Unique solutions found for Plateau problems in smooth and continuous calibrations.
problem Finding unique solutions to the Plateau problem for specific types of currents.
method Boundary regularity theory for area-minimizing currents and unique continuation argument.
result Every compactly supported smoothly or continuously calibrated integral current is the unique solution to the Plateau problem for its boundary data.
We equip many non compact non simply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly non generic property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new result…
Hyperplanes, hyperspheres and hypercylinders in R n \Bbb R^n R n with suitable densities are proved to be weighted minimizing by a calibration argument. Also calibration method is used to prove a weighted minimal hypersurface is weighted area-minimizing locally.
Solves Plateau's Problem in Heisenberg group for graphs.
problem Plateau's Problem in the Heisenberg group for intrinsic graphs.
method Geometric construction and calibration argument.
result Solves Plateau's Problem under smallness conditions.
We propose nonparametric methods for individual calibration in regression models.
problem Uncertainty quantification and individual calibration for regression models.
method Nonparametric methods agnostic of the underlying model, combining nonparametric and covering number arguments.
result Established matching upper and lower bounds for calibration error.
Simple algorithm achieves distance to calibration error of at most 2√T+1.
problem Achieving distance to calibration error of O(√T) in adversarial setting.
method An extremely simple, efficient, deterministic algorithm.
result Obtains distance to calibration error at most 2√T+1.
Develops forecast hedging for improved calibration of forecasts.
problem Improving the accuracy of forecasted frequencies.
method Combines deterministic and stochastic approaches to forecast hedging.
result Ensures expected track record can only improve.
Based on a calibration argument, we prove a Bernstein type theorem for entire minimal graphs over Gauss space G n \mathbb{G}^n G n by a simple proof.
Framework calibrates ML models for risk control in various tasks.
problem Achieving statistical guarantees for model predictions.
method Reframing risk control as multiple hypothesis testing, applying statistical techniques.
result New calibration methods for multi-label classification, instance segmentation, outlier detection, and confidence set coverage.
Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping the closedness assumption on $\om$ , we get an almost hermitian manifold $(M, \om, …
For product manifolds, cohomologically calibrated affine connections are geometrically irreducible.
problem Establishing geometric irreducibility of cohomologically calibrated affine connections on product manifolds.
method Proof relies on Hodge theory and integral arguments showing non-cancellation of off-diagonal components in the Riemann curvature tensor.
result Cohomologically calibrated affine connections on product manifolds are holonomically irreducible.
The paper addresses decision making with partially calibrated forecasts, offering a robust approach.
problem Developing a decision-making strategy for forecasts that are only partially calibrated.
method A minimax approach to mapping predictions to actions, considering worst-case distributions.
result The minimax optimal decision rule is to trust predictions and act accordingly, even for partially calibrated forecasts.
The paper studies the distance from calibration in sequential prediction, proving upper and lower bounds.
problem The challenge is to measure and minimize the deviation from perfect calibration in sequential binary prediction.
method The approach involves proving an O ( T ) O(\sqrt{T}) O ( T ) upper bound and an Ω ( T 1 / 3 ) Ω(T^{1/3}) Ω ( T 1/3 ) lower bound, using structural results and minimax arguments. result An O ( T ) O(\sqrt{T}) O ( T ) upper bound on the calibration distance is achieved, with an Ω ( T 1 / 3 ) Ω(T^{1/3}) Ω ( T 1/3 ) lower bound showing the inherent difficulty. The paper extends conformal risk control to be valid with high probability over a growing calibration dataset.
problem Valid risk control over a growing calibration dataset.
method Quantile-based arguments for anytime-valid control.
result Guarantees remain valid with high probability over a cumulatively growing calibration dataset.
Minimal networks minimize length and mass in certain configurations.
problem Finding minimal networks that minimize length and mass.
method Global and local calibrations to prove minimization properties.
result Minimal networks minimize mass and interfaces in partitions.
