Related papers: Optimization for Amortized Inverse Problems
Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications. However, finding these directions usually requires an iterative optimization procedure over the space of…
Inspired and underpinned by the idea of integral feedback, a distributed constant gain algorithm is proposed for multi-agent networks to solve convex optimization problems with local linear constraints. Assuming agent interactions are…
Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
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…
For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
Advanced machine learning methods, and more prominently neural networks, have become standard to solve inverse problems over the last years. However, the theoretical recovery guarantees of such methods are still scarce and difficult to…
Deep learning-based methods have revolutionized the field of imaging inverse problems, yielding state-of-the-art performance across various imaging domains. The best performing networks incorporate the imaging operator within the network…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…