Goal-oriented adaptive sampling under random field modelling of response probability distributions

• URL: http://arxiv.org/abs/2102.07612v1
• Date: Mon, 15 Feb 2021 15:55:23 GMT
• Title: Goal-oriented adaptive sampling under random field modelling of response probability distributions
• Authors: Ath\'ena\"is Gautier, David Ginsbourger, Guillaume Pirot
• Abstract summary: We consider cases where the spatial variation of response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions.
• Score: 0.6445605125467573
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision space. We consider cases where the spatial variation of these response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in particular to a spatial extension of the logistic Gaussian model. The considered models deliver probabilistic predictions of response distributions at candidate points, allowing for instance to perform (approximate) posterior simulations of probability density functions, to jointly predict multiple moments and other functionals of target distributions, as well as to quantify the impact of collecting new samples on the state of knowledge of the distribution field of interest. In particular, we introduce adaptive sampling strategies leveraging the potential of the considered random distribution field models to guide system evaluations in a goal-oriented way, with a view towards parsimoniously addressing calibration and related problems from non-linear (stochastic) inversion and global optimisation.

Related papers

• Enhanced Importance Sampling through Latent Space Exploration in Normalizing Flows [69.8873421870522]
  importance sampling is a rare event simulation technique used in Monte Carlo simulations. We propose a method for more efficient sampling by updating the proposal distribution in the latent space of a normalizing flow.
  arXiv  Detail & Related papers  (2025-01-06T21:18:02Z)
• Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data [2.6499018693213316]
  We introduce a novel generative model for the representation of joint probability distributions of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical submanifold of factorizing distributions.
  arXiv  Detail & Related papers  (2024-06-06T21:58:33Z)
• Uncertainty Quantification via Stable Distribution Propagation [60.065272548502]
  We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity.
  arXiv  Detail & Related papers  (2024-02-13T09:40:19Z)
• Invariant Probabilistic Prediction [45.90606906307022]
  We show that arbitrary distribution shifts do not, in general, admit invariant and robust probabilistic predictions. We propose a method to yield invariant probabilistic predictions, called IPP, and study the consistency of the underlying parameters.
  arXiv  Detail & Related papers  (2023-09-18T18:50:24Z)
• Learning Invariant Representations under General Interventions on the Response [2.725698729450241]
  We focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP) We analyze the generalization errors of our method under both the discrete and continuous environment settings.
  arXiv  Detail & Related papers  (2022-08-22T03:09:17Z)
• An Invariant Matching Property for Distribution Generalization under Intervened Response [19.786769414376323]
  We show a novel form of invariance by incorporating the estimates of certain features as additional predictors. We provide an explicit characterization of the linear matching and present our simulation results under various intervention settings.
  arXiv  Detail & Related papers  (2022-05-18T18:25:21Z)
• Wrapped Distributions on homogeneous Riemannian manifolds [58.720142291102135]
  Control over distributions' properties, such as parameters, symmetry and modality yield a family of flexible distributions. We empirically validate our approach by utilizing our proposed distributions within a variational autoencoder and a latent space network model.
  arXiv  Detail & Related papers  (2022-04-20T21:25:21Z)
• Personalized Trajectory Prediction via Distribution Discrimination [78.69458579657189]
  Trarimiy prediction is confronted with the dilemma to capture the multi-modal nature of future dynamics. We present a distribution discrimination (DisDis) method to predict personalized motion patterns. Our method can be integrated with existing multi-modal predictive models as a plug-and-play module.
  arXiv  Detail & Related papers  (2021-07-29T17:42:12Z)
• Achieving Efficiency in Black Box Simulation of Distribution Tails with Self-structuring Importance Samplers [1.6114012813668934]
  The paper presents a novel Importance Sampling (IS) scheme for estimating distribution of performance measures modeled with a rich set of tools such as linear programs, integer linear programs, piecewise linear/quadratic objectives, feature maps specified with deep neural networks, etc.
  arXiv  Detail & Related papers  (2021-02-14T03:37:22Z)
• Estimating Generalization under Distribution Shifts via Domain-Invariant Representations [75.74928159249225]
  We use a set of domain-invariant predictors as a proxy for the unknown, true target labels. The error of the resulting risk estimate depends on the target risk of the proxy model.
  arXiv  Detail & Related papers  (2020-07-06T17:21:24Z)
• Decision-Making with Auto-Encoding Variational Bayes [71.44735417472043]
  We show that a posterior approximation distinct from the variational distribution should be used for making decisions. Motivated by these theoretical results, we propose learning several approximate proposals for the best model. In addition to toy examples, we present a full-fledged case study of single-cell RNA sequencing.
  arXiv  Detail & Related papers  (2020-02-17T19:23:36Z)

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.