The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All metrics (resp. transports) consistent with a given transport (resp. metric) are e…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “consistency metric”
CCE improves anomaly detection metrics by measuring both confidence and consistency.
problem Existing anomaly detection metrics lack discriminative power, hyperparameter dependency, and robustness to perturbations.
method CCE uses Bayesian estimation to quantify uncertainty and constructs global and event-level confidence and consistency scores.
result CCE demonstrates strict boundedness, robustness, and linear time complexity.
We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting any such learner, making it an "optimistically universal" Bayes-consistent learner. This is the first learning algorithm known to e…
The paper establishes conditions for Bayesian consistency in supremum metric.
problem Ensuring Bayesian consistency in the supremum metric.
method Using a triangle inequality and weak convergence, the paper establishes conditions for Bayesian consistency.
result Demonstrates supremum consistency with weaker conditions than previously used.
New algorithm learns mappings between metric spaces, achieving strong consistency.
problem Learning mappings between metric spaces with unbounded loss.
method Metric medoids and semi-stable compression.
result Strong Bayes-consistency for topologically separable spaces and bounded labels.
Consistent algorithms for multiclass learning with complex metrics and constraints.
problem Learning with complex performance metrics and constraints.
method General framework for designing consistent algorithms by viewing the problem as an optimization over feasible confusion matrices.
result Rates of convergence to the optimal (feasible) classifier, showing asymptotic consistency.
Estimates means in metric spaces using quantization.
problem No practical estimator for Fréchet means in all metric spaces.
method Introduced estimators based on random quantization and data-driven partitioning.
result Universal consistency of estimators across separable metric spaces and Banach spaces.
Universal consistency and rates of convergence of multiclass prototype algorithms in metric spacescs.LG
Prototype rules simplify multiclass classification in metric spaces, achieving consistency and reduced complexity.
problem Multiclass classification in metric spaces, focusing on universal consistency and convergence rates.
method Novel Proto-NN and hybrid rules for multiclass classification in metric spaces, analyzing convergence rates.
result Proto-NN is universally consistent and simpler to implement, with similar computational advantages.
Consistency of k-NN rule proven in sigma-finite dimensional metric spaces.
problem Proving consistency of k-NN rule in metric spaces.
method Direct proof using Stone's theorem, investigating metric properties.
result Universal consistency of k-NN rule in sigma-finite dimensional metric spaces.
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…
Learning rule consistency tied to non-existence of real-valued measurable cardinals.
problem Consistency of k-NN learning rule in metric spaces.
method Analyzing separable subspaces and density conditions.
result The k-NN classifier's consistency depends on the absence of real-valued measurable cardinals.
Implementing -NN classification using Gromov--Wasserstein distances
problem Comparing metric measure spaces
method Gromov--Wasserstein and fused Gromov--Wasserstein distances
result Universal consistency of -NN classifiers
Study finds AUC is most consistent across different prevalence in binary classification.
problem Consistency of model evaluation metrics across varying prevalence in binary classification.
method Analysis of 156 data scenarios with 18 metrics, 5 models, and a random guess model.
result AUC has the smallest variance in evaluating individual models and ranking of models.
Develops algorithms for optimizing multi-label metrics with provable guarantees.
problem Optimizing complex multi-label metrics like F-measure and Jaccard index.
method Principled learning algorithms based on H-consistency for generalized metrics.
result Provable -consistency bounds for multi-label metric optimization.
New algorithms for regression with adversarial responses on various metric spaces.
problem Regression with adversarial responses under non-i.i.d. sequences.
method Proves universal consistency for a wide range of non-stationary processes.
result Achieves universal consistency for a broader class of sequences than stationary processes.
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…
This paper establishes a theoretical foundation for consistency training in diffusion models.
problem Lack of a comprehensive theoretical understanding of consistency training in diffusion models.
method Demonstrates the necessity of a number of steps in consistency learning exceeding for generating samples within proximity to the target distribution.
result Establishes rigorous insights into the validity and efficacy of consistency models, offering theoretical underpinnings for their utility.
