First proper learning algorithm for Gaussian halfspaces with matching sample and computational complexity.
problem Agnostically learning halfspaces under Gaussian distribution.
method First proper learning algorithm with matching sample and computational complexity.
result First proper learning algorithm for agnostically learning halfspaces under Gaussian distribution with matching sample and computational complexity.
Study on proper learning under relaxed worst-case robust loss for VC classes.
problem Proper adversarially robust PAC learning under relaxed worst-case robust loss.
method Introduced a family of robust loss relaxations and showed their effectiveness for proper learnability.
result VC classes are properly PAC learnable with sample complexity close to standard PAC learning setup.
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.
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.
Proper learning is possible with labeled data, but unlabeled data can improve performance.
problem Problems that can only be learned improperly, like multiclass classification.
method Distributional regularization and worst-case performance evaluation.
result Proper learnability is possible under certain conditions involving unlabeled data.
New binary classification techniques help multiclass classification by aggregating proper learners.
problem Multiclass classification faces a properness barrier that prevents optimal learning by proper learners.
method Aggregations of proper binary learners, generalized to multiclass settings, achieve optimal sample complexity.
result Optimal binary learners can achieve sample complexity $O\left(\frac{d_G + \ln(1 / δ)}ε
ight)$ for classes with finite Graph dimension dG. Paper characterizes classes for which optimal sample complexity can be achieved by proper learning algorithms.
problem Characterizing classes for which optimal sample complexity can be achieved by proper learning algorithms.
method Identifying dual Helly number and its relation to proper learning algorithms.
result Optimal sample complexity can be achieved by proper learning algorithms for classes with bounded dual Helly number.
New insights into learning from only positive examples.
problem Characterizing proper learning from positive-only samples.
method Introducing a new combinatorial condition for proper positive-only learning.
result Proper positive-only learning is characterized by finite VC dimension and uniform exterior separability.
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.
Optimizing proper loss yields calibrated models under specific conditions.
problem Understanding when optimizing proper loss functions leads to calibrated predictions.
method Local optimality condition and Lipschitz functions.
result Predictors with local optimality are nearly calibrated and nearly locally optimal.
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.
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.
Optimal multiclass U-calibration error found to be Θ(√KT).
problem Online multiclass U-calibration with low regret for all bounded proper losses.
method Follow-the-Perturbed-Leader algorithm and lower bound construction.
result Optimal U-calibration error is Θ(√KT).
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…
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.
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.
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…
Classifies π1-injective maps between non-compact surfaces.
problem Characterizing maps with injective fundamental groups.
method Proper homotopy classification of maps.
result All π1-injective proper maps are classified. Study on learning halfspaces under adversarial perturbations, finding computational hardness.
problem Learning halfspaces in the presence of adversarial noise.
method Introduced an efficient learning algorithm and proved a nearly matching computational hardness result.
result The L∞ perturbations case is provably computationally harder than 2≤p<∞. We show that immersed minimal surfaces of R3 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…
In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar Kähler metric on a compact Kähler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates needed, but rather there are necessary modifications adapted to th…
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.
The paper introduces new measures for quantifying uncertainty in machine learning.
problem Uncertainty representation and quantification in machine learning.
method Proper scoring rules for aleatoric and epistemic uncertainty quantification.
result Established a natural bridge between credal set and second-order distribution representations of uncertainty.
Proposes measures for uncertainty quantification using proper scoring rules.
problem Uncertainty quantification for prediction tasks.
method Decomposes proper scoring rules into divergence and entropy components, tailoring uncertainty quantification to specific tasks.
result Flexibility in uncertainty quantification improves performance in selective prediction and active learning.
We study learning problems involving arbitrary classes of functions F, distributions X and targets Y. Because proper learning procedures, i.e., procedures that are only allowed to select functions in F, tend to perform poorly unless the problem satisfies some additional structural property (e.g., that F is co…
Improving Bayesian filtering with strictly proper scoring rules
problem Bayesian filtering of partially and noisily observed dynamical systems
method Proper scoring ensemble filter (PSEF)
result Accurate approximation of challenging filtering distributions
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.