The paper studies Pansu spheres in a sub-Riemannian 3-sphere and their area-minimizing properties.
problem The study of Pansu spheres and their area-minimizing properties in a sub-Riemannian 3-sphere.
method Calibration arguments.
result The closed half-spheres of S 0 \mathcal{S}_0 S 0 with boundary C 0 C_0 C 0 minimize sub-Riemannian area among compact C 1 C^1 C 1 surfaces with the same boundary. Study optimal healthcare spending under Epstein-Zin preferences for longevity.
problem Optimizing healthcare spending to extend longevity under Epstein-Zin preferences.
method Formulated Epstein-Zin utilities over a controllable random horizon using backward stochastic differential equations and HJB equations.
result Calibrated model accurately reflects actual mortality data and compares healthcare efficacy between countries.
Improved non-squeezing theorem for calibrated geometries proved.
problem Proving an improved non-squeezing theorem for calibrated geometries.
method Two proofs: direct and reduction to classical case.
result Established an improved non-squeezing theorem for calibrated geometries.
New method calibrates false detection rates in sequential change detection.
problem Challenges in setting time-invariant thresholds for false positives.
method Simulation-based approach to time-varying thresholds.
result Accurately targets desired expected runtime while keeping false positive rate constant.
Alternative perspective on mean-field LIBOR market model, maintaining practicality and applicability.
problem Maintaining practicality and applicability of mean-field LIBOR market model.
method Embedding mean-field model in a classical setup, controlling term rate variances over large time horizons.
result Framework can be directly applied to model term rates from SOFR, ESTR, or other nearly risk-free overnight rates.
Curves in higher dimensions are either affine or have super-Euclidean energy growth.
problem Characterizing entire conformal curves in higher-dimensional spaces.
method Blow-down argument and interaction of generalized Cauchy--Riemann equations with calibrated geometries.
result Entire conformal curves are either affine or have super-Euclidean energy growth.
The paper proves monotonicity formulas for minimal connections and their applications.
problem Understanding critical points of volume functionals in Riemannian geometry.
method Developed monotonicity formulas for minimal connections under specific conditions.
result Established vanishing theorems for minimal connections on Euclidean spaces and dDT connections on G2-manifolds.
In this paper we present a new method to compute the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility of Fouque \textit{et al.} (2011, CUP). It provides an alternative method to the singular perturbation technique presented in Hikspoors and Jaimungal (2…
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion aroun…
In this work we address the problem of argument search. The purpose of argument search is the distillation of pro and contra arguments for requested topics from large text corpora. In previous works, the usual approach is to use a standard search engine to extract text parts which are relevant to the given topic and su…
It has been suggested that adversarial examples cause deep learning models to make incorrect predictions with high confidence. In this work, we take the opposite stance: an overly confident model is more likely to be vulnerable to adversarial examples. This work is one of the most proactive approaches taken to date, as…
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.
Proposes new method for calibrating treatment effect predictors.
problem Calibrating predictors of heterogeneous treatment effects.
method Causal isotonic calibration and cross-calibration.
result Achieves fast calibration rates under weak conditions.
We use variational arguments to introduce a notion of mean curvature for surfaces in the Heisenberg group H^1 endowed with its Carnot-Carathéodory distance. By analyzing the first variation of area, we characterize C^2 stationary surfaces for the area as those with mean curvature zero (or constant if a volume-preservin…
Proposes top-label calibration and M2B framework for multiclass to binary calibration.
problem Multiclass calibration and interpretation issues.
method Top-label calibration and M2B reduction framework.
result M2B + HB achieves lower calibration error than other methods.
Study explores calibration properties in neural architectures.
problem Calibration issues in deep neural networks despite improved accuracy.
method Leverages Neural Architecture Search (NAS) to evaluate 117,702 neural networks.
result Identifies key architectural designs beneficial for calibration.
A new perfectly truthful calibration measure improves prediction reliability.
problem Improving the reliability of predictions by ensuring they are conditionally unbiased.
method Designing a simple, perfectly truthful calibration measure called ATB.
result ATB is the first perfectly truthful calibration measure in the batch setting.
New truthful calibration errors improve model ranking in multiclass prediction.
problem Non-truthful calibration errors can mislead model comparisons.
method Introduced perfectly truthful calibration errors for multiclass predictions.
result Truthful calibration errors preserve decision-theoretic dominance and stabilize model rankings.
