Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifold-based inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, appl…
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48 results for “metric matching”
Match van Stockum dust to vacuum metrics with a single parameter.
problem Matching van Stockum dust to vacuum metrics.
method 1-parametric family of non-static Papapetrou vacuum metrics, Ehlers and Kramer--Neugebauer transformations.
result Explicit examples of matching, including Bonnor metric and Lanczos--van Stockum dust metric.
New method for comparing curves with flexible matching constraints.
problem Comparing plane curves with general elastic metrics.
method Combining transform for elastic metrics with parametrization-invariant fidelity metrics.
result Simple optimization problem for discretized curves.
Riemannian metric matching learns the geometry of high-dimensional datasets using neural networks.
problem Estimating the geometry of high-dimensional datasets from samples
method Riemannian metric matching using neural networks
result Riemannian metric matching rivals or improves -NN-based diffusion geometry estimators
KDM unifies feature matching in neural networks.
problem Matching neural network activations for knowledge transfer.
method Formalizes distribution matching strategy.
result New theoretical results for KD.
We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the duality gives a version of global calibrations for 1-chains with coefficients in $…
Proposes DWMD for better matching of hidden representations across domains.
problem Measuring data distribution discrepancy between semantically related domains for feature representation matching.
method DWMD, a moment-based probability distribution metric that explicitly orders and weights higher-order moments.
result DWMD is error-free and can strictly reflect distribution differences without feature distribution assumptions.
Paper computes optimal matching between curves on manifolds.
problem Matching curves on infinite-dimensional manifolds.
method Geodesic computation using Riemannian metric and quotient structure.
result Algorithm for computing geodesics in shape space.
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the prism of Riemannian submersions, with shape space metrics being induced from metrics…
Matched Machine Learning combines machine learning and matching for causal inference.
problem Non-interpretable methods for causal inference.
method Combines machine learning and matching for interpretable causal inference.
result Performs as well as black-box machine learning methods and better than existing matching methods.
MFM improves generative model interpolations by learning approximate geodesics on data manifolds.
problem Straight interpolations fail to capture dynamics on data manifolds.
method Metric Flow Matching (MFM) learns approximate geodesics by minimizing kinetic energy of a data-induced Riemannian metric.
result MFM outperforms Euclidean baselines, achieving SOTA on single-cell trajectory prediction.
In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the …
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
We introduce new families of Integral Probability Metrics (IPM) for training Generative Adversarial Networks (GAN). Our IPMs are based on matching statistics of distributions embedded in a finite dimensional feature space. Mean and covariance feature matching IPMs allow for stable training of GANs, which we will call M…
When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a growing number of continuous features, a curse of dimensionality applies making asym…
New metric captures individual neuron tuning across neural networks.
problem Need a metric that respects individual neuron tuning across different neural networks.
method Derived a 'soft' permutation-based metric using optimal transport theory.
result Metric avoids counter-intuitive outcomes and captures geometric insights.
A new method matches similar regions in non-rigid shapes using spectra of differential operators.
problem Evaluating similarity of non-rigid shapes with partiality.
method Alignment of spectra of differential operators (SI-LBO and regular LBO) on a manifold with multiple metrics.
result Matching spectra outperforms competing methods on standard benchmarks.
A2A metric evaluates bias correction methods, reducing ATE estimation errors.
problem Selection biases in non-randomized studies of medical treatments.
method Propensity score matching (PSM) with novel metric A2A.
result Reduces ATE estimation errors by up to 90% across synthetic and real-world datasets.
Study uses complex networks and machine learning to predict soccer match outcomes.
problem Predicting soccer match outcomes with complex networks and machine learning.
method Complex network metrics and match statistics were used to build machine learning models.
result Models based on passing networks were as effective as traditional models using match statistics.
This study analyzes the quadratic Wasserstein metric's effects on inverse data matching.
problem Analyzing the quadratic Wasserstein metric's impact on inverse data matching.
method Characterizes and numerically analyzes the smoothing effect and convexity improvement of distance.
result The distance improves convexity and reduces resolution for reconstructed objects at a given noise level.
We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic matching framework. In the latter approach a deformation is pr…
We study completeness properties of the Sobolev diffeomorphism groups endowed with strong right-invariant Riemannian metrics when the underlying manifold is or compact without boundary. The main result is that for , the group is geodesically and me…
A classical problem in causal inference is that of matching, where treatment units need to be matched to control units based on covariate information. In this work, we propose a method that computes high quality almost-exact matches for high-dimensional categorical datasets. This method, called FLAME (Fast Large-scale …
Unified calibration metrics improve forecast sharpness and accuracy.
problem Improving the sharpness of probabilistic forecasts while maintaining calibration.
method Kernel-based calibration metrics that unify and generalize existing methods for classification and regression.
result Enhanced calibration, sharpness, and decision-making across various tasks.
New algorithms solve partial optimal transport problems for applications like PU learning.
problem Optimal transport constraints on equal mass distributions limit applicability.
method Developed exact algorithms for partial Wasserstein and Gromov-Wasserstein problems.
result Partial Wasserstein metrics show effectiveness in positive-unlabeled learning.
