Linguistic calibration improves long-form text confidence.
problem LMs hallucinate, leading to suboptimal decisions.
method Defining linguistic calibration, training framework, reinforcement learning.
result Llama 2 7B is significantly more calibrated than baselines.
New forms calibrate minimal graphs in arbitrary dimensions.
problem Calibrating minimal graphs in arbitrary codimension.
method Constructing closed forms from minimal graphs and estimating their comass.
result Conditions ensuring minimal graphs are calibrated and area-minimizing.
Study uses Lie group subgroups to identify special subspaces in calibrations.
problem Identifying calibrated subspaces in Lie groups.
method Utilizes the principal three-dimensional subgroup of a simple Lie group.
result Identifies certain special subspaces as calibrated for invariant forms.
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.
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
The paper explores various forms of calibration scores and their implications for fairness.
problem The evaluation of probabilistic predictions through calibration.
method The authors organize three grouping choices and one agglomeration of group errors, providing a framework for comparing and creating new calibration scores.
result The study demonstrates that appropriate choices of grouping can provide notions of (sub-)group or individual fairness.
We present a new bound for the worldvolume actions of branes with a Wess-Zumino term. For this we introduce a generalization of calibrations for which the calibration form is not closed. We then apply our construction to find the M-5-brane worldvolume solitons in an AdS background that saturate this bound. We show that…
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
problem Calibrating CDS spreads in the SSRD model with correlated processes.
method Asymptotic coefficient expansion to approximate solutions of nonlinear PDEs.
result Our approximation does not require uncorrelated interest rate and default intensity processes.
Temperature scaling fails for distributions with class overlaps, while Mixup improves calibration.
problem Temperature scaling's performance degrades with class overlaps, leading to poor calibration.
method Identified temperature scaling's limitations and compared it with Mixup for calibration.
result Mixup significantly outperforms temperature scaling in calibration metrics with class overlaps.
The paper explores connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
problem Exploring connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
method Starting from collections of 'Kähler 2-forms', the paper constructs canonical 4-forms and calibrated 4-planes in dimensions 8 and 16.
result Explicit formulas for canonical 4-forms ΦSpin(8) and ΦSpin(7)U(1) are derived, and their calibrated 4-planes are characterized. 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.
Simplified matrix generator resolves credit migration model calibration issues.
problem Fundamental difficulties in calibrating Markovian credit migration models.
method Simplified matrix generator and elementary ideas from differential geometry.
result Risk-neutral calibration requires volatility information and is unstable.
Every graph can be represented as a singular set of a special surface.
problem Representing any finite graph as the singular set of a compact 3D surface.
method Constructing a calibrated 3-dimensional homologically area minimizing surface with a special Lagrangian form.
result The singular set of the surface is precisely the given graph.
Study of geometric properties of almost calibrated forms on Kähler manifolds.
problem Understanding the geometry of almost calibrated (1,1) forms on compact Kähler manifolds. method Investigates the infinite dimensional Riemannian manifold structure, CAT(0) geodesic metric space, and geodesics of the space of almost calibrated forms.
result The space of almost calibrated forms is an infinite dimensional Riemannian manifold with non-positive sectional curvature and CAT(0) geodesic metric space.
In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distri…
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.
Calibrating American options is sped up using model reduction techniques.
problem Calibrating American options is computationally challenging due to their flexibility and constraints.
method Two model reduction strategies: reduced basis method and de-Americanization.
result Calibration process is significantly faster with reduced model complexity.
The paper derives closed-form approximations for mean-reverting SABR models and calibrates them to equity volatilities.
problem Calibration of mean-reverting SABR models to equity volatilities.
method Derive closed-form approximations using a CIR process for volatility, lognormal process for volatility, and CIR process for squared volatility. Calibrate to empirical volatilities using a computer algebra system.
result Calibrated mean-reverting SABR models provide excellent fits to equity volatilities with only five parameters per surface.
Given a transportation cost c:M×Mˉ→R, optimal maps minimize the total cost of moving masses from M to Mˉ. We find a pseudo-metric and a calibration form on M×Mˉ such that the graph of an optimal map is a calibrated maximal submanifold. We define the mass of space-like current…
New method calibrates classifier probabilities with guaranteed coverage.
problem Inaccurate probability estimates by classifiers in high-risk applications.
method Adaptive temperature scaling algorithm for conformal prediction.
result Improves calibration error measures and standard metrics across various tasks.
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.
Study adiabatic limits of calibrated submanifolds in Riemannian geometry.
problem Understanding the behavior of calibrated submanifolds under adiabatic limits.
method Define a 1-parameter family of forms and study their adiabatic limit, showing it is a generalized calibration.
result Adiabatic calibrated submanifolds are anisotropic minimal in the classical sense.
New findings show that not all area-minimizing surfaces are calibrated, even on complex manifolds.
problem Understanding when area-minimizing surfaces cannot be calibrated.
method Analyzing homology classes and metrics on manifolds to determine if area-minimizers are calibrated.
result Calibrated area-minimizers are non-generic, challenging the common assumption that they are typical.
The paper studies deformations of submanifolds using a new algebraic structure.
problem Deformations of submanifolds in geometric contexts.
method Introduces strongly homotopy Lie algebras to govern deformations of submanifolds.
result Deformations of submanifolds form an analytic variety under certain assumptions.
New conditions for calibrated submanifolds in Riemannian geometry.
problem Characterizing calibrated submanifolds with extrinsic geometry.
method Introducing compliancy condition and analyzing extrinsic geometry.
result Conditions for extrinsic geometry of calibrated submanifolds.