The nearest neighbor rule is proven consistent in a broad setting.
problem Proving consistency of the nearest neighbor rule in various settings.
method Proving online consistency for all measurable functions in doubling metric spaces under mild assumptions.
result The nearest neighbor rule is online consistent in all measurable functions in doubling metric spaces.
We propose a framework for constructing and analyzing multiclass and multioutput classification metrics, i.e., involving multiple, possibly correlated multiclass labels. Our analysis reveals novel insights on the geometry of feasible confusion tensors -- including necessary and sufficient conditions for the equivalence…
A new framework for consistent segmentation evaluation reduces operating losses.
problem Inconsistent thresholding-based segmentation methods lead to suboptimal solutions.
method Developed a consistent ranking-based framework (RankDice/RankIoU) using Bayes rules and Dice-/IoU-calibration.
result The proposed framework is Dice-/IoU-calibrated and provides excess risk bounds and convergence rates.
Curved Frobenius manifolds link to Hessian metrics in geometry.
problem Understanding curved Frobenius manifolds and their relation to Hessian metrics.
method Analyzing the relationship between curved Frobenius structures and Hessian metrics on spaces with non-vanishing curvature.
result Consistent curved Frobenius structures on constant curvature spaces are linked to Hessian metrics.
Novel framework for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models with metric responses.
method Developed algorithms for large datasets, agnostic to predictive models, with asymptotic and non-asymptotic guarantees.
result Asymptotic and non-asymptotic guarantees for special cases, demonstrated in clinical applications.
Validation of uncertainty quantification metrics: a primer based on the consistency and adaptivity conceptsphysics.chem-ph
This study revisits UQ validation methods based on consistency and adaptivity concepts.
problem Lack of comprehensive validation methods for UQ metrics across input feature ranges.
method Revisit and extend common validation methods for UQ metrics based on consistency and adaptivity concepts.
result Improved understanding and capabilities of UQ metrics validation methods.
New method evaluates language model forecasters by checking consistency of predictions.
problem Evaluating the performance of language model forecasters is difficult due to lack of ground truth.
method Developed a consistency check framework based on arbitrage to evaluate forecasters.
result Consistency metrics correlate with ground truth performance of LLM forecasters.
We consider the space of all quasifuchsian metrics on the product of a surface with the real line. We show that, in a neighborhood of the submanifold consisting of fuchsian metrics, every non-fuchsian metric is completely determined by the bending data of its convex core.
Estimates scalar curvature of point clouds without embedding.
problem Estimating scalar curvature of data sets without embedding.
method Intrinsic estimator based on metric structure, consistent and stable.
result Estimator converges to scalar curvature as sample size increases.
Saliency maps are a popular approach to creating post-hoc explanations of image classifier outputs. These methods produce estimates of the relevance of each pixel to the classification output score, which can be displayed as a saliency map that highlights important pixels. Despite a proliferation of such methods, littl…
In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin methods---have their own distinct strengths but also possess significant drawbacks. Conditio…
Study constructs non-Riemannian Finsler metrics using warped product.
problem Finding Ricci-flat Finsler metrics.
method Used warped product and PDE characterization for static spacetimes.
result Explicitly constructed two non-Riemannian examples.
Study shows -NN classifier is not universally consistent on but consistent on discrete and specific measure spaces.
problem Consistency of -NN classifier under Wasserstein distance on measure spaces.
method Analysis of -NN classifier properties under Wasserstein distance, use of -finite metric dimension, geodesic structures of Wasserstein spaces.
result Consistency of -NN classifier on specific measure spaces (discrete, Gaussian, wavelet series) but not on .
It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…
Conditional Generative Adversarial Networks (cGANs) are finding increasingly widespread use in many application domains. Despite outstanding progress, quantitative evaluation of such models often involves multiple distinct metrics to assess different desirable properties, such as image quality, conditional consistency,…
New algorithms optimize metrics for binary classification with class imbalance.
problem Optimizing metrics like Fβ, AM, Jaccard for imbalanced classes.
method Reformulates metric optimization as cost-sensitive learning, using surrogate loss functions.
result METRO algorithms provide strong theoretical guarantees and outperform baselines.
