Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows. Based on the fact, that proximal neural networks are by definition averaged operators, we ensure invertibility of certain residual blocks. Moreover, we extend the architecture to conditional proximal residual flows for posterior reconstruction within Bayesian inverse problems. We demonstrate the performance of proximal residual flows on numerical examples.
Proximal-Based Generative Modeling for Bayesian Inverse Problems
School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences（中国科学院大学先进交叉科学学院）；School of Mathematics, Sichuan University（四川大学数学学院）；School of Mathematical Sciences, Beijing University of Posts and Telecommunications（北京邮电大学数学科学学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Ministry of Education Key Laboratory of Mathematics and Information Networks（教育部数学与信息网络重点实验室）
ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding
University of Oxford（牛津大学）；Harvard University（哈佛大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；Vector Institute（向量研究所）；University College London（伦敦大学学院）
Recovering images from undersampled linear measurements typically leads to an ill-posed linear inverse problem, that asks for proper statistical priors. Building effective priors is however challenged by the low train and test overhead dictated by real-time tasks; and the need for retrieving visually "plausible" and physically "feasible" images with minimal hallucination. To cope with these challenges, we design a cascaded network architecture that unrolls the proximal gradient iterations by permeating benefits from generative residual networks (ResNet) to modeling the proximal operator. A mix…
Beijing University of Aeronautics and Astronautics（北京航空航天大学）；University of Utah（犹他大学）；Chongqing University（重庆大学）；Beihang University（北京航空航天大学）
Challenges in multi-fidelity modeling relate to accuracy, uncertainty estimation and high-dimensionality. A novel additive structure is introduced in which the highest fidelity solution is written as a sum of the lowest fidelity solution and residuals between the solutions at successive fidelity levels, with Gaussian process priors placed over the low fidelity solution and each of the residuals. The resulting model is equipped with a closed-form solution for the predictive posterior, making it applicable to advanced, high-dimensional tasks that require uncertainty estimation. Its advantages ar…
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…
Optimizing the Unknown: Black Box Bayesian Optimization with Energy-Based Model and Reinforcement Learning
University of California, Los Angeles（加州大学洛杉矶分校）；The Hong Kong University of Science and Technology (Guangzhou)（香港科学与技术大学（广州））；The Hong Kong University of Science and Technology（香港科学与技术大学）
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the recurrent application of proximal gradient algorit…
Informed and robust decision making in the face of uncertainty is critical for robots that perform physical tasks alongside people. We formulate this as Bayesian Reinforcement Learning over latent Markov Decision Processes (MDPs). While Bayes-optimality is theoretically the gold standard, existing algorithms do not scale well to continuous state and action spaces. Our proposal builds on the following insight: in the absence of uncertainty, each latent MDP is easier to solve. We first obtain an ensemble of experts, one for each latent MDP, and fuse their advice to compute a baseline policy. Nex…
Online Optimization of Difference-of-Convex Compositions with Smooth Mappings
Management Science and Engineering, Stanford University（斯坦福大学管理科学与工程系）；The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California（南加州大学丹尼尔·J·埃普斯坦工业与系统工程系）
Pushing the Limits of Distillation-Based Continual Learning via Classifier-Proximal Lightweight Plugins
National Key Laboratory for Novel Software Technology, Nanjing University, China（南京大学计算机软件新技术国家重点实验室）；School of Artificial Intelligence, Nanjing University, China（南京大学人工智能学院）；Department of Computer Science and Technology, Nanjing University, China（南京大学计算机科学与技术系）；School of Electronic Science and Engineering, Nanjing University, China（南京大学电子科学与工程学院）
Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations
Department of Applied Mathematics and Computer Science (DTU Compute)（应用数学与计算机科学系（DTU Compute））；Technical University of Denmark（丹麦技术大学）
Technion - Israel Institute of Technology（以色列理工学院）
This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized with multiple (simple) functions. Motivated by high-dimensional applications in which exact projection/proximal computations are not tractable, we propose a \textit{projection-free} augmented Lagrangian-based method, in which primal updates are carried out using a \textit{weak proximal oracle} (WPO). In an earlier work, WPO was shown to be more powerful than…
Sparse Transformer Architectures via Regularized Wasserstein Proximal Operator with $L_1$ Prior
Department of Mathematics, University of California, Los Angeles, CA, USA（加州大学洛杉矶分校数学系）；Department of Mathematics, University of South Carolina, Columbia, SC, USA（南卡罗来纳大学数学系）
ProFlow: Zero-Shot Physics-Consistent Sampling via Proximal Flow Guidance
University of Science；School of Mathematical Sciences, Fudan University, Shanghai 200433, China；Department of Electronic Engineering；Information Science, University of Science；School of Computing；Data Science, The University of Hong Kong；School of Mathematical Sciences, Fudan University, Shanghai 200433, China \& Shanghai Key Laboratory of Contemporary Applied Mathematics, Shanghai 200433, China
Constrained and Composite Sampling via Proximal Sampler
Department of Computer Science, University of Rochester（计算机科学系，罗切斯特大学）；Goergen Institute for Data Science and Artificial Intelligence (GIDS-AI)（数据科学与人工智能研究所（GIDS-AI））
Convergence of flow-based generative models via proximal gradient descent in Wasserstein space
Department of Mathematics, Duke University（杜克大学数学系）；Department of Physics and Department of Chemistry, Duke University（杜克大学物理系和化学系）；H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（佐治亚理工学院H. Milton Stewart工业与系统工程学院）
