Related papers: Sasaki Metric for Spline Models of Manifold-Valued Trajectories

Sasaki Metric for Spline Models of Manifold-Valued Trajectories

URL: http://arxiv.org/abs/2303.17299v1
Date: Thu, 30 Mar 2023 11:24:56 GMT
Title: Sasaki Metric for Spline Models of Manifold-Valued Trajectories
Authors: Esfandiar Nava-Yazdani, Felix Ambellan, Martin Hanik, Christoph von Tycowicz
Abstract summary: We propose a generic framework to analyze manifold-valued measurements. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite B\' ezier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate average trajectories as group-wise trends. We evaluate our framework in comparison to state-of-the-art methods within qualitative and quantitative experiments on hurricane tracks. Notably, our results demonstrate the superiority of spline-based approaches for an intensity classification of the tracks.

Related papers

Analyzing Generative Models by Manifold Entropic Metrics [8.477943884416023]
We introduce a novel set of tractable information-theoretic evaluation metrics. We compare various normalizing flow architectures and $beta$-VAEs on the EMNIST dataset. The most interesting finding of our experiments is a ranking of model architectures and training procedures in terms of their inductive bias to converge to aligned and disentangled representations during training.
arXiv Detail & Related papers (2024-10-25T09:35:00Z)
CRITERIA: a New Benchmarking Paradigm for Evaluating Trajectory Prediction Models for Autonomous Driving [6.868387710209245]
We propose a new benChmarking paRadIgm for evaluaTing trajEctoRy predIction Approaches (CRITERIA) We show that the proposed benchmark can produce a more accurate ranking of the models and serve as a means of characterizing their behavior.
arXiv Detail & Related papers (2023-10-11T18:28:15Z)
A Geometric Perspective on Diffusion Models [57.27857591493788]
We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
arXiv Detail & Related papers (2023-05-31T15:33:16Z)
Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
arXiv Detail & Related papers (2022-06-29T22:19:03Z)
Riemannian Metric Learning via Optimal Transport [34.557360177483595]
We introduce an optimal transport-based model for learning a metric from cross-sectional samples of evolving probability measures. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data.
arXiv Detail & Related papers (2022-05-18T23:32:20Z)
Divergence Frontiers for Generative Models: Sample Complexity, Quantization Level, and Frontier Integral [58.434753643798224]
Divergence frontiers have been proposed as an evaluation framework for generative models. We establish non-asymptotic bounds on the sample complexity of the plug-in estimator of divergence frontiers. We also augment the divergence frontier framework by investigating the statistical performance of smoothed distribution estimators.
arXiv Detail & Related papers (2021-06-15T06:26:25Z)
MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
arXiv Detail & Related papers (2021-06-03T12:59:16Z)
GELATO: Geometrically Enriched Latent Model for Offline Reinforcement Learning [54.291331971813364]
offline reinforcement learning approaches can be divided into proximal and uncertainty-aware methods. In this work, we demonstrate the benefit of combining the two in a latent variational model. Our proposed metrics measure both the quality of out of distribution samples as well as the discrepancy of examples in the data.
arXiv Detail & Related papers (2021-02-22T19:42:40Z)
Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric [0.0]
We present a novel class of projected methods, to perform statistical analysis on a data set of probability distributions on the real line. We focus in particular on Principal Component Analysis (PCA) and regression. Several theoretical properties of the models are investigated and consistency is proven.
arXiv Detail & Related papers (2021-01-22T10:24:49Z)
On the minmax regret for statistical manifolds: the role of curvature [68.8204255655161]
Two-part codes and the minimum description length have been successful in delivering procedures to single out the best models. We derive a sharper expression than the standard one given by the complexity, where the scalar curvature of the Fisher information metric plays a dominant role.
arXiv Detail & Related papers (2020-07-06T17:28:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.