The conformally covariant split system generates non-constant mean curvature vacuum initial data.
problem Creating non-constant mean curvature vacuum initial data for the Einstein equations.
method Proved existence of solutions to the conformally covariant split system on compact 3-manifolds using the implicit function theorem.
result The conformally covariant split system provides non-constant mean curvature vacuum initial data for the Einstein equations.
New adaptive conformal predictive systems developed.
problem Severe restrictions on adapting predictive distributions to test objects.
method Calibrating existing predictive systems to ensure full adaptability and validity.
result Developed fully adaptive split-conformal and cross-conformal predictive systems.
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.
Filtered conformal ellipsoids for graph-native time series
problem Joint prediction sets for multivariate time series
method Filtered conformal ellipsoids
result Sharper at-target ellipsoids than static-covariance and non-filter baselines
We propose further conformal parametrizations for initial data in some modified Einstein gravity theories. Some of them give rise to conformally covariant systems.
Kandinsky conformal prediction expands conditional coverage guarantees.
problem Disparities in coverage guarantees across different subpopulations.
method Flexible handling of overlapping and fractional group memberships.
result Minimax-optimal high-probability conditional coverage bound.
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.
Study optimizes prediction intervals in conformal regression.
problem Optimizing the length of prediction intervals in conformal regression.
method Introduces EffOrt and Ad-EffOrt methodologies to minimize interval length.
result Demonstrates theoretical and empirical improvements over classical methods.
WCPS extends CPS to handle covariate shifts, providing probabilistically calibrated predictions.
problem Applying CPS to scenarios with covariate shifts.
method WCPS uses likelihood ratios between training and testing covariate distributions.
result WCPS are probabilistically calibrated under covariate shift.
We revisit the Lichnerowicz-York method, and an alternative method of York, in order to obtain some conformally covariant systems. This type of parameterization is certainly more natural for non constant mean curvature initial data.
New methods improve anomaly detection with reduced false positives.
problem Effective anomaly detection with controlled error rates.
method Leave-one-out-, bootstrap-, and cross-conformal anomaly detection methods.
result Improved anomaly detection with reduced false positives.
Improved multivariate conformal prediction by standardizing residuals.
problem Weak conditional coverage in heteroskedastic multivariate settings.
method Natural extension of univariate normalization to multivariate setting, whitening residuals and standardizing local variance.
result Standardized residuals yield asymptotic conditional coverage under certain distributions.
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.
Superintegrable systems on surfaces are classified geometrically.
problem Classifying superintegrable systems on conformal surfaces.
method Geometric structures on conformal surfaces, conformal covariant structural equations.
result Explicit set of algebraic equations defining superintegrable systems on all constant curvature surfaces.
We develop a general framework for distribution-free predictive inference in regression, using conformal inference. The proposed methodology allows for the construction of a prediction band for the response variable using any estimator of the regression function. The resulting prediction band preserves the consistency …
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
New privacy-preserving method for conformal prediction without splitting data.
problem Privacy and uncertainty quantification in data-driven decision making.
method Proposes a full-data privacy-preserving conformal prediction framework using differential privacy.
result Demonstrates improved prediction sets compared to split-based private baselines.
Optimizes data splitting for shorter conformal prediction intervals.
problem Minimizing prediction interval length while maintaining coverage.
method Theoretical framework for optimal data splitting in split conformal prediction.
result Analytical characterizations of length-optimal split ratios in various settings.
This paper improves STL inference reliability under covariate shift.
problem Ensuring correct STL formulas in real-world settings with distribution shift.
method Proposes a conformalized STL inference framework that addresses covariate shift.
result Significantly improves symbolic learning reliability at deployment time.
A method for non-parametric conditional distribution estimation using CRPS-optimal binning.
problem Non-parametric conditional distribution estimation.
method Partitioning covariate-sorted observations into bins to minimize LOO-CRPS, selecting K by K-fold cross-validation of test CRPS.
result Produces narrower prediction intervals with near-nominal coverage compared to split-conformal competitors.
Study robustness of split conformal prediction in data contamination setting.
problem Robustness of split conformal prediction under data contamination.
method Analyze split conformal prediction's performance in a contaminated data setting and propose a new method.
result Demonstrated the impact of corrupted data on prediction intervals' coverage and efficiency.
A new method identifies class-specific covariates in multi-class prediction tasks.
problem Identifying covariates specifically associated with one or more outcome classes in multi-class prediction tasks.
method Introducing multi forests (MuFs) with multi-way and binary splits to measure class-associated discriminatory ability.
result The multi-class VIM specifically ranks class-associated covariates highly, unlike conventional VIMs.
Adaptive monitoring for AI systems detects and diagnoses shifts in data distribution.
problem Continuous monitoring of AI systems to detect and address unsafe behavior.
method Weighted-conformal martingales (WCTMs) for online monitoring of AI systems.
result Improved performance over state-of-the-art baselines on real-world datasets.
Proposes a method for generating prediction intervals in dose-response models using conformal prediction.
problem Uncertainty quantification in continuous treatments for personalized healthcare decisions.
method Causal dose-response problem framed as covariate shift, using weighted conformal prediction with propensity estimation and kernel functions.
result Demonstrates the significance of covariate shift assumptions for robust prediction intervals.
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.
