Related papers: Optimization for Amortized Inverse Problems

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…

We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling. This approach allows for the efficient inference of theoretical parameters in high-dimensional…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Feature attribution methods, or saliency maps, are one of the most popular approaches for explaining the decisions of complex machine learning models such as deep neural networks. In this study, we propose a stochastic optimization approach…

Generative models, such as GANs, learn an explicit low-dimensional representation of a particular class of images, and so they may be used as natural image priors for solving inverse problems such as image restoration and compressive…

Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new…

We study an inverse design problem for the linear multiple fragmentation equation arising in particle dynamics. Our objective is to reconstruct an unknown initial size distribution that evolves, under a prescribed fragmentation law, into a…

In this paper, we present a distributed algorithm for solving convex, constraint-coupled, optimization problems over peer-to-peer networks. We consider a network of processors that aim to cooperatively minimize the sum of local cost…

A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…

Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…

Image denoisers have been shown to be powerful priors for solving inverse problems in imaging. In this work, we introduce a generalization of these methods that allows any image restoration network to be used as an implicit prior. The…

We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…