Study confirms conjecture about Kähler metrics on smooth minimal models.
problem Behavior of constant scalar curvature Kähler metrics on smooth minimal models.
method Analysis of metrics in a neighborhood of the canonical class.
result Convergence to singular Kähler Einstein metric in the canonical class.
This paper argues that a class of Riemannian metrics, called warped metrics, plays a fundamental role in statistical problems involving location-scale models. The paper reports three new results : i) the Rao-Fisher metric of any location-scale model is a warped metric, provided that this model satisfies a natural invar…
Paper introduces new metrics for evaluating model accuracy.
problem Improving model accuracy and calibration.
method Developed two second-order accuracy metrics with integral and numerical representations.
result Validates model calibration settings and reveals distortions.
A new metric model for quasi-Fuchsian space defined by Bers metrics.
problem Understanding the quasi-Fuchsian space of a surface.
method Introducing Bers metrics and studying their properties to model QF(S).
result New integral representations of the Goldman symplectic form and holomorphic extension of the Weil-Petersson metric.
Extremal metrics exist if uniformly K-stable over models.
problem Existence of extremal metrics on complex projective varieties.
method Uniform K-stability over models of extremal tori. result Extremal metrics exist if uniformly K-stable. 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.
We turn the definition of individual fairness on its head---rather than ascertaining the fairness of a model given a predetermined metric, we find a metric for a given model that satisfies individual fairness. This can facilitate the discussion on the fairness of a model, addressing the issue that it may be difficult t…
New metric evaluates generative models across domains, diagnosing fidelity, diversity, and generalization.
problem Evaluating generative models in diverse domains with limited metrics.
method Introduces a 3D evaluation metric (α-Precision, β-Recall, Authenticity) for domain-agnostic diagnostics. result Unified metric characterizes fidelity, diversity, and generalization, diagnosing model performance.
This paper evaluates and improves metrics for identifying important features in machine learning models.
problem Evaluation metrics for explainable AI are limited by multicollinearity and model accuracy.
method Proposes Expected Accuracy Interval (EAI) to predict model accuracy with multicollinearity.
result EAI is a useful metric for identifying important features in models with multicollinearity.
A simpler metric for latent space geometry.
problem Complexity in capturing geometric structure of data manifolds.
method Prior-based approximate latent Riemannian metric.
result The proposed metric is simple, efficient, and robust.
The paper studies scaling limits of Wasserstein metrics on Gaussian mixture models.
problem Understanding the scaling limits of Wasserstein metrics on Gaussian mixture models.
method Scaling limit approach on Gaussian mixture models, including inhomogeneous and extended models.
result Existence of the limit of the Wasserstein metric after renormalization for GMMs with zero variance.
The paper introduces new metrics for evaluating generative models of behavior.
problem Lack of quantitative evaluation criteria for unsupervised behavior discovery.
method Proposed and investigated several metrics for generative models of behavior.
result The proposed metrics correspond with biologists' intuitions and allow for model evaluation and bias understanding.
Metric learning enhances combinatorial coverage metrics' ability to predict classification errors.
problem Dataset dependence of combinatorial coverage metrics in anticipating classification errors.
method Metric learning to improve latent space separation of data classes.
result Metric learning increases SDCCMs' ability to distinguish between correctly and incorrectly classified data.
New method recovers hyperkähler metrics from twistor models.
problem Constructing and recovering hyperkähler metrics from twistor models.
method Construction of principal twistor models and universality theorem.
result Universality theorem for recovering hyperkähler metrics from twistor spaces.
We classify all Kahler metrics in an open subset of C2 whose real geodesics are circles. All such metrics are equivalent (via complex projective transformations) to Fubini metrics (i.e. to Fubini-Study metric on CP2 restricted to an affine chart, to the complex hyperbolic metric in the unit ball model or to the E…
Study analyzes neural network models to understand generalization performance.
problem Understanding good generalization in neural networks.
method Analyzed a corpus of models from a public contest, breaking ALPHAHAT into scale and shape metrics.
result Identified a Simpson's paradox in metric performance across different model depths and regularization hyperparameters.
Study shows label errors impact model disparity metrics, proposing mitigation methods.
problem Impact of label errors on model disparity metrics.
method Empirical study, characterizing label error effects; proposing estimation and relabeling methods.
result Label errors significantly affect model disparity metrics, particularly for minority groups.
New Calabi-Yau metrics converge polynomially to Calabi model space.
problem Finding complete Calabi-Yau metrics with polynomial convergence rate.
method Defined new metrics on Calabi-Yau complements with ample normal bundles.
result Uniqueness of these metrics within a cohomology class.
As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties of Vaidya metric. It is shown that Vaidya metric can be cons…
This paper reviews metrics for evaluating multi-class classification models.
problem Evaluating and comparing multi-class classification models.
method Review and analysis of metrics.
result Promising multi-class metrics are highlighted and their usages are demonstrated.
This work evaluates and benchmarks calibration metrics for data-driven regression models.
problem Conflicting results from different calibration metrics make it hard to compare and interpret model performance.
method Systematically extracted and benchmarked 14 regression calibration metrics across various data types and recalibration methods.
result Many metrics disagree on the same recalibration result, highlighting the need for careful metric selection.
Study on metric bubbles in complex dimensions 1 and 2.
problem Understanding degenerations of Kähler-Einstein metrics.
method Investigation of metric bubble trees for non-collapsing cases.
result Description of a conjectural higher-dimensional picture.
The paper explores metrics and models for analyzing biological shapes.
problem Analyzing biological shapes using mathematical metrics.
method Review of Riemannian metrics and evolution equations, focusing on diffeomorphic shape analysis.
result Introduction of a new class of metrics involving optimization of a growth tensor.
