Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification

• URL: http://arxiv.org/abs/2006.12394v3
• Date: Thu, 8 Apr 2021 20:21:01 GMT
• Title: Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification
• Authors: Antoine Blanchard, Themistoklis Sapsis
• Abstract summary: We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active learning, whereby existing samples of a black-box function are utilized to optimize the next most informative sample. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events. The acquisition functions introduced in this work leverage the properties of the likelihood ratio, a quantity that acts as a probabilistic sampling weight and guides the active-learning algorithm towards regions of the input space that are deemed most relevant. We demonstrate superiority of the proposed approach in the uncertainty quantification of a hydrological system as well as the probabilistic quantification of rare events in dynamical systems and the identification of their precursors.

Related papers

• Differentiating Policies for Non-Myopic Bayesian Optimization [5.793371273485735]
  We show how to efficiently estimate rollout functions and their gradient, enabling sampling policies. In this paper, we show how to efficiently estimate rollout functions and their gradient, enabling sampling policies.
  arXiv  Detail & Related papers  (2024-08-14T21:00:58Z)
• Latent Energy-Based Odyssey: Black-Box Optimization via Expanded Exploration in the Energy-Based Latent Space [65.44449711359724]
  High-dimensional and highly-multimodal input design space of black-box function pose inherent challenges for existing methods. We consider finding a latent space that serves as a compressed yet accurate representation of the design-value joint space. We propose Noise-intensified Telescoping density-Ratio Estimation scheme for variational learning of an accurate latent space model.
  arXiv  Detail & Related papers  (2024-05-27T00:11:53Z)
• Identifiability and Characterization of Transmon Qutrits Through Bayesian Experimental Design [0.0]
  We present an online, Bayesian approach for quantum characterization of qutrit systems. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. We provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable.
  arXiv  Detail & Related papers  (2023-12-15T22:02:54Z)
• Rare Event Probability Learning by Normalizing Flows [27.34331961951239]
  A rare event is defined by a low probability of occurrence. We propose normalizing flow assisted importance sampling, termed NOFIS. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations.
  arXiv  Detail & Related papers  (2023-10-29T21:59:33Z)
• Metrics for Bayesian Optimal Experiment Design under Model Misspecification [3.04585143845864]
  The utility function defines the objective of the experiment where a common utility function is the information gain. This article introduces an expanded framework for this process, where we go beyond the traditional Expected Information Gain criteria. The functionality of the framework is showcased through its application to a scenario involving a linearized spring mass damper system and an F-16 model.
  arXiv  Detail & Related papers  (2023-04-17T02:13:20Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Generalizing Bayesian Optimization with Decision-theoretic Entropies [102.82152945324381]
  We consider a generalization of Shannon entropy from work in statistical decision theory. We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures. We then show how alternative choices for the loss yield a flexible family of acquisition functions.
  arXiv  Detail & Related papers  (2022-10-04T04:43:58Z)
• Sensing Cox Processes via Posterior Sampling and Positive Bases [56.82162768921196]
  We study adaptive sensing of point processes, a widely used model from spatial statistics. We model the intensity function as a sample from a truncated Gaussian process, represented in a specially constructed positive basis. Our adaptive sensing algorithms use Langevin dynamics and are based on posterior sampling (textscCox-Thompson) and top-two posterior sampling (textscTop2) principles.
  arXiv  Detail & Related papers  (2021-10-21T14:47:06Z)
• Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
  Inferring the parameters of a model based on experimental observations is central to the scientific method. A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations. We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
  arXiv  Detail & Related papers  (2021-02-12T12:23:13Z)
• Video Prediction via Example Guidance [156.08546987158616]
  In video prediction tasks, one major challenge is to capture the multi-modal nature of future contents and dynamics. In this work, we propose a simple yet effective framework that can efficiently predict plausible future states.
  arXiv  Detail & Related papers  (2020-07-03T14:57:24Z)
• A practical and efficient approach for Bayesian quantum state estimation [0.0]
  We introduce an improved, self-contained approach for Bayesian quantum state estimation. Our formulation relies on highly efficient preconditioned Crank--Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets.
  arXiv  Detail & Related papers  (2020-02-24T16:32:28Z)

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.