Proposes a neural network method to improve consistencies in high dimensional data analysis.
problem Inconsistencies among dimensionality reduction, clustering, and visualization tasks in high dimensional data analysis.
method Consistent Representation Learning (CRL) neural network that performs NLDR transformations to satisfy LGP constraints.
result Improves consistencies in data interpretation through end-to-end task execution.
Note shows equivalence of recent NEC reformulation to classical NEC for -metrics.
problem Consistency of null energy condition in Lorentzian length spaces.
method Shows equivalence of recent reformulation of null energy condition to classical formulation for -metrics.
result Equivalence of recent reformulation of null energy condition to classical formulation for -metrics.
Study pressure metrics for cusped Hitchin representations.
problem Characterize cusped Hitchin representations of Fuchsian groups.
method Develop pressure metrics associated to fundamental weights and roots.
result New pressure metrics for Hilbert length when .
Paper introduces a medoid-based approach for efficient Fréchet regression.
problem Regression in metric spaces with random objects.
method Adapted random forest algorithm with medoid-based splitting rule.
result Asymptotic equivalence and consistency of the regression estimator.
Deconfounds neural network representation similarity metrics to improve consistency and accuracy.
problem Confounding by population structure in similarity metrics like RSA and CKA.
method Covariate adjustment regression to adjust for confounders.
result Improves detection of semantically similar neural networks and consistency in transfer learning.
New complete Calabi-Yau metrics found in complex space.
problem Finding metrics on complex spaces with specific conditions.
method Generalized Calabi ansatz, non-archimedean Monge-Ampère equation.
result Complete Calabi-Yau metrics constructed in Fano manifolds.
We consider three-dimensional Lorentzian metrics that locally admit four independent Killing vectors. Their classification is summarized, and conditions for characterizing them are found. These consist of algebraic classification of the traceless Ricci tensor, and other conditions satisfied by the curvature and its der…
The prescribed Ricci curvature problem consists in finding a Riemannian metric on a manifold such that the Ricci curvature of equals a given -tensor field . We survey the recent progress on this problem in the case where is a homogeneous space.
A new metric assesses causal graphs using node permutations to detect inconsistencies.
problem Quantifying the goodness of causal graphs and distinguishing them from random graphs.
method Constructing a baseline through node permutations and comparing inconsistencies.
result The proposed metric can distinguish between true and wrong causal graphs.
Paper tackles efficient learning of non-convex hypotheses in metric spaces.
problem Efficiently find consistent hypotheses for non-convex hypotheses composed of possibly several disconnected regions.
method Proposes a general domain-independent algorithm for finding consistent weakly convex hypotheses and proves sufficient conditions for its efficiency.
result Shows that consistent hypothesis finding problem can be solved in polynomial time for a broad class of weakly convex hypotheses over metric spaces.
We define a partition of the space of projectively flat metrics in three classes according to the sign of the Chern scalar curvature; we prove that the class of negative projectively flat metrics is empty, and that the class of positive projectively flat metrics consists precisely of locally conformally flat-Kähler met…
A necessary and sufficient condition for energy-momentum conservation is proved within a topological, pre-metric approach to classical electrodynamics including magnetic as well as electric charges. The extended Lorentz force, consisting of mutual actions by F=(E, B) on the electric current and G=(H, D) on the magnetic…
A unique hyperbolic metric is found for each spherical cone-metric on the boundary of a hyperbolizable 3-manifold.
problem Finding a hyperbolic metric for a given spherical cone-metric on the boundary of a hyperbolizable 3-manifold.
method Constructing a strictly polyhedral hyperbolic metric on the 3-manifold such that the given spherical cone-metric is the induced dual metric on the boundary.
result The existence and uniqueness of a strictly polyhedral hyperbolic metric for a given spherical cone-metric on the boundary of a hyperbolizable 3-manifold.
Adapts EGOP to multi-class setting and proposes a simple rough estimator.
problem Recovering relevant directions for multi-class regression.
method Adapt EGOP to multi-class setting, propose a simple rough estimator.
result Simple rough estimator of EJOP remains statistically consistent.
In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in are Kossowski metrics, and t…