New method quantifies classifier uncertainty, revealing large variability in performance metrics.
problem Uncertainty in classifier performance metrics due to small data sets.
method Probability model of the confusion matrix to quantify uncertainty.
result Large uncertainties in classification performance metrics can lead to misleading conclusions.
Classifies metrics on specific Lie groups.
problem Classifying Riemannian metrics on nonunimodular Lie groups.
method Automorphism classification of inner products on Lie algebras.
result Classification of metrics on 4D nonunimodular Lie groups.
New robustness metric helps select reliable classifiers.
problem Evaluating reliability of classifier predictions.
method Proposed new robustness metric for any classifier and feature type.
result Demonstrated ability to distinguish reliable from unreliable predictions.
Given a binary prediction problem, which performance metric should the classifier optimize? We address this question by formalizing the problem of Metric Elicitation. The goal of metric elicitation is to discover the performance metric of a practitioner, which reflects her innate rewards (costs) for correct (incorrect)…
We propose a novel classifier accuracy metric: the Bayesian Area Under the Receiver Operating Characteristic Curve (CBAUC). The method estimates the area under the ROC curve and is related to the recently proposed Bayesian Error Estimator. The metric can assess the quality of a classifier using only the training datase…
Classifies Einstein metrics on 4-manifolds with specific symmetry groups.
problem Classifying Einstein metrics on 4-manifolds with certain symmetry properties.
method Analyzes cohomogeneity-one Einstein metrics and uses symmetry properties.
result Locally symmetric or homothetic to the Page metric on CP2♯CP2. We introduce a new metric to evaluate corruption robustness of ML classifiers.
problem Evaluating corruption robustness of machine learning classifiers.
method We propose a test data augmentation method using minimal class separation distance to derive a robustness distance ε and a metric MSCR.
result The MSCR metric allows interpretable comparison of classifier robustness on different datasets.
Paper classifies Schouten-like metrics on 5D nilpotent Lie groups.
problem Finding Riemannian metrics with prescribed Ricci curvature.
method Introduced Schouten-like metrics and classified them on 5D nilpotent Lie groups.
result Comprehensive classification of 5D nilpotent Lie groups' Schouten-like metrics.
Study classifies special metrics on specific surfaces.
problem Classifying extremal Kähler metrics with singularities.
method Analyzes Hessian of the Curvature of the Metric on K-surfaces.
result Identifies non-CSC HCMU metrics on S{α}2 and S{α,β}2. Classifies metric lines in Engel-type groups, a step towards solving sub-Riemannian manifold problems.
problem Classifying metric lines in Engel-type groups.
method Sequence method to study metric lines in jet space.
result Classified metric lines of Engel-type groups $\Eng(n)$.
The study evaluates saliency metrics for image classifier outputs, finding inconsistencies and unreliability.
problem Inconsistencies and unreliability in saliency metrics for evaluating pixel relevance.
method Investigated existing saliency metrics, calculated and compared their consistency, and applied psychometric testing methods.
result Saliency metrics can be statistically unreliable and inconsistent, affecting comparative rankings.
This paper reviews metrics to assess AI model calibration accuracy.
problem AI model probabilities do not always match their true accuracy.
method Comprehensive review of 82 probability calibration metrics.
result Identified 4 classifier families and 1 object detection family of metrics.
The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.
problem Investigating compatibility conditions on spherically symmetric Finsler metrics.
method Using the inverse problem of calculus of variations, the paper focuses on Landsberg and Berwald types.
result All Landsberg spherically symmetric manifolds in higher dimensions are either Riemannian or have specific geodesic spray formulas.
The paper classifies specific types of metrics on 5D Lie groups.
problem Classifying (α,β)-metrics on five dimensional nilpotent Lie groups. method Left-invariant metrics and vector fields classification.
result Geometric properties of classified metrics.
Classifies Riemannian manifolds with specific torsion properties.
problem Classifying Riemannian manifolds with parallel, non-twistorial torsion.
method Classifies complete simply connected Riemannian manifolds with a metric connection having parallel torsion, non-zero vectorial component, and zero twistorial component.
result Classifies complete simply connected Riemannian manifolds with the specified torsion properties.
