A new method using energy distance for ensemble and scenario reduction.
problem Solving complex dynamic and stochastic programs, especially in energy systems.
method Proposes a new method based on energy distance for ensemble and scenario reduction.
result Reduced scenario sets exhibit better statistical properties for energy distance than Wasserstein distance.
Balls, circles, and spheres identified by energy of distances.
problem Identifying shapes using energy of distances.
method Using generalized Riesz energy to identify shapes.
result Balls, circles, and spheres identified by energy of distances.
Energy distance measures feature heterogeneity in federated learning.
problem Heterogeneity across data sources hinders model aggregation in federated learning.
method Introduced Taylor approximations of energy distance for efficient computation.
result Taylor approximations accurately capture feature discrepancies, improving convergence.
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproduc…
The study finds optimal minimum distances for Green's energy points on compact manifolds.
problem Finding optimal minimum distances for Green's energy points on compact Riemannian manifolds.
method Analyzing point configurations minimizing discrete energy with the Green's function for the Laplacian.
result Every point in a minimizing configuration lies inside a harmonic ball, and the minimum distance has optimal asymptotic order.
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
Paper extends multivariate rank tests for robust subspace detection.
problem Testing distributional similarity in multivariate data.
method Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport.
result Trade-off between detection power and false alarm rate via projections.
This work examines the sensitivity of energy distance to mean differences compared to covariance differences.
problem The sensitivity of energy distance to mean differences compared to covariance differences when distributions are close.
method Analyzes the energy distance in the case where distributions are close, focusing on sensitivity to mean and covariance differences.
result Energy distance is more sensitive to mean differences than covariance differences when distributions are close.
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…
Proposes an energy-based sliced Wasserstein distance for improved probability measure comparison.
problem Inefficiencies and limitations in existing sliced Wasserstein distance approaches.
method Introduces an energy-based slicing distribution for better performance and stability.
result Demonstrates superior performance of the EBSW distance in various applications.
OT-GAN uses optimal transport to improve GANs stability and performance.
problem Improving stability and performance of GANs.
method Combines optimal transport and energy distance in adversarially learned feature space.
result OT-GAN achieves state-of-the-art results on image generation benchmarks.
Study spider mechanism configuration spaces using squared distance function.
problem Understand configuration spaces of spider mechanisms.
method Use Morse theory of squared distance function from body to fixed point.
result List and describe critical manifolds of squared distance function as products of polygon spaces.
Energy functional for Legendrian knots in Heisenberg group, invariant under PU(2,1).
problem Energy functional for Legendrian knots in Heisenberg group.
method Regularization of divergent integral with Korányi distance, invariant under PU(2,1).
result Characterization of minimizers and Heisenberg analog of Doyle-Schramm cosine formula.
Study geodesic distances and convexity in contact sets.
problem Understanding geodesic distances and convexity in contact sets.
method Extending results on quasi-psh functions and big cohomology classes, studying Monge-Ampère measures on contact sets.
result Convexity of the K-energy in big and nef cohomology classes.
New metrics for high-dimensional data improve on energy distance.
problem Testing equality of distributions and independence in high dimensions.
method Proposed new metrics inheriting properties of energy distance and others.
result Improved metrics detect homogeneity and independence in high dimensions.
Lowered regularity assumption for a phase-dependent Helfrich energy equation.
problem Analyzing the phase separation line of the Helfrich energy.
method Used a carefully chosen test function with a signed distance function.
result Regularity assumption lowered from C2 to C1,1 for the phase separation line. Paper proves stability of positive mass theorem for specific types of manifolds.
problem Stability of positive mass theorem for compact graphical manifolds.
method Used Federer--Fleming flat distance and static quasi-local Brown-York energy.
result Proved stability of positive mass theorem for compact (locally) hyperbolic graphical manifolds.
New distances for comparing heterogeneous probability measures efficiently.
problem Comparing probability measures across different spaces.
method Introducing Anchor Energy (AE) and Anchor Wasserstein (AW) distances, and a sweep line algorithm for exact computation.
result Exact computation of AE and AW distances in log-quadratic time, significantly faster than GW.
In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all Kähler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound estimate of the K energy in terms of the geodesic distance and the Calabi energy. This is…
Study the hanging chain shape around a circle.
problem Finding the shape of a curve extremizing potential energy to a circle.
method Analyzes curves minimizing potential energy to a circle, considering both inside and outside.
result Describes shapes of curves for different powers of distance to the circle.
New method improves speech synthesis quality.
problem Efficiently train parallel speech synthesis models.
method Spectral energy distance for implicit generative models.
result State-of-the-art generation quality achieved.
Paper proposes Gini distance statistics for estimating feature-label dependence.
problem Identifying statistical dependence between features and categorical labels.
method Generalized Gini distance in RKHS for feature-label dependence estimation.
result Gini distance statistics converge faster and have tighter error bounds than distance covariance.
Paper proposes a new method for estimating treatment effects using interpretable deep learning models.
problem Estimating treatment effects from observational data with interpretability.
method Proposes a novel objective function using energy distance balancing score and neural additive models for improved interpretability.
result Demonstrates superior performance over state-of-the-art methods in semi-synthetic experiments.
In this paper we study 1/k-geodesics, those closed geodesics that minimize on any subinterval of length l(γ)/k. We employ energy methods to provide a relationship between the 1/k-geodesics and what we define as the balanced points of the uniform energy. We show that classes of balanced points of the uniform energy pe…
We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the Moebius Energy of the smooth knot as the polygons converge to the smooth knot. However, the polygons must converge in a ``nice'' way, and th…
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy …
New neural method calculates EMD for particle physics data.
problem Metric for particle collider events based on Wasserstein metric.
method Neural network architecture estimating EMD using Kantorovich-Rubinstein duality.
result Differentiable way to calculate EMD for geometric fitting.
