robust conformal method for set estimation using non-conformity scores.
problem Lack of robustness in standard conformal prediction methods for outliers or heavy tails.
method Robust conformal method based on non-conformity score defined as half-mass radius.
result Empirical conformal regions converge to robust population central set.
The paper defines and explores Clairaut conformal submersions in Riemannian geometry.
problem Defining and characterizing Clairaut conformal submersions.
method Analyzing necessary and sufficient conditions, deriving geometric properties, and providing examples.
result Clairaut conformal submersions have constant dilation along fibers and are harmonic.
Efficiently samples conformal boundaries in high dimensions using flows.
problem Difficulty in interpreting and using prediction sets in high-dimensional or structured output spaces.
method Flow-based approach using differentiable nonconformity scores to induce deterministic flows on the output space.
result Sampling conformal boundaries in arbitrary dimensions becomes computationally efficient and training-free.
We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in terms of the conformal weight, the Hausdorff dimension of the limit set, and the m…
Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
A method for predicting credal sets in classification tasks using conformal prediction.
problem Designing methods for learning credal set predictors in machine learning.
method Incorporates conformal prediction for predicting credal sets in classification tasks.
result Conformal credal sets are guaranteed to be valid with high probability.
Paper proposes faster adaptation to distribution shifts in online settings.
problem Violation of exchangeability assumption in evolving data environments.
method Online conformal inference with retrospective adjustment.
result Faster adaptation to distributional shifts demonstrated through numerical studies.
This paper develops methods for obtaining distribution-free prediction regions for invariant representations.
problem Distributional shifts in machine learning models.
method Invariant risk minimization and weighted conformity scores.
result Proves the effectiveness of adaptive conformal intervals for uncertainty estimation.
E-values enhance conformal prediction methods.
problem Distribution-free uncertainty quantification.
method Reformulation of conformal prediction using e-values.
result E-values offer new theoretical and practical capabilities.
Conformal prediction provides distribution-free uncertainty quantification for black-box models.
problem Uncertainty quantification for high-risk machine learning applications.
method Conformal prediction creates valid uncertainty sets without distributional assumptions.
result Sets contain the ground truth with a specified probability, e.g., 90%.
New method uses optimal transport to improve conformal prediction under distribution shifts.
problem Improving conformal prediction's coverage in non-exchangeable settings.
method Optimal transport to estimate and mitigate distribution shifts.
result Estimates and mitigates loss in coverage for arbitrary distribution shifts.
The paper reviews exchangeability and its implications for conformal prediction and rank tests.
problem Ensuring distribution-free predictive inference in machine learning and statistics.
method Explains exchangeability and its role in conformal prediction and rank tests.
result Discovers similarities between conformal prediction and rank tests based on exchangeability.
We prove that given a pseudo-Riemannian conformal structure whose conformal holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is, wrt. a local metric in the conformal class defined off a singular set, a parallel, totally lightlike distribution on the tangent bundle which contains …
Audited Conformal Prediction improves conditional coverage in pretrained models under distribution shift.
problem Uncertainty quantification for pretrained models under unknown distribution shift
method Leverages a small labeled dataset to train an audit model for marginal coverage, integrates outputs into conformal prediction framework
result Significantly higher conditional coverage than existing approaches