Synthetic Ricci flows defined for metric measure spaces.
problem Characterizing Ricci flows for non-smooth spaces.
method Heat flow, optimal transport, volume asymptotics.
result Equivalent characterizations of weighted Ricci flow.
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48 results for “Synthetic metric”
A framework evaluates synthetic tabular data quality objectively.
problem Lack of an objective interpretation of tabular data metrics.
method Proposes a single mathematical objective for synthetic tabular data distribution, structurally decomposes it, and unifies existing metrics.
result Synthesizers that represent tabular structure outperform other methods, especially on smaller datasets.
Develops new synthetic Ricci flow concepts for metric measure spaces.
problem No specific problem stated; focuses on new mathematical concepts.
method Formulated in terms of dynamic convexity and local concavity of entropy, and global/short-time asymptotic transport cost estimates.
result Shows these properties characterise smooth (weighted) Ricci flows.
Study compares synthetic and distributional Ricci curvature bounds.
problem Comparing synthetic and distributional approaches to lower Ricci curvature bounds.
method Analyzes synthetic via weak displacement convexity and distributional via non-negativity of Ricci-tensor.
result Distributional bounds imply entropy bounds for metrics and vice versa for under convergence condition.
Unified study of Riemannian and sub-Riemannian geometries with synthetic Ricci curvature bounds.
problem Unified framework for Riemannian and sub-Riemannian geometries.
method Study of gauge metric measure spaces.
result Unified synthetic Ricci curvature lower bounds for both Riemannian and sub-Riemannian structures.
Synthetic data augmentation can improve imbalanced classification metrics.
problem Improving imbalanced classification metrics
method Developing a framework for analyzing the effects of synthetic data augmentation on score-based classification
result Augmentation can improve AUROC, AUPRC, balanced accuracy, and F1 score
Study evaluates synthetic data augmentation for small datasets, highlighting inconsistencies in traditional metrics.
problem Inconsistent validation of synthetic data generated for small sample sizes.
method Proposes a normalized Bottleneck distance metric to evaluate synthetic tabular data.
result Common metrics like propensity scoring and MMD fail for small datasets, showing instability and high variability.
Paper establishes utility theory for synthetic data generation.
problem Lack of theoretical understanding in synthetic data utility.
method Statistical learning framework with two utility metrics: generalization and model ranking.
result Theoretical bounds for synthetic data utility metrics ensure comparable generalization and consistent model comparison.
We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. of Categories 32 (2017), 803-822
Study the metric geometry of Cauchy hypersurfaces in spacetimes.
problem Properties of the space of Cauchy hypersurfaces.
method Equipped with a Hausdorff-type metric, studied completeness and local compactness.
result Generalized completeness results for spacetimes.
What's Wrong with Your Synthetic Tabular Data? Using Explainable AI to Evaluate Generative Modelscs.LG
AI techniques explain synthetic tabular data weaknesses.
problem Challenges in evaluating synthetic tabular data quality.
method Apply explainable AI to a binary detection classifier.
result Reveals inconsistencies, unrealistic dependencies, or missing patterns in synthetic data.
Uniformly Euclidean metrics with isolated singularities on certain manifolds are Ricci flat and have nonnegative synthetic Ricci curvature.
problem Proving the existence of Ricci flat metrics with isolated singularities on specific manifolds.
method Demonstrating nonnegative synthetic Ricci curvature using the RCD(0, n) condition.
result Uniformly Euclidean metrics with isolated singularities on are Ricci flat and extend smoothly over the singularity.
We introduce the DP-auto-GAN framework for synthetic data generation, which combines the low dimensional representation of autoencoders with the flexibility of Generative Adversarial Networks (GANs). This framework can be used to take in raw sensitive data and privately train a model for generating synthetic data that …
XAI-Bench releases synthetic datasets for evaluating feature attribution methods.
problem Evaluating and comparing feature attribution methods is challenging.
method Released synthetic datasets and benchmarking library.
result Efficiently evaluates feature attribution methods across various metrics.
Optimal transport explored on a specific geometric space.
problem Optimal transport problem in sub-Lorentzian Heisenberg group.
method Synthetic metric spacetime structure analysis and sub-Lorentzian version of Brenier's theorem.
result Established sub-Lorentzian version of Brenier's theorem and derived Monge-Ampère equation.
Develops a method to control model behavior with synthetic data.
problem Controlling language model behavior via synthetic training data.
method Dataset Policy Gradient (DPG) to optimize synthetic data generators.
result Can cause target models to embed specific patterns or rephrase inputs.