The article classifies G2-structures with conformally flat metrics.
problem Identifying G2-structures with specific geometric properties.
method Classifying closed G2-structures with conformally flat metrics.
result Any closed G2-structure with conformally flat metric is locally equivalent to one of three explicit examples.
Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.
problem Classifying and understanding CKY 2-forms on 5D Lie groups.
method Classification and analysis of 5D metric Lie algebras with CKY tensors.
result First examples of CKY 2-forms on metric Lie algebras without Sasakian structures.
We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification acc…
Classifies self-dual almost-Kähler 4-manifolds, proving uniqueness up to rescaling.
problem Classifying self-dual almost-Kähler four-manifolds.
method Using LeBrun's result and properties of Ricci tensor, the authors classify manifolds of different types.
result Any self-dual almost-Kähler metric on CP2 is the Fubini-Study metric up to rescaling. EAST aligns neural network classifiers with user-defined evaluation metrics.
problem Mismatch between neural network training and evaluation metrics leads to suboptimal performance.
method EAST uses dynamic thresholding, soft-set confusion matrix, and annealing to align neural network predictions with target evaluation metrics.
result EAST improves alignment between training objectives and evaluation metrics, outperforming existing methods.
The paper classifies structures on specific Lie groups.
problem Classifying almost contact metric structures on Lie groups.
method Investigation of left-invariant structures on three-dimensional non-unimodular Lie groups.
result Classification of left-invariant almost contact metric structures.
We develop techniques for classifying the nonnegatively curved left-invariant metrics on a compact Lie group G. We prove rigidity theorems for general G and a partial classification for G=SO(4). Our approach is to reduce the general question to an infinitesimal version; namely, to classify the directions one can move a…
Study locally conformally balanced metrics on specific Lie algebras.
problem Characterize and classify locally conformally balanced metrics on almost abelian Lie algebras.
method Characterizations and classifications based on specific properties of Lie algebras.
result Classification of six-dimensional almost abelian Lie algebras with locally conformally balanced metrics.
This paper visualizes uncertainty in classifier performance metrics.
problem Overemphasis on model performance metrics risks overlooking uncertainty.
method Developed visualizations of confusion matrix metric distributions.
result Uncertainty in performance metrics can overshadow model differences.
New metrics improve performance in imbalanced classification problems.
problem Established metrics favor classifiers ignoring minority classes.
method Introduce robust modifications of F-score and MCC.
result TPR is bounded away from 0 in imbalanced settings.
PolyGraph Discrepancy improves graph generative model evaluation.
problem Inability of existing metrics to provide an absolute performance measure and comparability across different graph descriptors.
method Approximates Jensen-Shannon distance using binary classifiers trained to distinguish between real and generated graphs.
result PGD provides a more robust and insightful evaluation compared to MMD metrics.
Classifies metrics with specific curvature properties on a ball.
problem Classifying conformal metrics with constant σk curvature and constant boundary mean curvature. method Uses the Obata-Escobar argument to classify metrics on the upper hemisphere.
result Extends a result of Escobar for k=1 to include positive and negative cones. The paper classifies quasi-Einstein 3-manifolds and their properties.
problem Classifying compact locally homogeneous non-gradient quasi-Einstein 3-manifolds.
method Analyzing quotient spaces of Lie groups and using properties of quasi-Einstein metrics.
result Identifies conditions for the existence of nontrivial quasi-Einstein metrics.
The study classifies metrics with vanishing curvature on complex manifolds.
problem Understanding metrics with vanishing curvature on complex manifolds.
method Analyzing Hermitian metrics, pluriclosed metrics, and metrics with real bisectional curvature.
result Hermitian metrics with vanishing curvature are Kähler and conformally balanced.
Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.
problem Classifying Lorentzian symmetric spaces with Einstein-Yang-Mills properties.
method Classification based on invariant metric connections and diagonal metrics.
result Four-dimensional symmetric spaces with nontrivial isotropy groups are classified.
Study classifies metrics on anti-de Sitter spacetime with specific symmetries.
problem Classifying metrics with specific symmetries on anti-de Sitter spacetime.
method Used classification techniques for pseudo-Riemannian and almost contact metric structures.
result Obtained classifications of homogeneous structures on anti-de Sitter spacetime.
