Nonparametric Multi-shape Modeling with Uncertainty Quantification

• URL: http://arxiv.org/abs/2206.09127v2
• Date: Wed, 22 Jun 2022 02:45:06 GMT
• Title: Nonparametric Multi-shape Modeling with Uncertainty Quantification
• Authors: Hengrui Luo, Justin D. Strait
• Abstract summary: We propose and investigate a multiple-output, multi-dimensional Gaussian process modeling framework. We illustrate the proposed methodological advances, and demonstrate the utility of meaningful uncertainty quantification. This model-based approach not only addresses the problem of inference on closed curves (and their shapes) with kernel constructions, but also opens doors to nonparametric modeling of multi-level dependence for functional objects in general.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed curves, which often exhibit structural similarities at multiple levels. Modeling multiple closed curves in a way that efficiently incorporates such between-curve dependence remains a challenging problem. In this work, we propose and investigate a multiple-output (a.k.a. multi-output), multi-dimensional Gaussian process modeling framework. We illustrate the proposed methodological advances, and demonstrate the utility of meaningful uncertainty quantification, on several curve and shape-related tasks. This model-based approach not only addresses the problem of inference on closed curves (and their shapes) with kernel constructions, but also opens doors to nonparametric modeling of multi-level dependence for functional objects in general.

Related papers

• Physics-constrained symbolic regression for discovering closed-form equations of multimodal water retention curves from experimental data [1.1278037007482673]
  We introduce a physics-constrained machine learning framework designed for meta-modeling, enabling the automatic discovery of closed-form mathematical expressions for multimodal water retention curves directly from experimental data.<n>Our results demonstrate that the proposed framework can discover closed-form equations that effectively represent the water retention characteristics of porous materials with varying pore structures.
  arXiv  Detail & Related papers  (2026-02-24T18:48:15Z)
• Modelling non-stationary extremal dependence through a geometric approach [0.0]
  Non-stationary extremal dependence is commonly observed in environmental and financial data sets.<n>A recent approach to multivariate extreme value modelling uses a geometric framework, whereby extremal dependence features are inferred through the limiting shapes of scaled sample clouds.<n>This framework can capture a wide range of dependence structures, and a variety of inference procedures have been proposed in the stationary setting.
  arXiv  Detail & Related papers  (2025-09-26T15:42:57Z)
• A general physics-constrained method for the modelling of equation's closure terms with sparse data [8.927683811459543]
  We introduce a Series-Parallel Multi-Network Architecture that integrates physical constraints and heterogeneous data from multiple initial and boundary conditions.<n>We employ dedicatedworks to independently model unknown closure terms, enhancing generalizability across diverse problems.<n>These closure models are integrated into an accurate Partial Differential Equation (PDE) solver, enabling robust solutions to complex predictive simulations in engineering applications.
  arXiv  Detail & Related papers  (2025-04-30T14:41:18Z)
• Identifiable Multi-View Causal Discovery Without Non-Gaussianity [63.217175519436125]
  We propose a novel approach to linear causal discovery in the framework of multi-view Structural Equation Models (SEM) We prove the identifiability of all the parameters of the model without any further assumptions on the structure of the SEM other than it being acyclic. The proposed methodology is validated through simulations and application on real data, where it enables the estimation of causal graphs between brain regions.
  arXiv  Detail & Related papers  (2025-02-27T14:06:14Z)
• Continuous Bayesian Model Selection for Multivariate Causal Discovery [22.945274948173182]
  We propose a scalable algorithm leveraging a continuous relaxation of the discrete model selection problem.<n>We employ the Causal Gaussian Process Conditional Density Estimator (CGP-CDE) as a Bayesian non-parametric model.<n>This matrix is then optimised using the marginal likelihood and an acyclicity regulariser, giving the maximum a posteriori causal graph.
  arXiv  Detail & Related papers  (2024-11-15T12:55:05Z)
• Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihood [13.175343048302697]
  We propose a model-free approach for estimating such latent structures whenever they are present, without assuming they exist a priori. As an application, we design a clustering algorithm based on the proposed procedure and demonstrate its effectiveness in capturing a wide range of latent structures.
  arXiv  Detail & Related papers  (2024-10-29T17:11:33Z)
• Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data [15.26007975367927]
  We introduce a functional linear structural equation model for causal structure learning. To enhance interpretability, our model involves a low-dimensional causal embedded space. We prove that the proposed model is causally identifiable under standard assumptions.
  arXiv  Detail & Related papers  (2023-10-31T15:19:24Z)
• Multi-Response Heteroscedastic Gaussian Process Models and Their Inference [1.52292571922932]
  We propose a novel framework for the modeling of heteroscedastic covariance functions. We employ variational inference to approximate the posterior and facilitate posterior predictive modeling. We show that our proposed framework offers a robust and versatile tool for a wide array of applications.
  arXiv  Detail & Related papers  (2023-08-29T15:06:47Z)
• Partial Counterfactual Identification from Observational and Experimental Data [83.798237968683]
  We develop effective Monte Carlo algorithms to approximate the optimal bounds from an arbitrary combination of observational and experimental data. Our algorithms are validated extensively on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-10-12T02:21:30Z)
• Approximate Latent Force Model Inference [1.3927943269211591]
  latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. We show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation.
  arXiv  Detail & Related papers  (2021-09-24T09:55:00Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Compositional Modeling of Nonlinear Dynamical Systems with ODE-based Random Features [0.0]
  We present a novel, domain-agnostic approach to tackling this problem. We use compositions of physics-informed random features, derived from ordinary differential equations. We find that our approach achieves comparable performance to a number of other probabilistic models on benchmark regression tasks.
  arXiv  Detail & Related papers  (2021-06-10T17:55:13Z)
• Nonlinear Independent Component Analysis for Continuous-Time Signals [85.59763606620938]
  We study the classical problem of recovering a multidimensional source process from observations of mixtures of this process. We show that this recovery is possible for many popular models of processes (up to order and monotone scaling of their coordinates) if the mixture is given by a sufficiently differentiable, invertible function.
  arXiv  Detail & Related papers  (2021-02-04T20:28:44Z)
• Disentangling Observed Causal Effects from Latent Confounders using Method of Moments [67.27068846108047]
  We provide guarantees on identifiability and learnability under mild assumptions. We develop efficient algorithms based on coupled tensor decomposition with linear constraints to obtain scalable and guaranteed solutions.
  arXiv  Detail & Related papers  (2021-01-17T07:48:45Z)
• Accounting for Unobserved Confounding in Domain Generalization [107.0464488046289]
  This paper investigates the problem of learning robust, generalizable prediction models from a combination of datasets. Part of the challenge of learning robust models lies in the influence of unobserved confounders. We demonstrate the empirical performance of our approach on healthcare data from different modalities.
  arXiv  Detail & Related papers  (2020-07-21T08:18:06Z)
• Bayesian Sparse Factor Analysis with Kernelized Observations [67.60224656603823]
  Multi-view problems can be faced with latent variable models. High-dimensionality and non-linear issues are traditionally handled by kernel methods. We propose merging both approaches into single model.
  arXiv  Detail & Related papers  (2020-06-01T14:25:38Z)

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

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.