Propensity score matching improves fairness in machine learning models.
problem Bias in training data affects fairness metrics in machine learning models.
method Propensity score matching to evaluate and mitigate bias in test data.
result FairMatch significantly reduces bias in test data without sacrificing predictive performance.
Develops Hamiltonian Score Matching and Generative Flows for machine learning.
problem Estimating score functions and designing generative models.
method Introduces Hamiltonian velocity predictors (HVPs) for score matching and generative flows.
result Hamiltonian Generative Flows (HGFs) rival leading generative modeling techniques.
Partial soft-matching distance improves neural representation comparison by allowing some neurons to remain unmatched.
problem Neural representations are noisy and contain outliers, making traditional matching methods unreliable.
method Extends soft-matching distance to a partial optimal transport setting, allowing some neurons to remain unmatched.
result Partial soft-matching provides robust correspondences that are more reliable under noise and outliers.
CFMI improves missing data imputation across various data types and dimensions.
problem Imputing missing data in complex, high-dimensional datasets.
method Combines normalising flows, flow-matching, and shared conditional modelling.
result Outperforms traditional and modern imputation methods across multiple metrics.
New method improves robust point matching under probabilistic settings.
problem Insufficient theoretical understanding of existing point matching methods.
method Distance profiles and modified matching procedure.
result Improved robustness under probabilistic settings.
Almost Hermitian Ricci flowmath.DG
New flow preserves almost Hermitian metrics for manifold study.
problem Curvature flow for almost Hermitian manifolds.
method Introducing a new curvature flow matching Ricci flow and preserving almost Hermitian condition.
result Ricci flow can be used to study almost Hermitian manifolds.
Complete constant positive scalar curvature metrics on S^n - {p_1, ..., p_k} admit a definite asymptotic structure; i.e. the metric is asymptotic to a specific S^{n-1}-invariant metric near the puncture points. This allows one to glue together two such metrics near their puncture points, provided the asymptotic structu…
New method for partial matching of shapes with Varifolds.
problem Matching structures with topological or shape differences.
method Varifold shape representation and LDDMM framework.
result Effective partial matching despite topological differences.
DFM simplifies CNF training without interpolants.
problem Efficiently training CNFs with computationally expensive ODE solving.
method DFM optimizes dual vector fields for bijective transformations.
result DFM outperforms CNF trained with FM or ML objectives.
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimension…
A new numerical framework simplifies elastic surface matching and comparison.
problem Challenging problem in surface comparison and matching in computer vision.
method Relaxing the geodesic boundary constraint using a varifold fidelity metric.
result Flexibility to deal with arbitrary topologies and sampling patterns, scalability to large meshes.
Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this paper, we study nearest neighbor matching (NNM), which makes estimates of populati…
We argue that the existing regret matchings for Nash equilibrium approximation conduct "jumpy" strategy updating when the probabilities of future plays are set to be proportional to positive regret measures. We propose a geometrical regret matching which features "smooth" strategy updating. Our approach is simple, intu…
Score matching method improves image generation quality.
problem Score matching method underperforms GANs in metrics like Fréchet Inception Distance.
method DSM-ALS with denoising and improved sampling techniques.
result Score matching methods can match GANs in image generation quality.
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.
Numerical Solutions of Kahler-Einstein metrics on with conical singularities along a conic curvemath.DG
We solve for the SO(3)-invariant Kahler-Einstein metric on with cone singularities along a smooth conic curve using numerical approach. The numerical results show the sharp range of angles () for the solvability of equations, and the right limit metric space (). These results exactly …
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
Proposes a new metric for comparing shapes in different spaces.
problem Comparing shapes in different metric spaces with unequal mass.
method Developed a Partial Gromov-Wasserstein (PGW) metric and algorithms to solve it.
result PGW is a well-defined metric between metric measure spaces.
The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an op…
We investigate shock-wave solutions of the Einstein equations in the case when the speed of propagation is equal to the speed of light. The work extends the shock matching theory of Smoller and Temple, which characterizes solutions of the Einstein equations when the spacetime metric is only Lipschitz continuous across …
We improve density-based distances using normalizing flows and score matching.
problem Inaccurate density estimates and poor convergence in graph-based methods for high-dimensional spaces.
method Learn densities with normalizing flows and refine geodesics with a score model.
result Improved density-based distances that scale to high dimensions and improve numerical stability.
A geometric theory explains loss functions for robust representation learning.
problem Treats robustness, domain adaptation, and sensor drift as separate literatures.
method Estimates covariance Sigma_task and uses it to pin Jacobian penalties.
result Proves optimality and necessity of range coverage for penalty matrices.
New algorithm speeds up causal discovery for network data.
problem Scalability issues in score-matching for temporal network data.
method Developed a new parent-finding subroutine for DAGs, improving score matching efficiency.
result Efficiency-lifted score matching for both i.i.d. and temporal data on networks.