Study evaluates relevance metrics for similarity-based model explanations.
problem Providing understandable explanations for complex model predictions.
method Evaluated three relevance metrics using three tests.
result Cosine similarity of gradients performs best for explanations.
The paper quantifies uncertainty in aggregated machine learning metrics.
problem Uncertainty in summarizing model performance across multiple tasks.
method Statistical methodologies including bootstrapping and Bayesian modeling.
result Insights into model performance dominance for specific tasks.
A new metric assesses latent variable models using data and model moments.
problem Difficulty in assessing the quality of unsupervised learning models.
method A moment-matching metric using matrix norms to compare data and model moments.
result The proposed metric is faster and has less variance than alternative methods.
Develops a new family of signature-changing models on metric manifolds.
problem Signature changes in metric manifolds.
method One-parameter family of Lorentz-Riemann models, local expressions around change.
result Generalizes existing signature-changing models.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
Despite the growing importance of multilingual aspect of web search, no appropriate offline metrics to evaluate its quality are proposed so far. At the same time, personal language preferences can be regarded as intents of a query. This approach translates the multilingual search problem into a particular task of searc…
Optimal transport learns Riemannian metrics for evolving probability measures.
problem Learning metrics for evolving probability measures on Riemannian manifolds.
method Neural parametrization of a metric tensor via optimal transport, alternating optimization scheme.
result Improved trajectory inference on scRNA and bird migration data.
This paper improves probabilistic latent models on hyperbolic spaces.
problem Uncertainty in predictions due to geodesics crossing low-data regions.
method Augmenting hyperbolic manifold with a pullback metric for probabilistic pullback metrics.
result Geodesics on pullback metric respect both geometry and data distribution, reducing uncertainty.
Interactive tool helps choose and understand classification metrics.
problem Common metrics for binary classification have limitations.
method Graphical application to visualize and explore evaluation metrics.
result Promotes careful attention to interpretation of metrics.
Study on Einstein metrics on complex projective spaces with specific group actions.
problem Finding Einstein metrics invariant under cohomogeneity one Lie group actions.
method Analyzing Einstein equation for diagonal invariant metrics under five Takagi models.
result Nonexistence of smooth globally defined invariant Einstein metrics in four models, necessary condition in the fifth.
Study on the asymptotic geometry of Higgs bundles over projective line.
problem Understanding the asymptotic behavior of Hitchin's metric on moduli spaces of rank two irregular Higgs bundles.
method Analysis of Hitchin's hyperkähler metric and comparison with semiflat and ALG/ALG∗ models. result Hitchin's metric is asymptotic to semiflat and ALG/ALG∗ models at polynomial and exponential rates. We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over…
Defines curvature for metric triples in metric spaces.
problem No standard curvature for metric triples in general metric spaces.
method Defines curvature kX(T) using side lengths and distances to points in X. result Curvature kX(T) enables isometric embedding into model spaces. 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.
Topic models are typically evaluated with respect to the global topic distributions that they generate, using metrics such as coherence, but without regard to local (token-level) topic assignments. Token-level assignments are important for downstream tasks such as classification. Even recent models, which aim to improv…
IRT metrics improve model evaluation by assessing latent characteristics.
problem Limitations of classic metrics like precision and F1.
method Introducing psychometric metrics like Item Response Theory (IRT).
result IRT complements classical metrics, offering new insights.
We study the model selection problem in conditional average treatment effect (CATE) prediction. Unlike previous works on this topic, we focus on preserving the rank order of the performance of candidate CATE predictors to enable accurate and stable model selection. To this end, we analyze the model performance ranking …
Study flaws in generative model evaluation metrics, especially for diffusion models.
problem Flaws in existing metrics for evaluating generative models, particularly for diffusion models.
method Systematic study of generative models, human perception experiments, and analysis of feature extractors.
result State-of-the-art perceptual realism of diffusion models is not reflected in commonly reported metrics.
Metrics assess uncertainty structure and distribution for regression models.
problem Quantifying uncertainty in high-dimensional and nonlinear regression tasks.
method Two bounded comparison metrics for uncertainty structure and distribution.
result DNNs and DNOs provide encouraging uncertainty metric values in high dimensions.
A comparison theorem for the isoperimetric profile on the universal cover of surfaces evolving by normalised Ricci flow is proven. For any initial metric, a model comparison is constructed that initially lies below the profile of the initial metric and which converges to the profile of the constant curvature metric. Th…
New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.
problem Maintaining the Fisher metric structure in statistical models.
method Characterizing statistics that maintain the Fisher metric structure bi-Lipschitz equivalently.
result Characterized statistics that preserve the Fisher metric structure closely.
Algorithm learns similarity metrics for individual fairness.
problem Difficulty in learning similarity metrics for individual fairness.
method Gradient descent and Bradley-Terry model for pairwise comparisons.
result Algorithm converges to ground truth metric for individual fairness.
We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.
The paper defines and analyzes Kähler metrics near a compact manifold, showing their deviation from Poincaré-type metrics.
problem Understanding the behavior of Kähler metrics near a compact manifold.
method Defining and analyzing Kähler metrics on a trivial holomorphic open disk bundle, showing their deviation from Poincaré-type metrics.
result The Kähler metrics near a compact manifold deviate exponentially from Poincaré-type metrics, and they arise naturally in perturbing cscK metrics.
New metrics improve scRNA-seq perturbation modeling by reducing mode collapse.
problem Outperformed by simple mean prediction in scRNA-seq perturbation modeling.
method Introduce DEG-aware metrics (WMSE, Rw2(Δ)) and negative/positive baselines. result WMSE loss function reduces mode collapse and improves model performance.