The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.
problem Understanding the behavior of solutions near singularities in conformal geometry.
method Linear and nonlinear potential theory applied to conformal geometry problems.
result Established Huber's type theorems and Hausdorff dimension estimates for conformal geometry.
Local gradient estimates for eigenfunctions on conformal solitons improve Liouville theorems.
problem Estimating eigenfunctions on conformal solitons.
method Proving local gradient estimates for positive eigenfunctions of L-operator. result Improved Liouville theorems for Lu=0 on conformal solitons. In this paper we first use the result in [12] to remove the assumption of the L2 boundedness of Weyl curvature in the gap theorem in [9] and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…
Introduces conformal Bach flow and proves its well-posedness and backward uniqueness.
problem Analyzing the long-time behavior of conformal Bach flow.
method Establishes well-posedness and backward uniqueness; derives L2-estimates of curvatures. result Derives Shi's pointwise-estimate of derivatives of curvatures without assuming Sobolev constant bound.
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.
Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation
problem Failure probability estimation in structural reliability analysis
method Active learning framework with conformal prediction
result Improved uncertainty quantification and reliability of failure probability estimates
Paper proposes real-time VaR estimation using quantile regression forest with conformal calibration.
problem Real-time estimation of Value at Risk (VaR) in rapidly changing markets.
method Quantile regression forest trained offline, real-time VaR estimates via observed risk factors, conformalized estimator for reliability.
result The proposed method provides reliable real-time VaR estimates.
New theorem proves convergence of various discrete conformal structures to conformal maps.
problem Proving convergence of discrete conformal structures to conformal maps.
method General theorem using piecewise linear discrete conformal mappings and Riemannian barycentric coordinates.
result Discrete conformal mappings converge to conformal maps under certain conditions.
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
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.
Study local curvature estimates and existence of conformal metrics on noncompact manifolds.
problem Deriving local C0-estimates and existence of conformal metrics with prescribed curvature. method Utilizing Aviles-McOwen's result and its nonlinear extension, combined with asymptotic conditions.
result Proved existence of complete conformal metrics with prescribed curvature functions.
Paper addresses travel time tomography stability and statistical inversion.
problem Determining conformal factors of metrics from geodesic lengths.
method Established forward and inverse stability estimates; applied to Bayesian statistical inversion.
result Consistency of statistical inversion technique for travel time tomography.
Improved conformalized quantile regression for adaptive prediction intervals.
problem Lack of adaptiveness in the conformal step of conformalized quantile regression.
method Cluster explanatory variables by permutation importance and apply k conformal steps.
result Improved prediction intervals are more adaptive to heteroscedasticity.
We consider natural conformal invariants arising from the Gauss-Bonnet formulas on manifolds with boundary, and study conformal deformation problems associated to them. The key technique we used is to derive boundary C^2 estimates directly from C^0 estimates for fully nonlinear equations. The main result has appeared i…
The paper uses conformal prediction to detect railway signals with confidence.
problem Deploying deep learning models in certified systems requires accurate uncertainty estimates.
method The paper uses conformal prediction and risk control to detect railway signals.
result The conformal prediction framework provides reliable and trustworthy uncertainty estimates for model performance.
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.
We prove a conformally invariant estimate for the index of Schrödinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index in terms of its energy which is conformally invariant, and captures th…
Establishes refined singularity estimate for nonnegative n-superharmonic functions in locally conformally flat manifolds.
problem Analyzing volume growth and verifying Cohn-Vossen inequality in locally conformally flat manifolds.
method Refined singularity estimate and characterization of volume growth.
result Analytically characterizes volume growth and verifies Cohn-Vossen inequality.
Normalizing flows can now estimate densities on unknown manifolds.
problem Normalizing flows struggle with data on unknown low-dimensional manifolds.
method Conformal Embedding Flows, which combine standard flows with trainable conformal embeddings.
result Tractable density estimation on manifold-supported data is possible.
Proposes a method to estimate drug sensitivity uncertainty using deep regression forests.
problem Lack of confidence intervals in deep learning models for critical tasks.
method Uses Deep Regression Forests to estimate variance and uncertainty for drug sensitivity prediction.
result Improves efficiency and coverage of uncertainty estimates for drug sensitivity predictions.
CTI produces efficient prediction intervals with guaranteed coverage.
problem Efficient and reliable uncertainty quantification in regression.
method CTI estimates conditional density for interval length, then thresholds intervals based on this density.
result CTI achieves smaller prediction sets with guaranteed coverage compared to existing methods.
Paper accelerates conformal prediction by using approximate leave-one-out estimators.
problem Limited computational cost for conformal prediction.
method Incorporates approximate leave-one-out estimators to accelerate conformal prediction.
result ALO-based methods achieve comparable coverage and efficiency to exact methods but with significantly reduced runtime.
This work connects conformal prediction to information theory for uncertainty estimation.
problem Uncertainty estimation in machine learning models.
method Information theory applied to conformal prediction.
result Proven ways to upper bound intrinsic uncertainty using information theory.
In this article we study the short-time existence of conformal Ricci flow on asymptotically hyperbolic manifolds. We also prove a local Shi's type curvature derivative estimate for conformal Ricci flow.
New method improves conditional coverage of conformal prediction.
problem Improving conditional coverage in conformal prediction.
method Trainable transformation of conformity scores to improve conditional coverage.
result Highly adaptive to local data structure, outperforming existing methods.