Paper uses news data to model asset correlations without market data.
problem Traditional risk models rely on market data; this paper offers an alternative.
method Uses encoder-only language models to embed news data, then calculates asset return distributions and covariance through Energy Distance.
result Established connections between distributional differences and excess returns co-movements using Energy Distance.
Study finite-energy metrics over complex manifold degenerations.
problem Finite-energy metrics on complex manifolds with singularities.
method Investigate spaces of plurisubharmonic metrics with finite-energy conditions.
result Complete and geodesic metric structure on finite-energy metrics space.
Sharp stability result for maps near infinitely concentrated minimisers.
problem Stability of maps near minimisers with infinite concentration.
method Dynamic approach to deform maps into harmonic maps, controlling topology changes.
result Sharp quantitative estimates on map distance to infinitely concentrated minimisers.
We show that K-energy minimizing movements agree with smooth solutions to Calabi flow as long as the latter exist. As corollaries we conclude that in a general Kahler class long time solutions of Calabi flow minimize both K-energy and Calabi energy. Lastly, by applying convergence results from the theory of minimizing …
Study distances between special functions on Kähler manifolds.
problem Measuring distances between plurisubharmonic functions on Kähler manifolds.
method Introduce a distance function ρ[u,v] and explore its properties.
result Properties of ρ[u,v] generalize Darvas's metrics.
Given a closed submanifold, or a compact regular domain, in euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two different regularization techniques (Hadamard's finite part and analytic continuatio…
Algorithm finds best Dirac mass approximation of target measure.
problem Finding optimal Dirac mass approximation of target measure.
method Minimizes statistical distance between original measure and quantized version using Huber-energy kernel.
result HEMQ algorithm robust and versatile, matches intuitive behavior.
Entropy convexity characterizes strong energy condition in spacetimes.
problem Characterizing strong energy condition in nonsmooth spacetimes.
method Lifting fractional powers of Lorentz distance to probability measures and showing geodesic convexity of Boltzmann-Shannon entropy.
result Strong energy condition is equivalent to geodesic convexity of Boltzmann-Shannon entropy.
In a vacuum spacetime equipped with the Bondi's radiating metric which is asymptotically flat at spatial infinity including gravitational radiation ({\bf Condition D}), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbatio…
Connected surfaces with boundary minimize Willmore energy under certain conditions.
problem Finding connected compact surfaces with minimal Willmore energy.
method Minimizing the Willmore energy on integer rectifiable curvature varifolds with boundary constraints.
result Existence of connected minimizers when the infimum of the problem is less than 4π.
Meta learns low-rank covariance factors for better uncertainty estimation.
problem Sub-optimal covariance matrices in multi-task settings.
method Meta learns diagonal or diagonal plus low-rank factors using an attentive set encoder.
result Efficiently constructed task-specific covariance matrices improve uncertainty estimation.
Geometric insights improve convergence of implicit generative models.
problem Improving convergence of implicit generative models.
method Analyzing geometries induced by Wasserstein distance and other criteria.
result Established surprising approximate global convergence guarantees for the 1-Wasserstein distance.
Quantitative stability for nearly minimizing Yamabe metrics.
problem Understanding the stability of nearly minimizing metrics in Riemannian geometry.
method Proving quantitative closeness of nearly minimizing metrics to minimizing metrics in a specific sense.
result The distance between nearly minimizing metrics and minimizing metrics is controlled quadratically by the Yamabe energy deficit.
Study exact Lagrangian cobordisms in cotangent bundles, proving bounds on sheaf interleaving distance and shadow distance.
problem Understanding Lagrangian cobordisms and their properties in cotangent bundles.
method Use microlocal theory of sheaves, sheaf quantization, and cone decompositions.
result Interleaving distance of sheaves is bounded by the shadow distance of the cobordism.
Study non-asymptotic behavior of Coulomb gas on compact manifolds.
problem Understand the behavior of Coulomb gas on compact manifolds.
method Use Kantorovich-Wasserstein distance, empirical measure, and heat kernel.
result Prove concentration inequality in Kantorovich-Wasserstein distance.
DCMA uses generative models to analyze complex treatment effects on outcome distributions.
problem Analyzing complex and nonlinear causal mechanisms through outcome-level summary contrasts.
method Generative learning framework for identifying and estimating treatment effects on entire outcome distributions.
result Reconstructs interventional outcome distributions via Monte Carlo forward simulation, capturing both summary and distributional contrasts.
Study of geometric analysis on asymmetric metric spaces, including heat flow and Sobolev spaces.
problem Analysis of geometric properties on asymmetric metric measure spaces.
method Introduction of upper gradients, q-Laplacian, and q-heat flow in asymmetric settings. result Extension of concepts from symmetric to asymmetric metric measure spaces.
Develops Morse theory for uniform energy using geodesics.
problem Minimizing properties of closed geodesics.
method One-sided directional derivative of distance function, gradient-like vectors, restarted negative gradient flow.
result Improved minimizing properties of closed geodesics.
We consider least energy solutions to the nonlinear equation −Δgu=f(r,u) posed on a class of Riemannian models (M,g) of dimension n≥2 which include the classical hyperbolic space Hn as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is …
Classifies soap film surfaces with vertical potentials.
problem Classifying soap film surfaces with vertical potentials.
method Variational characterization of n-elastic curves. result Obtains a full description of n-elastic curves. The paper studies properties of Sliced Wasserstein energy for discrete measures.
problem Optimizing discrete probability measures using Sliced Wasserstein loss.
method Investigates the regularity and optimisation properties of the Sliced Wasserstein energy and its Monte-Carlo approximation.
result Convergence results on the critical points of Monte-Carlo approximations to the Sliced Wasserstein energy.