Related papers: Joint learning of variational representations and …

Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…

Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…

Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…

Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conventional reduced setting, the model equation is eliminated…

Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…

Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori}…

Employing deep neural networks as natural image priors to solve inverse problems either requires large amounts of data to sufficiently train expressive generative models or can succeed with no data via untrained neural networks. However,…

Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…

We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…

We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…

In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…

We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to…

Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework…

We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

Among other uses, neural networks are a powerful tool for solving deterministic and Bayesian inverse problems in real-time, where variational autoencoders, a specialized type of neural network, enable the Bayesian estimation of model…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…

Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…