The paper classifies geodesic orbit spaces with simple isotropy groups.
problem Classifying geodesic orbit spaces with simple isotropy groups.
method Classifying G-naturally reductive and G-geodesic orbit metrics on M. result Classification of geodesic orbit spaces with simple isotropy groups.
The paper classifies contact 3-manifolds with critical metrics and connects entropy to optimization.
problem Classifying contact 3-manifolds with critical metrics and understanding their entropy.
method Critical metrics optimization and entropy analysis.
result Anosov contact metrics' optimization is linked to Reeb dynamics and entropy.
The paper classifies Landsberg metrics on a 2D Lie group and proves a conjecture.
problem Classifying Landsberg metrics on a 2D Lie group.
method Analyzing left invariant conic Finsler metrics on a 2D non-Abelian Lie group.
result Any left invariant conic Landsberg metric on G must be Berwald. Classifies Einstein metrics on R^4 with Heisenberg symmetry, finding incomplete Ricci-flat metrics and two complete negative-curvature examples.
problem Classifying Einstein metrics on R4 with Heisenberg symmetry. method Invariant under a four-dimensional group of isometries including the Heisenberg group, analyzing Ricci-flat and negative-curvature metrics.
result Found two complete negative-curvature examples: complex hyperbolic metric and one-loop deformed universal hypermultiplet.
The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.
In this paper, we study an important class of Finsler metrics--square metrics. We give two expressions of such metrics in terms of a Riemannian metric and a 1-form. We show that Einstein square metrics can be classified up to the classification of Einstein Riemannian metrics.
Classifies Heisenberg-invariant self-dual Einstein manifolds with explicit metrics.
problem Classifying self-dual Einstein manifolds invariant under Heisenberg group actions.
method Explicit construction of metrics and analysis of completeness.
result Einstein constants can vary and solutions exist for non-zero Ricci curvature.
We classify left invariant metrics with nonnegative curvature on SO(3) and U(2).
This paper introduces metrics to evaluate robustness of neural networks to natural adversarial examples.
problem Measuring robustness of neural networks to natural adversarial examples.
method Proposes latent space performance metrics based on generative models.
result Latent adversarial perturbations are often perceptually small and associated with classifier accuracy.
We classify the contact metric 3-manifolds that satisfy ||gradλ||=1 and \nabla_{ξ}τ=2aτφ.
Unified framework for classifying Sasakian, K-contact, and (κ, μ)-manifolds.
problem Classifying and understanding different types of contact metric manifolds.
method Investigating metric structures on symplectizations and proving the existence of a unique metric symplectization.
result Unified framework for classifying Sasakian, K-contact, and (κ, μ)-manifolds.
Study classifies biharmonic and harmonic homomorphisms between specific Lie groups.
problem Classifying biharmonic and harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups.
method Classification based on left invariant Riemannian metrics.
result Classification of biharmonic and harmonic homomorphisms between specific Lie groups.
Classifies all flat Riemannian metrics on the plane, including complete and incomplete cases.
problem Classifying all flat Riemannian metrics on the plane.
method Examined conformal metrics of the form \( e^{2\varphi}g_0 \) where \( \varphi \) is a harmonic function.
result All flat Riemannian metrics on the plane, including complete and incomplete cases, arise from Riemann surfaces.
Study on nilpotent Lie algebras with specific metrics.
problem Classifying nilsolitons in nilpotent Lie algebras.
method Classification up to dimension 9, reduction to linear and polynomial equations.
result Complete classification of nice nilsolitons in various dimensions and signatures.
Extracts fairness truth from classifiers using an oracle.
problem Fairness in classification algorithms without context.
method Uses fairness oracle to learn underlying fairness truth.
result Extracts metric fairness from classifiers.
We study consistency of learning algorithms for a multi-class performance metric that is a non-decomposable function of the confusion matrix of a classifier and cannot be expressed as a sum of losses on individual data points; examples of such performance metrics include the macro F-measure popular in information retri…
Classifies Killing forms of arbitrary degree on specific nilpotent Lie groups.
problem Classifying Killing forms of arbitrary degree on specific Lie groups.
method Analyzing left-invariant Killing forms on simply connected 2-step nilpotent Lie groups with left-invariant metrics.
result Classified Killing forms when center is at most 2-dimensional.