Systematic review of conformal inference for treatment effect estimation.
problem Uncertainty quantification in treatment effect estimation.
method Conformal prediction methods for treatment effect estimation.
result Current state-of-the-art conformal prediction methods identified and described.
Enhances conformal prediction for better uncertainty estimates in armed conflict fatalities.
problem Lack of individual-level uncertainty estimates in existing forecasting models.
method Introduces bin-conditional conformal prediction (BCCP) to improve coverage rates across subsets of the outcome variable.
result Demonstrates improved local coverage and well-calibrated uncertainty estimates across various ranges of fatalities.
CPA framework assesses conditional validity of conformal prediction.
problem Challenges in evaluating conditional validity of conformal prediction.
method Reframes conditional coverage evaluation as a supervised learning task.
result Establishes convergence rates and proves CVI consistency.
Develops an efficient approximation for full conformal prediction regions.
problem Computing exact full conformal prediction regions is computationally infeasible.
method Generates an approximate confidence region that can be efficiently computed.
result Introduces a new notion of thickness to quantify approximation tightness.
Proposes a new model for estimating individual treatment effects.
problem Estimating individual treatment effects from observational data is challenging.
method Integrates diffusion modeling and conformal inference with propensity score and covariate approximation.
result Establishes rigorous theoretical guarantees and demonstrates competitive performance.
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.
MD-split+ creates locally valid prediction regions for complex data.
problem Localized prediction regions for complex data.
method Localized model performance-based partitioning of feature space X.
result MD-split+ creates valid prediction regions that scale to high dimensions.
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.
We extend Eardley and Moncrief's L∞ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates to…
A new method improves efficiency of conformal prediction for ensemble models.
problem Efficiently estimating uncertainty for ensemble models without distributional assumptions.
method Proposes a multivariate score function to merge prediction regions of individual models, reducing conservatism.
result Demonstrates more efficient prediction regions compared to existing methods.
Paper introduces PCP for efficient, reliable predictive inference.
problem Developing reliable predictive inference methods for target variables.
method Probabilistic conformal prediction using conditional random samples.
result PCP provides sharper predictive sets compared to existing methods.
Proposes a weighted conformal approach for cluster label uncertainty.
problem Cluster label uncertainty in unlabeled data.
method Develops a conformal inference algorithm to correct label mismatch.
result Improves confidence set size in nonlinear and high-dimensional clustering.
JANET improves time series prediction with adaptive uncertainty regions.
problem Time series data's lack of exchangeability and multi-step prediction challenges.
method Proposes JANET, a framework for joint adaptive prediction regions with controlled error rates.
result Demonstrates superior performance in multi-step prediction tasks across diverse datasets.
ST-BCP narrows the coverage gap in BCP by transforming nonconformity scores.
problem The looseness in BCP's coverage guarantee due to Markov's inequality.
method Introduces a data-dependent transformation of nonconformity scores.
result Reduces the average coverage gap from 4.20% to 1.12% on benchmarks.
VR-ConfTr reduces noise in CP training, leading to more stable and efficient model performance.
problem Improving the efficiency and stability of conformal prediction during model training.
method Variance-reduced conformal training (VR-ConfTr) that incorporates variance reduction in gradient estimation.
result VR-ConfTr achieves faster convergence and smaller prediction sets compared to existing methods.
Sharp estimate on harmonic maps at conformal points in balls.
problem Estimating harmonic maps at conformal points in balls.
method Sharp estimate on differential norm using Schwarz-Pick lemma.
result Generalizes classical Schwarz-Pick lemma and gives optimal for n≥3. The paper estimates surface diameter in conformal spaces.
problem Estimating the diameter of surfaces in conformally flat spaces.
method Using mean curvature and boundary length, the paper gives an upper bound for the intrinsic diameter.
result The result provides an a priori estimate for connected solutions of Plateau's problem and a necessary condition for the existence of such solutions.
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.
Upper bounds for Steklov eigenvalues on manifolds with boundary.
problem Investigating upper bounds for the spectrum of the Steklov-type operator on Riemannian manifolds with boundary.
method Extending the Fraser-Schoen estimate to higher Steklov eigenvalues, using relative conformal volume and isoperimetric ratio.
result Established bounds for the Steklov eigenvalues in terms of relative conformal volume and isoperimetric ratio.
New method for predicting paths of unpredictable objects with high confidence.
problem Need for dependable uncertainty estimates in motion planning with diverse unpredictable objects.
method Blend online conformal prediction, multiple time series techniques, and heteroscedasticity addressing.
result Simultaneous forecasting bands that cover entire paths with high probability.
The paper studies heat kernels on modified manifolds and bounds their properties.
problem Bounding heat kernels on modified Riemannian manifolds.
method Derives upper bounds and gradient estimates for the heat kernel of (M,ildeg). result Establishes upper bounds and gradient estimates for the heat kernel of modified manifolds.
Research uses CPS to estimate uncertainty in ML radio metric models.
problem Estimating uncertainty in machine learning models for radio metrics and path loss.
method Conformal Prediction (CP) in Conformal Predictive Systems (CPS) with diverse difficulty estimators.
result CPS models maintain high coverage and reliability across different cities.
New method improves deep learning models' uncertainty estimates.
problem Overconfidence in deep learning predictions.
method Develops a novel training algorithm using conformal inference.
result Produces more reliable uncertainty estimates without sacrificing accuracy.