Fast ABC with joint generative modelling and subset simulation

• URL: http://arxiv.org/abs/2104.08156v1
• Date: Fri, 16 Apr 2021 15:03:23 GMT
• Title: Fast ABC with joint generative modelling and subset simulation
• Authors: Eliane Maalouf, David Ginsbourger and Niklas Linde
• Abstract summary: We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent space.
• Score: 0.6445605125467573
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent space. By jointly modelling input and output variables and endowing the latent with a prior distribution, the fitted probabilistic model indirectly gives access to the approximate conditional distributions of interest. Since model error and observational noise with unknown distributions are common in practice, we resort to likelihood-free inference with Approximate Bayesian Computation (ABC). Our method calls on ABC by Subset Simulation to explore the regions of the latent space with dissimilarities between generated and observed outputs below prescribed thresholds. We diagnose the diversity of approximate posterior solutions by monitoring the probability content of these regions as a function of the threshold. We further analyze the curvature of the resulting diagnostic curve to propose an adequate ABC threshold. When applied to a cross-borehole tomography example from geophysics, our approach delivers promising performance without using prior knowledge of the forward nor of the noise distribution.

Related papers

• A Stein Gradient Descent Approach for Doubly Intractable Distributions [5.63014864822787]
  We propose a novel Monte Carlo Stein variational gradient descent (MC-SVGD) approach for inference for doubly intractable distributions. The proposed method achieves substantial computational gains over existing algorithms, while providing comparable inferential performance for the posterior distributions.
  arXiv  Detail & Related papers  (2024-10-28T13:42:27Z)
• Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations [1.371691382573869]
  We develop and enhance score-based diffusion models in field reconstruction tasks. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions. We demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results.
  arXiv  Detail & Related papers  (2024-08-30T19:46:23Z)
• Amortizing intractable inference in diffusion models for vision, language, and control [89.65631572949702]
  This paper studies amortized sampling of the posterior over data, $mathbfxsim prm post(mathbfx)propto p(mathbfx)r(mathbfx)$, in a model that consists of a diffusion generative model prior $p(mathbfx)$ and a black-box constraint or function $r(mathbfx)$. We prove the correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from
  arXiv  Detail & Related papers  (2024-05-31T16:18:46Z)
• Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems [4.42498215122234]
  This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. A novel convergence analysis is conducted, inspired by the fixed-point methods established for traditional regularization-by-denoising algorithms.
  arXiv  Detail & Related papers  (2024-05-24T16:17:01Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models [98.95988351420334]
  We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting.
  arXiv  Detail & Related papers  (2023-07-02T17:21:30Z)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• ManiFlow: Implicitly Representing Manifolds with Normalizing Flows [145.9820993054072]
  Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. We propose an optimization objective that recovers the most likely point on the manifold given a sample from the perturbed distribution. Finally, we focus on 3D point clouds for which we utilize the explicit nature of NFs, i.e. surface normals extracted from the gradient of the log-likelihood and the log-likelihood itself.
  arXiv  Detail & Related papers  (2022-08-18T16:07:59Z)
• Sparse Interaction Neighborhood Selection for Markov Random Fields via Reversible Jump and Pseudoposteriors [0.0]
  We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions. We propose a Reversible Jump Monte Carlo Markov Chain algorithm that jumps across subsets of a maximal range neighborhood.
  arXiv  Detail & Related papers  (2022-04-12T16:34:33Z)
• Resampling Base Distributions of Normalizing Flows [0.0]
  We introduce a base distribution for normalizing flows based on learned rejection sampling. We develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the reverse Kullback-Leibler divergence.
  arXiv  Detail & Related papers  (2021-10-29T14:44:44Z)
• Generative Modeling with Denoising Auto-Encoders and Langevin Sampling [88.83704353627554]
  We show that both DAE and DSM provide estimates of the score of the smoothed population density. We then apply our results to the homotopy method of arXiv:1907.05600 and provide theoretical justification for its empirical success.
  arXiv  Detail & Related papers  (2020-01-31T23:50:03Z)

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.