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.
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.
Critiques binary classification evaluation methods, advocating for proper scoring rules.
problem The dominance of top-K metrics and fixed-threshold evaluations in machine learning.
method Introduces a decision-theoretic framework mapping evaluation metrics to their use cases, and implements a clipped Brier score variant.
result Demonstrates the clinical utility of proper scoring rules through a Python package, exttt{briertools}.
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.
Authors create stable proper biharmonic maps from unit ball to spheres.
problem Constructing stable proper biharmonic maps from compact domains.
method Established second variation formula of bienergy, examined stability of previously constructed maps.
result Existence of an explicit family of stable proper biharmonic maps to Euclidean spheres.
Reduces constructing multiplicative connections to simpler tasks.
problem Constructing multiplicative connections on proper Lie groupoids.
method Reduction to simpler tasks involving proper and regular Lie groupoids.
result Simpler methods for constructing multiplicative connections.
Proper actions on bornological spaces are characterized with compatible coarse structures.
problem Characterizing proper actions on bornological spaces.
method Proving the existence of compatible coarse structures for proper actions.
result Bornological spaces admit compatible coarse structures for proper actions.
New method constructs proper affine actions of groups in higher dimensions.
problem Finding proper affine actions of discrete groups in higher-dimensional spaces.
method Higher strip deformations and Margulis invariant for properness.
result Affine actions of convex cocompact groups and virtually free groups are constructed properly.
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.
Proves existence of proper solutions for inverse mean curvature flow.
problem Existence of proper solutions for inverse mean curvature flow.
method Proves existence theorem assuming non-degeneracy conditions on isoperimetric profile.
result No curvature assumption in existence theorem.
In this paper we prove that every proper Lie groupoid admits a desingularization to a regular proper Lie groupoid. When equipped with a Riemannian metric, we show that it admits a desingularization to a regular Riemannian proper Lie groupoid, arbitrarily close to the original one in the Gromov-Hausdorff distance betwee…
Study proper actions of Lie groups on symmetric spaces, finding rigidity results and Hurwitz-Radon numbers.
problem Proper actions of non-compact semisimple Lie groups on pseudo-Riemannian symmetric spaces.
method Analysis of symmetric spaces and rigidity results.
result Any connected non-compact semisimple Lie group acting properly on these spaces must be globally isomorphic to Spin(n,1) up to compact factors. We prove that every bordered Riemann surface admits a complete proper holomorphic immersion into a ball of C^2, and a complete proper holomorphic embedding into a ball of C^3.
First we show that a curvature-adapted proper complex equifocal submanifold is a principal orbit of a Hermann type action under certain condition. Next we show that a proper complex equifocal submanifold is curvature-adapted under certain condition.
In this paper, using the framework of equivariant differential geometry, we study proper SO(p+1)×SO(q+1)-invariant biconservative hypersurfaces into the Euclidean space Rn (n=p+q+2) and proper SO(p+1)-invariant biconservative hypersurfaces into the Euclidean space Rn (n=p+2). Mo…
Study shows improper learning can outperform proper learning in misspecified models.
problem Misspecification in probabilistic prediction models.
method Investigates the performance of proper and improper learning strategies in misspecified models.
result Improper learning can achieve lower regret compared to proper learning, especially in high-dimensional settings.
Proper proximality proved for various groups on non-positive curvature spaces.
problem Proper proximality of groups acting on non-positive curvature spaces.
method Established proper proximality for groups acting on CAT(0) spaces and hierarchically hyperbolic groups. result Proper proximality of many groups including mapping class groups and subgroups of curve graphs.
In [5] I solved the Thom's conjecture that a proper Thom map is triangulable. In this paper I drop the properness condition in the semialgebraic case and, moreover, in the definable case in an o-minimal structure.
In this paper, we study Mabuchi metrics on Fano manifolds. We prove that Mabuchi metrics exist if the modified Ding functional is proper modulo a reductive subgroup of its automorphism group. On the other hand, the inverse that Mabuchi metrics implies the properness is obtained by using Darvas-Rubinstein's properness p…