Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantification
Georgia Institute of Technology（佐治亚理工学院）；Rice University（莱斯大学）；University Medical Center Utrecht（乌得勒支大学医学中心）；Centrum Wiskunde & Informatica（荷兰数学与计算机科学研究院）
Rafael Orozco, Mathias Louboutin, Ali Siahkoohi, Gabrio Rizzuti, Tristan van Leeuwen, Felix Herrmann
备注：
Accepted into PMLR Medical Imaging with Deep Learning (MIDL) 2023
We present a novel approach to transcranial ultrasound computed tomography that utilizes normalizing flows to improve the speed of imaging and provide Bayesian uncertainty quantification. Our method combines physics-informed methods and data-driven methods to accelerate the reconstruction of the final image. We make use of a physics-informed summary statistic to incorporate the known ultrasound physics with the goal of compressing large incoming observations. This compression enables efficient training of the normalizing flow and standardizes the size of the data regardless of imaging configurations. The combinations of these methods results in fast uncertainty-aware image reconstruction that generalizes to a variety of transducer configurations. We evaluate our approach with in silico experiments and demonstrate that it can significantly improve the imaging speed while quantifying uncertainty. We validate the quality of our image reconstructions by comparing against the traditional physics-only method and also verify that our provided uncertainty is calibrated with the error.
Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿罗森多夫研究中心）；European XFEL（欧洲X射线自由电子激光器）；University of Siegen（锡根大学）；Forschungszentrum Jülich（于利希研究中心）
Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a modern imaging technique used in material research to study nanoscale materials. Reconstruction of the parameters of an imaged object imposes an ill-posed inverse problem that is further complicated when only an in-plane GISAXS signal is available. Traditionally used inference algorithms such as Approximate Bayesian Computation (ABC) rely on computationally expensive scattering simulation software, rendering analysis highly time-consuming. We propose a simulation-based framework that combines variational auto-encoders and normalizing…
Amortized Sampling with Transferable Normalizing Flows
University of Oxford（牛津大学）；Université de Montréal（蒙特利尔大学）；Mila - Quebec AI Institute（魁北克AI研究所）；Freie Universität Berlin（柏林自由大学）；Valence Labs（Valence实验室）；AITHYRA；Institut Courtois（科特伊研究所）
Amortized Filtering and Smoothing with Conditional Normalizing Flows
School of Mathematics and Statistics（数学与统计学学院）；The University of Sydney（悉尼大学）；Faculty of Science and Technology（科学与技术学院）；Beijing Normal-Hong Kong Baptist University（北京师范大学-香港 Baptist大学）；Institute of Computational Mathematics and Scientific/Engineering Computing（计算数学与科学/工程计算研究所）；Academy of Mathematics and Systems Science（数学与系统科学学院）；Chinese Academy of Sciences（中国科学院）；Department of Mathematics and Center for Computation and Technology（数学系与计算技术中心）；Louisiana State University（路易斯安那州立大学）
University of Waterloo（滑铁卢大学）；Vector Institute（矢量研究所）；University of Edinburgh（爱丁堡大学）
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but would like to exploit the superior density estimation performance of normalizing flows and allow for arbitrary noise distributions. Since both adjustments lead to an intractable likelihood, we resort to amortized variational inference. We demonstrate some problems involved in this approach, however, experiments on real data demonstrate that flows can alread…
Frequently, population studies feature pyramidally-organized data represented using Hierarchical Bayesian Models (HBM) enriched with plates. These models can become prohibitively large in settings such as neuroimaging, where a sample is composed of a functional MRI signal measured on 300 brain locations, across 4 measurement sessions, and 30 subjects, resulting in around 1 million latent parameters.Such high dimensionality hampers the usage of modern, expressive flow-based techniques.To infer parameter posterior distributions in this challenging class of problems, we designed a novel methodolo…
Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained unconditional flow model. We first establish that this is computationally hard for a large class of flow models. Motivated by this, we propose a framework for approximate inference that estimates the target conditional as a composition of two flow models. This formulation leads to a stable variational inference training procedure that avoids adversarial training. Our …
Stellenbosch University（斯泰伦博斯大学）；National Institute for Theoretical and Computational Sciences（国家理论与计算科学研究所）
Initial work on variational autoencoders assumed independent latent variables with simple distributions. Subsequent work has explored incorporating more complex distributions and dependency structures: including normalizing flows in the encoder network allows latent variables to entangle non-linearly, creating a richer class of distributions for the approximate posterior, and stacking layers of latent variables allows more complex priors to be specified for the generative model. This work explores incorporating arbitrary dependency structures, as specified by Bayesian networks, into VAEs. This…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizi…
This paper studies the cooperative learning of two generative flow models, in which the two models are iteratively updated based on the jointly synthesized examples. The first flow model is a normalizing flow that transforms an initial simple density to a target density by applying a sequence of invertible transformations. The second flow model is a Langevin flow that runs finite steps of gradient-based MCMC toward an energy-based model. We start from proposing a generative framework that trains an energy-based model with a normalizing flow as an amortized sampler to initialize the MCMC chains…
StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow
Institute of Astronomy（天文研究所）；Kavli Institute for Cosmology, University of Cambridge, Cambridge, UK（剑桥大学卡文迪许实验室，剑桥，英国）；Research Computing Services, University of Cambridge, Cambridge, UK（剑桥大学研究计算服务）；The Oskar Klein Centre, Department of Physics, Stockholm University, Stockholm, SE（斯德哥尔摩大学物理系奥斯卡·克莱因中心）；Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, UK（剑桥大学物理系卡文迪许实验室）
Unifying supervised learning and VAEs -- coverage, systematics and goodness-of-fit in normalizing-flow based neural network models for astro-particle reconstructions