In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invari…
MCP extends conformal prediction to vector-valued score functions without data splitting.
problem Fixed prediction set shapes in scalar score functions limit coverage guarantees.
method MCP uses a single optimization problem for prediction set design and calibration, eliminating data splitting.
result RemMCP and RelMCP achieve target coverage with smaller or comparable prediction set sizes, reducing variance.
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.
LoBoost improves local conformal prediction for gradient-boosted trees without extra data splits.
problem Quantifying uncertainty in gradient-boosted tree predictions.
method Model-native local conformal prediction using leaf structure.
result Competitive interval quality and improved test MSE with large calibration speedups.
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
problem Improving accuracy and efficiency in nonlinear uncertainty propagation.
method Preserving mean and covariance, novel heuristics for selecting splitting direction informed by initial uncertainty and nonlinear function properties.
result Improved accuracy and efficiency in uncertainty propagation compared to existing techniques.
Develops conformalized prediction intervals for bounded continuous outcomes.
problem Predicting continuous outcomes within bounded ranges, especially when models are misspecified.
method Conformal prediction intervals based on transformation regression models, accounting for heteroscedasticity and asymmetry.
result Valid finite-sample coverage confirmed in simulations and real data applications.
Paper presents unsupervised calibration for split conformal classification.
problem Inconvenient requirement of labeled calibration samples.
method Uses unsupervised calibration samples alongside supervised training samples.
result Achieves comparable performance to supervised calibration methods.
Proposes SCD-split for CP to balance interpretability and efficiency.
problem Difficult interpretation of disconnected subintervals in CP prediction sets.
method Incorporates smoothing operations into CP framework.
result SCD-split balances interval length and subinterval number, theoretically provable.
Study of conformal limits for special opers in Lie groups.
problem Analyzing conformal limits in specific Lie groups.
method Investigates Gaiotto's conformal limit for GR-Hitchin equations. result Identifies Θ-positive opers as a new class of solutions. Characterizes Kerr spacetimes using conformal methods.
problem Understanding Kerr spacetimes through conformal transformations.
method Conformally covariant characterization approach.
result Ideal characterization of Kerr spacetimes.
New methods improve prediction regions for high-dimensional data.
problem Creating effective prediction regions for high-dimensional data.
method CD-split and HPD-split methods that combine split method and data-driven partition.
result CD-split and HPD-split converge to oracle highest predictive density set and satisfy local and asymptotic conditional validity.
This work improves multi-task regression performance using approximations of full-conformal prediction.
problem Jointly solve multiple regression tasks with better performance than individual tasks.
method Design an approximating prediction region in RKHS for full-conformal multi-task regression.
result The approximating prediction region improves upon split-conformal prediction on synthetic data.
This is the second in a series of papers on natural modification of the normal tractor connection in a parabolic geometry, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short review of the general procedure developed in [5] and then compute the prolongation …
CAOS aggregates multiple one-shot predictors for efficient uncertainty quantification.
problem Lack of principled uncertainty quantification in one-shot prediction.
method CAOS, a conformal framework that aggregates multiple one-shot predictors and uses a leave-one-out calibration scheme.
result CAOS produces smaller prediction sets with reliable coverage compared to split conformal baselines.
Researchers create a family of conformally covariant operators.
problem Developing a comprehensive set of conformally covariant operators.
method Constructing a family of conformally covariant tridifferential operators as tangential operators in the Fefferman--Graham ambient space.
result Symmetrization of ambient operators is formally self-adjoint.
Adapts conformal prediction for missing data, ensuring valid coverage.
problem Uncertainty quantification with missing covariates.
method Proposes a reweighted conformal prediction procedure for handling missing values.
result Guaranteed Marginal Coverage and Mask-Conditional Validity for general missing data mechanisms.
Paper proposes a new method for conditional coverage in conformal prediction.
problem Lack of strong conditional coverage guarantees in existing conformal prediction methods.
method Modified non-conformity score using local approximation of conditional distribution.
result Unified framework and empirical evaluations show advantage of the new method.
Two new methods generate probabilistic forecasts of individual treatment effects.
problem Generating probabilistic forecasts of individual treatment effects for risk-aware decision-making.
method Proposes CCT and CMC meta-learners combining conformal predictive systems with analytic convolution or Monte Carlo sampling.
result Achieve probabilistically calibrated predictive distributions and performant continuous ranked probability scores.
Study robustness of split conformal prediction under adversarial attacks.
problem Ensuring distribution-free coverage guarantees in CP under adversarial conditions.
method Theoretical analysis and extensive experiments on split conformal prediction robustness.
result Prediction coverage varies with calibration-time attack strength, enabling control over coverage under adversarial tests.
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. Sparse covariance estimation in the vertical-split model achieves exponential improvement over dense estimates.
problem Minimax estimation error for distributed covariance matrix estimation in the vertical-split setting.
method Elementwise s-sparsity is shown to reduce communication and sample complexity. result Minimax lower bounds for 1-sparse cross-covariance estimation are established. The article defines conditions for a manifold to be conformal to an Einstein space.
problem Determining when a manifold is conformal to an Einstein space.
method Algorithmic conditions based on the metric tensor and the Weyl endomorphism.
result General necessary and sufficient conditions for a pseudo-Riemannian manifold to be conformal to an Einstein space.
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant operators, which include the edge Laplacian and the adjacency matrix on graphs. In the …