New framework for evaluating multiclass classifier calibration.
problem Ensuring classifiers are well-calibrated for trustworthy predictions.
method Utility Calibration framework that measures calibration error relative to a utility function.
result Unified and robust interpretation of existing calibration metrics.
We propose a new framework to improve the calibration of neural networks.
problem Improving the accuracy of model confidence predictions.
method Introducing a differentiable surrogate for expected calibration error (DECE) and a meta-learning framework to optimise model hyper-parameters for validation set calibration.
result Achieved competitive performance with existing calibration approaches.
Certified calibration methods protect model confidence from adversarial attacks.
problem Adversarial attacks degrade model calibration, reducing confidence in predictions.
method Developed certified calibration methods to provide worst-case bounds on calibration under adversarial perturbations.
result Certified calibration methods produce analytic and approximate bounds for the Brier score and expected calibration error.
Meta-Cal improves post-hoc calibration of neural networks.
problem Improving the accuracy of uncalibrated neural network predictions.
method Meta-Cal uses a base calibrator and a ranking model with constraints to provide high-probability bounds.
result Meta-Cal significantly outperforms existing methods in post-hoc multi-class classification calibration.
Post-processing predictors reduces calibration errors for decision-making.
problem Predictors with low calibration error for machine learning may have high error for decision-making.
method Post-processing with ε distance to calibration adds noise to make predictions differentially private.
result Post-processing achieves O(√ε) ECE and CDL, asymptotically optimal.
A new calibration metric bridges testability and actionability.
problem Combining testability and actionable insights for forecast probabilities.
method Cutoff Calibration Error (CCE) that assesses calibration over intervals of forecasted probabilities.
result Cutoff Calibration Error is both testable and actionable.
New study on neural network calibration, linking it to generalization gap.
problem Neural networks lack strong guarantees on calibration.
method Decomposed calibration error into train set and generalization gap.
result Models with small generalization gap are well-calibrated.
A new method for multiclass calibration using vector quantization.
problem Challenges in multiclass calibration, especially in high-stakes settings.
method Compositional approach via Vector Quantization (VQ) to learn region-specific calibration maps.
result Significant improvements in local calibration with competitive global calibration and predictive performance.
This post introduces model calibration and evaluation measures, highlighting issues with a common measure.
problem Ensuring model confidence accurately reflects true outcomes.
method Explains common calibration definition, ECE, and its drawbacks.
result New evaluation measures needed for comprehensive model calibration.
Unified calibration metrics improve forecast sharpness and accuracy.
problem Improving the sharpness of probabilistic forecasts while maintaining calibration.
method Kernel-based calibration metrics that unify and generalize existing methods for classification and regression.
result Enhanced calibration, sharpness, and decision-making across various tasks.
New decision-theoretic calibration error metric improves prediction reliability.
problem Improving the reliability of predictions for decision-making.
method Proposed Calibration Decision Loss (CDL) and an efficient algorithm to achieve near-optimal CDL.
result Near-optimal CDL guarantees vanishing payoff loss from miscalibration.
Cone structures over minimal products can't be calibrated smoothly.
problem Calibrating cones over minimal products with smooth calibrations.
method Extending a key result from [Zha26], showing obstruction.
result Cone structures over minimal products cannot be calibrated by smooth calibrations.
Post-hoc calibration improves uncertainty under domain shift.
problem Improving uncertainty calibration under domain shift.
method Apply perturbations to validation set before post-hoc calibration.
result Perturbation step results in better calibration under domain shift.
Smooth calibration improves forecast reliability even with leaked information.
problem Improving forecast reliability with leaked information.
method Combining nearby forecasts to ensure smooth calibration, which can be guaranteed by deterministic procedures.
result Smooth calibration can be guaranteed by deterministic procedures even with leaked forecasts, and it yields uncoupled finite-memory dynamics in games.
Planes are the only calibrated submanifolds with flat normal bundles.
problem Characterizing submanifolds with specific geometric properties.
method Using constant-coefficient differential forms and parallel calibrations.
result Calibrated submanifolds with flat normal bundles are planes.