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Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
The ELM method has become widely used for classification and regressions problems as a result of its accuracy, simplicity and ease of use. The solution of the hidden layer weights by means of a matrix pseudoinverse operation is a…
Deep image registration has demonstrated exceptional accuracy and fast inference. Recent advances have adopted either multiple cascades or pyramid architectures to estimate dense deformation fields in a coarse-to-fine manner. However, due…
This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
We propose a regularized saddle-point algorithm for convex networked optimization problems with resource allocation constraints. Standard distributed gradient methods suffer from slow convergence and require excessive communication when…
We consider truncated SVD (or spectral cut-off, projection) estimators for a prototypical statistical inverse problem in dimension $D$. Since calculating the singular value decomposition (SVD) only for the largest singular values is much…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
Inverse Problems in medical imaging and computer vision are traditionally solved using purely model-based methods. Among those variational regularization models are one of the most popular approaches. We propose a new framework for applying…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…