Paper analyzes proper losses and their performance in machine learning tasks.
problem Understanding the performance of estimators and forecasters in machine learning tasks.
method Analyzes surrogate regret and convergence rates for strictly proper losses.
result Strongly proper losses achieve the optimal convergence rate.
Estimates proper calibration errors and refinement terms in probabilistic predictions.
problem Lack of a general estimator for proper calibration errors and refinement terms with known statistical properties.
method Proposes a method for consistent, asymptotically unbiased estimation of proper calibration errors and refinement terms.
result Proves the relation between refinement and f-divergences, implying information monotonicity in neural networks.
New method uses GANs and proper scoring rules for robust scatter estimation.
problem Robust scatter estimation in statistics.
method General learning via classification framework based on proper scoring rules.
result Proposed robust scatter estimators achieve minimax rate under Huber's contamination model.
The paper explores proper actions and their relation to representation theory, with new quantitative methods.
problem Understanding proper actions and their connection to representation theory.
method Geometric criteria, sharpness measure, and dynamical volume estimates.
result New quantitative methods have established temperedness criteria for unitary representations.
Improves model calibration for deep neural networks using proper scores.
problem Calibration errors in deep neural networks are often biased and inconsistent.
method Introduces proper calibration errors related to proper scores.
result Demonstrates the superiority of proper scores over common estimators.
Paper develops proper, lower-bounded losses for weakly supervised classification.
problem Weakly supervised classification with corrupted labels.
method Representation theorem for proper losses, derived condition for lower-boundedness, generalized logit squeezing.
result Proper and lower-bounded losses for weak-label learning.
A novel framework quantifies uncertainty using proper scores for various tasks.
problem Uncertainty quantification in machine learning for reliable applications.
method Proposes a general framework based on proper scores for epistemic, aleatoric uncertainty, and model calibration.
result Achieves state-of-the-art uncertainty estimation for large language models and generative models.
The article reviews scoring rules for estimating and evaluating forecasts.
problem Evaluating probabilistic forecasts and estimating probability distributions.
method Mathematical foundations and characterization of scoring rules.
result Important families of scoring rules and their applications in statistics and machine learning.
We study proper losses for discrete generative models without knowing the target distribution.
problem Evaluating generative models in the discrete setting without direct access to the target distribution.
method Define and construct black-box proper losses using statistical estimation theory.
result Black-box proper losses must be of polynomial form and involve more samples than the polynomial degree.
This work introduces a bias-variance decomposition for proper scores, improving uncertainty estimation in predictive models.
problem Reliable uncertainty estimation for predictions in safety-critical applications, especially under domain drift.
method Developed a general bias-variance decomposition for proper scores, introducing the Bregman Information as the variance term.
result The decomposition provides novel formulations for different predictive tasks, including classification and model ensembles.
Paper extends Calabi's extremal metric existence to compact Kähler manifolds.
problem Existence of Calabi's extremal metric on compact Kähler manifolds.
method Adapting recent breakthroughs on constant scalar Kähler metrics to extremal case, proving properness of modified Mabuchi energy.
result Existence of extremal metric with extremal vector V V V if and only if modified Mabuchi energy is proper. Conditional forecasts improve performative prediction accuracy.
problem Performative predictions undermine standard forecasting methods.
method Condition forecasts on covariates to make them forecast-invariant.
result Proper scoring rules fail under conditioning, but two solutions are identified.
Estimates uncertainty in bounding box regression for object detection.
problem Reliable deployment of deep object detectors in safety-critical tasks.
method Training variance networks with energy score as a proper scoring rule.
result Energy score leads to better calibrated and lower entropy predictive distributions.
Sharp curvature estimates for expanding Ricci solitons in various dimensions.
problem Estimating curvature bounds for expanding Ricci solitons.
method Sharp lower and upper bounds derived for scalar curvature under specific conditions.
result Sharp curvature estimates provided for expanding Ricci solitons in dimensions three and four.