Proves equivalence of two types of Ricci curvature bounds.
problem Equivalence of distributional and synthetic Ricci curvature bounds.
method Analyzes weighted Riemannian manifolds with specific smoothness conditions.
result Proves equivalence of Ricci curvature bounds under given conditions.
Synthetic data improves financial models without real data.
problem Lack of real financial data due to privacy and regulation.
method Application of synthetic data across various financial data types.
result Synthetic data enhances financial model accuracy and fairness.
SHAP Distance assesses semantic fidelity of synthetic tabular data.
problem Semantic fidelity of synthetic tabular data is not well evaluated.
method SHAP Distance, defined as cosine distance between global SHAP attribution vectors.
result SHAP Distance detects semantic discrepancies overlooked by standard measures.
Refines d'Alembertian for signed Lorentz distance functions in metric measure spacetimes.
problem Exact representation and bounds of d'Alembertian for signed Lorentz distance functions.
method Metric geometry techniques, localization, Sobolev calculus.
result Distributional d'Alembertian is a signed measure with integration by parts formula.
Transformer model pretrains on synthetic graphs for AD detection.
problem Limited labeled data and class imbalance in AD diagnosis.
method Diffusion-generated synthetic graphs, Graph Transformers, transfer learning.
result Framework outperforms baselines in AD diagnosis metrics.
Example of spacetime with causal bubbling, splitting into timelike and spacelike parts.
problem Understanding causal bubbling in spacetimes.
method Example of a globally hyperbolic spacetime with a continuous metric, splitting orthogonally into timelike and spacelike parts.
result The synthetic timelike curvature-dimension (TCD) condition does not prevent causal bubbling.
Sharp inequality in spaces with non-negative Ricci curvature.
problem Proving a sharp isoperimetric inequality in metric measure spaces.
method Using volume entropy in non-compact metric measure spaces with non-negative synthetic Ricci curvature.
result Proved a sharp dimension-free isoperimetric inequality.
Develops a private synthetic graph generator using Gromov-Wasserstein distance.
problem Creating private synthetic networks for complex data.
method Random connection model, fused Gromov-Wasserstein distance, differential privacy.
result Effective algorithm for generating private synthetic graphs with theoretical guarantees.
The study improves theoretical understanding of using multiple synthetic datasets for better model accuracy.
problem Lack of theoretical understanding of using multiple synthetic datasets for supervised learning.
method Derive bias-variance decompositions for multiple synthetic datasets settings.
result A simple rule of thumb to select the appropriate number of synthetic datasets.
Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from spaces to spacesmath.DG
The study improves harmonic map theory for metric spaces with curvature bounds.
problem Harmonic maps between specific metric spaces with curvature constraints.
method Synthetic geometry, Optimal Transport, Heat Flow, viscosity theory.
result Established Lipschitz continuity and Bochner-Eells-Sampson inequality.
Scoping review and benchmarking of synthetic EHR data generation methods.
problem Creating realistic synthetic electronic health records for research and training.
method Conducted a scoping review and benchmarked seven methods on open-source EHR datasets.
result GAN-based methods excel in fidelity and utility, while rule-based methods excel in privacy protection.
Paper proposes a new metric to evaluate survival models, especially for censored data.
problem Challenges in evaluating survival prediction models due to censored data.
method Developed a novel approach to estimate Mean Absolute Error (MAE) for survival datasets with censored data.
result The proposed MAE metric using pseudo-observations accurately ranks model performance and closely matches true MAE.
Every year thousands of patients are diagnosed with a glioma, a type of malignant brain tumor. Physicians use MR images as a key tool in the diagnosis and treatment of these patients. Neural networks show great potential to aid physicians in the medical image analysis. This study investigates the use of varying amounts…
Synthetic data enhances analytics but requires careful volume management.
problem Accuracy of statistical methods on synthetic data vs. raw data.
method Synthetic Data Generation for Analytics framework using tabular diffusion models.
result Error rate decreases with more synthetic data but may stabilize or increase.
We will study metric measure spaces beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds BE for which we prove the equivalence with sharp gradient estimates, the class of which will be preserved under…
Paper proposes synthetic data generator to study and mitigate bias in machine learning.
problem Bias in machine learning data can lead to unfair outcomes.
method Developed a synthetic data generator to introduce and analyze various types of bias.
result Demonstrated how synthetic data can be used to study and mitigate bias in machine learning models.