In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that …
New formula found for a unique invariant 8-form on Riemannian manifolds with Spin(9) structure.
problem Finding a new explicit algebraic formula for a unique invariant 8-form.
method Generalizing the standard Kähler 2-form expression, constructing the invariant 8-form from octonion-valued coordinate 1-forms.
result A new explicit algebraic formula for the Spin(9)-invariant 8-form. The paper studies p-harmonic functions and their conjugates, showing they converge to calibrations of laminations.
problem Behavior of q-harmonic functions and their conjugates in the limit as qo1. method Analysis of p-harmonic conjugates and their convergence to calibrations of laminations. result The laminations calibrated by the limiting p-harmonic conjugates are exactly those arising from the 1-Laplacian. This work discusses AAD for financial model calibration and its parallelization benefits.
problem Calibrating stochastic financial models using Automatic Adjoint Differentiation.
method Demonstrates the use of Automatic Adjoint Differentiation for functions in financial models and its parallelization potential.
result Theoretical and numeric results show that AAD allows perfect SIMD parallelization and is efficient.
We use AD to compute gradients for complex functionals in stochastic model calibration.
problem Computing gradients for functions involving expectations in stochastic models.
method Automatic Adjoint Differentiation and parallelization.
result Faster and easier to implement approaches for gradient computation.
New PDEs for k-harmonic maps link to calibrated fibrations.
problem Understanding k-harmonic maps and their relation to calibrated fibrations. method Analyzing two special classes of k-harmonic maps between Riemannian manifolds. result Explicit noncompact examples of the second class of maps.
We introduce obstructions to the existence of a calibrated G_2-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. …
Combining ensembles and data augmentation harms model calibration.
problem Improving model calibration and robustness with ensembles and data augmentation leads to a trade-off.
method Combining ensemble averaging and data augmentation techniques.
result Combining ensembles and data augmentation can harm model calibration.
New algorithm calibrates stochastic volatility models without errors.
problem Calibration errors in stochastic volatility models.
method Monte Carlo based LSV calibration algorithm for all models.
result Closed-form and exact calibration method with variance reduction.
Survey on calibration in machine learning, viewing it as indistinguishability.
problem Evaluating continuous probability predictions in discrete outcome settings.
method Defining and measuring calibration error through indistinguishability.
result Calibration measures quantify distinguishability between hypothesized and real-world outcomes.
Study calibrates high-dimensional binary classifiers using angle between estimator and true weights.
problem Calibrating high-dimensional binary classifiers with provable properties.
method Interpolates with a chance classifier to construct well-calibrated predictor based on angle between estimator and true weights.
result Angular calibration approach is provably well-calibrated in high dimensions, minimizing Bregman divergence.
This paper calibrates Gaussian process predictive distributions for Bayesian optimization to improve sampling decisions.
problem Lower-tail miscalibration in GP predictive distributions affects BO sampling decisions.
method Introduces goal-oriented calibration for GP predictive distributions below a threshold t. result Post-hoc method tcGP improves lower-tail calibration and BO performance.
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.
New proof of minimal vector fields on spheres using calibrations.
problem Minimal volume vector fields on spheres.
method Calibration theory applied to spheres.
result Classification of calibrations on 3-manifolds.
There has been much recent interest in application of the pool-adjacent-violators (PAV) algorithm for the purpose of calibrating the probabilistic outputs of automatic pattern recognition and machine learning algorithms. Special cost functions, known as proper scoring rules form natural objective functions to judge the…
Unified binary and multiclass margin-based classification methods.
problem No consensus on multiclass loss functions analogous to binary margin loss.
method Showed multiclass loss functions can be expressed in relative margin form.
result Extended classification-calibration result to multiclass.
The paper extends Liouville's theorem to calibrated geometries in various dimensions.
problem Extending Liouville's theorem to calibrated geometries in different dimensions.
method Analyzing Sobolev mappings and calibrations in calibrated geometries.
result Calibrations in certain dimensions have the Liouville property.
SWIFT method speeds up Heston model calibration for European options.
problem Calibrating the Heston model for European options efficiently.
method Extends SWIFT method to Heston model, simplifying gradient computation.
result Extremely fast calibration, outperforming state-of-the-art methods.
We shall obtain unobstructed deformations of four geometric structures: Calabi-Yau, HyperKähler, $\G$ and Spin(7) structures in terms of closed differential forms (calibrations). We develop a direct and unified construction of smooth moduli spaces of these four geometric structures and show that the local Torelli type …
PosCal training improves classification models by calibrating posterior probabilities.
problem Poorly calibrated posterior probabilities in classification models.
method End-to-end training procedure that directly optimizes the objective while minimizing the difference between predicted and empirical posterior probabilities.
result PosCal training achieves about 2.5% task performance gain and 16.1% calibration error reduction.
A new framework for PPLS combines noise estimation, optimization, and calibration.
problem Probabilistic PLS models need interpretable latent factors and calibrated uncertainty.
method End-to-end pipeline combining noise estimation, constrained optimization, and prediction calibration.
result Achieves near-nominal coverage and native calibrated uncertainty across benchmarks.
The paper proposes a new method to calibrate multiple computer models simultaneously.
problem Calibrating multiple computer models one at a time is inefficient.
method Developed a probabilistic framework using customized neural networks.
result Simultaneous calibration improves predictive accuracy but can be non-identifiable in high dimensions.
Introduces Lorentzian Cayley form solving geometric puzzle.
problem Solving geometric puzzle in 4D Lorentzian geometry.
method Introduces complex Cayley forms and Lorentzian Cayley form.
result Lorentzian Cayley form solves geometric puzzle.