In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically consistent forecasts. Furthermore, a mathematical characterization of the proper…
We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determ…
We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian is far from zero near the boundary, and the proof is mainly based on an almost complex analogue of the scaling method. We also establish a link betwee…
New method for accurately predicting linear dynamical systems.
problem Forecasting and estimating system matrices of linear dynamical systems.
method Non-convex polynomial optimization approach with global convergence guarantee.
result Global convergence of numerical solutions to a least-squares estimator.
Extends loss function analysis to infinite dimensions for better machine learning.
problem Difficulty in separating machine learning problem study from loss function properties.
method Generalizes proper-composite representation to infinite dimensions, characterizing canonical link.
result Simple characterisation of canonical link in infinite dimensional setting.
The paper disproves the properness conjecture for higher-dimensional minimal hypersurfaces.
problem Properness of complete minimal hypersurfaces in higher dimensions.
method Chord-arc estimates and gluing techniques.
result Construction of a complete, improperly embedded minimal hypersurface in R n + 1 \mathbb{R}^{n+1} R n + 1 for every n ≥ 3 n\ge 3 n ≥ 3 . Improves observation-driven filters using proper scoring rules for better parameter estimation.
problem Improves parameter estimation in observation-driven filters.
method Replaces likelihood score with negative parameter derivative of a proper scoring rule.
result Establishes consistency and asymptotic normality for estimation.
We extend the estimate obtained in [1] for the mean curvature of a cylindrically bounded proper submanifold in a product manifold with an Euclidean space as one factor to a general product ambient space endowed with a warped product structure.
A new method learns proper multiclass losses and probabilities.
problem Learning proper multiclass losses for complex classification tasks.
method Extends monotonicity to multiclass problems using convex functions.
result Consistently outperforms natural multiclass baseline on up to 1,000 class datasets.
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process is uncorrelated with its complex conjugate. This assumption is a good model of th…
Survival regression method improves log-likelihood scores.
problem Improper scoring rules in survival regression models.
method SurvivalMonotonic-net (SuMo-net) with monotonic neural networks.
result SuMo-net achieves state-of-the-art log-likelihood scores.
New concept of proper-calibeating extends classic calibrated forecasts to proper scoring rules.
problem Defining and extending calibrated forecasts to proper scoring rules.
method Extending the concepts of calibrated and calibeating forecasts to proper scoring rules and proving their properties.
result Proper-calibration always implies calibration, but proper-calibeating does not necessarily imply calibeating.
We show that a projective manifold is stable if and only if the Mabuchi energy is proper on the space of algebraic metrics. We show that stability implies finite automorphism group.
This paper explores how to choose scoring rules for estimating properties with parametric assumptions.
problem Indirect elicitation of properties with parametric assumptions.
method Developed a framework for choosing proper scoring rules for indirect elicitation, considering constraints and optimal solutions.
result The optimal estimation of the target property changes monotonically with the increase of each weight, and often setting some weights as zero yields the best configuration.
Unified framework for estimating density ratios across multiple distributions.
problem Binary density ratio estimation for multiple distributions.
method Unified framework based on Bregman divergence minimization.
result Generalization of binary DRE methods to multiple distributions.
New method for simplifying knots with specific properties.
problem Understanding knots with a specific unknotting number.
method Derive and apply the Montesinos trick for proper rational tangle replacement.
result Prove that knots with proper rational unknotting number one are prime and classify certain types.
We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder B ( r ) × R ℓ B(r)\times\R^{\ell} B ( r ) × R ℓ in a product Riemannian manifold N n − ℓ × R ℓ N^{n-\ell}\times\R^{\ell} N n − ℓ × R ℓ . It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space canno…
The paper estimates heights of constant mean curvature graphs in specific spaces.
problem Estimating heights of constant mean curvature graphs in N i l 3 \mathrm{Nil}_3 Nil 3 and P S L ~ 2 ( R ) \widetilde{PSL}_2(\mathbb{R}) P S L 2 ( R ) . method Height estimates for compact, constant mean curvature graphs in N i l 3 \mathrm{Nil}_3 Nil 3 and P S L ~ 2 ( R ) \widetilde{PSL}_2(\mathbb{R}) P S L 2 ( R ) . result Announced a structure-type result for proper graphs defined on relatively compact domains.