We give a new proof that the completion of the Weil-Petersson metric on Teichmüller space is Gromov-hyperbolic if the surface is a five-times punctured sphere or a twice-punctured torus. Our methods make use of the synthetic geometry of the Weil-Petersson metric.
TimeGraph creates synthetic datasets for robust time-series causal discovery.
problem Lack of reliable synthetic benchmark datasets for robust time-series causal discovery.
method Developed comprehensive synthetic datasets with temporal properties, including trends, seasonality, and noise.
result Demonstrated significant variations in algorithm performance under realistic temporal conditions.
We study the deformation of spherical conical metrics with at least some of the cone angles larger than . We show in this note via synthetic geometry that for one family of such metrics, there is local rigidity in the choice of cone positions if angles are fixed. This gives an evidence of the analytic obstruction c…
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.
Synthetic scalar curvature defined via Gaussian integrals, applied to manifolds and flows.
problem Defining scalar curvature for non-smooth spaces and flows.
method Gaussian integral approach to scalar curvature, applied to manifolds and flows.
result Characterizes Ricci flows as minimal super-Ricci flows.
The study proposes conjectures on limit spaces of Riemannian manifolds with Ricci curvature.
problem Understanding the regularity of limit spaces of Riemannian manifolds with Ricci curvature.
method Synthetic treatment of lower bounds on Ricci curvature for metric measure spaces.
result Several conjectures on the regularity of limit spaces.
Study shows privacy and utility trade-offs in synthetic data models, impacting fairness and real-world performance.
problem Understanding the impact of differential privacy on fairness and model performance in synthetic data.
method Systematic analysis of differentially private synthetic datasets on classification models, measuring utility and bias using fairness metrics.
result More privacy does not necessarily mean more bias, but it can affect model performance when deployed on real data.
Sharp eigenvalue bounds on metric measure spaces extend Cheng's theorem.
problem Extending Cheng's eigenvalue comparison theorem to non-smooth spaces.
method Localization technique, synthetic Ricci curvature bounds via optimal transport.
result Sharp upper bounds on eigenvalues in metric measure spaces.
Synth-MIA assesses privacy leakage in synthetic tabular data models.
problem Challenges in evaluating privacy leakage in synthetic tabular data.
method Unified threat framework deploying multiple attacks.
result Higher synthetic data quality correlates with greater privacy leakage.
The paper proves metrizability and dynamics of Weil bundles.
problem Metrizability and dynamics of Weil bundles in differential geometry.
method Investigation of metrizability and dynamics of Weil bundles for smooth compact manifolds and Weil algebras.
result A canonical, complete, weighted metric \(\mathfrak{d}_w\) on \(M^\mathbf{A}\) that encodes geometry and deformations.
The paper studies moduli spaces of non-smooth metric structures with non-negative Ricci curvature.
problem Understanding moduli spaces of non-smooth metric structures with non-negative Ricci curvature.
method Relating convergence of RCD(0,N)-structures to their lifts, constructing Albanese and soul maps, proving their continuity, and constructing examples.
result Construction of moduli spaces with non-trivial rational homotopy groups.
Proves a synthetic Lorentzian Cartan-Hadamard theorem.
problem Formulates and proves a theorem for Lorentzian geometry.
method Uses an appropriate notion of local concavity for Lorentzian (pre-)length spaces.
result Establishes existence and uniqueness of timelike geodesics.
Measure contraction property is a synthetic Ricci curvature lower bound for metric measure spaces. We consider Sasakian manifolds with non-negative Tanaka-Webster Ricci curvature equipped with the metric measure space structure defined by the sub-Riemannian metric and the Popp measure. We show that these spaces satisfy…
Study on cones over metric spaces with curvature bounds.
problem Establishing curvature bounds for cones over metric spaces.
method Developed a localization technique to prove synthetic curvature bounds.
result Riemannian and Lorentzian cones over CD-spaces satisfy MCP and vice versa.
A new metric-based principal curve method learns 1D manifolds from spatial data.
problem Learning 1D manifolds from spatial data.
method Metric-based Principal Curve (MPC) approach.
result The method effectively learns the shape of 1D manifolds from synthetic and real datasets.
Study examines heart and football-shaped metrics, verifying geometric structure.
problem Analyzing reducible spherical conical metrics and their geometric properties.
method Examined 1-parameter heart shape and 3-parameter football shape families, verified structure theorem, used explicit metric and geodesic calculations.
result Naturally arise from Abelian differentials of the third kind, offer new evidence for spherical geometry and complex analytic structure interaction.