We derive a precise estimate on the volume growth of the level set of a potential function on a complete noncompact Riemannian manifold. As applications, we obtain the volume growth rate of a complete noncompact self-shrinker and a gradient shrinking Ricci soliton. We also prove the equivalence of weighted volume finit…
Proper Lie groupoids have real analytic structures.
problem Finding analytic structures for proper Lie groupoids.
method Demonstrating the existence of a compatible real analytic structure.
result Proper Lie groupoids have real analytic structures.
Local curvature estimate for stationary solutions in Einstein field equations.
problem Understanding stationary solutions to Einstein field equations with specific conditions.
method Deriving a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations.
result Any stationary geodesically complete solution with vanishing Poynting vector and proper coupling constants is flat.
We give sharp sectional curvature estimates for complete immersed cylindrically bounded m m m -submanifolds φ : M → N × R ℓ φ:M\to N\times\mathbb{R}^{\ell} φ : M → N × R ℓ , n + ℓ ≤ 2 m − 1 n+\ell\leq 2m-1 n + ℓ ≤ 2 m − 1 provided that either φ φ φ is proper with the second fundamental form with certain controlled growth or M M M has scalar curvature with strong quadratic decay. This l…
New examples of austere submanifolds and hypersurfaces with specific curvature properties.
problem Local classification of proper Dupin hypersurfaces.
method Construction of austere submanifolds in unit spheres.
result Found three irreducible proper Dupin hypersurfaces with 5 distinct principal curvatures.
Classifies π 1 π_1 π 1 -injective maps between non-compact surfaces.
problem Characterizing maps with injective fundamental groups.
method Proper homotopy classification of maps.
result All π 1 π_1 π 1 -injective proper maps are classified. Study Mabuchi metrics on Fano manifolds proving their existence and properness.
problem Existence and properness of Mabuchi metrics on Fano manifolds.
method Prove existence using properness of modified Ding functional and inverse implication.
result Establish criterion for Mabuchi metrics existence on Fano group compactifications.
The paper establishes curvature estimates for solitons in higher dimensions.
problem Curvature estimates for steady and expanding solitons in higher dimensions.
method Curvature estimates using gradient Ricci solitons and integral estimates.
result Curvature operator decays at specific rates for different cases of solitons.
We show that immersed minimal surfaces of R 3 \mathbb{R}^{3} R 3 with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map is injective the whole surface is a wide component. Prior to these results it wa…
Optimal learning procedure for arbitrary function classes.
problem Learning arbitrary function classes without structural properties.
method Unrestricted learning procedure that selects functions outside given class.
result Optimal sample complexity for arbitrary function classes.
Non-proper surface group action on product of trees found.
problem Proper surface group action on product of trees proposed, but not proper.
method Demonstrated non-properness of the surface group action.
result Surface group action on product of trees is not proper.
Analytic linearization and holomorphic extensions for proper groupoids.
problem Analytic linearization and holomorphic extensions of proper groupoids.
method Establish analytic linearization around invariant submanifolds and apply to holomorphic extensions.
result Proper groupoids admit holomorphic extensions.
Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.
problem Classifying non-linear proper Fredholm maps between Hilbert spaces.
method Using stable homotopy groups of spheres to classify maps up to proper homotopy.
result Determines the non-trivial kernel of the map from stable homotopy groups to non-linear proper Fredholm maps.
First example of open manifold with positive Ricci curvature and non-proper Busemann function.
problem Counterexample to Busemann function properness in open manifolds with nonnegative Ricci curvature.
method Provided an open manifold with positive Ricci curvature and non-proper Busemann function.
result First example of open manifold with positive Ricci curvature and non-proper Busemann function.
A study of proper affine vector fields in plane symmetric static space-times by using the rank of the Rieman matrix and holonomy. Studying proper affine vector fields in each case, It is shown that the special class of the above space-times admit proper affine vector fields.
Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.
problem Estimating the essential spectrum of minimal submanifolds.
method Using volume growth to bound the bottom of the essential spectrum.
result Improved essential spectrum estimate for minimal submanifolds.