Related papers: Approximate Regularization Paths for Nuclear Norm …
Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of…
The goal of this paper is to find a low-rank approximation for a given tensor. Specifically, we give a computable strategy on calculating the rank of a given tensor, based on approximating the solution to an NP-hard problem. In this paper,…
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…
In the present paper we propose two new algorithms of tensor completion for three-order tensors. The proposed methods consist in minimizing the average rank of the underlying tensor using its approximate function namely the tensor nuclear…
We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear…
Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing…
Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
A regularization algorithm (AR1pGN) for unconstrained nonlinear minimization is considered, which uses a model consisting of a Taylor expansion of arbitrary degree and regularization term involving a possibly non-smooth norm. It is shown…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Penalizing the nuclear norm of a function's Jacobian encourages it to locally behave like a low-rank linear map. Such functions vary locally along only a handful of directions, making the Jacobian nuclear norm a natural regularizer for…
As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
Classical approach to regularization is to design norms enhancing smoothness or sparsity and then to use this norm or some power of this norm as a regularization function. The choice of the regularization function (for instance a power…
We consider the identification of scattering and absorption rates in the stationary radiative transfer equation. For a stable solution of this parameter identification problem, we consider Tikhonov regularization within Banach spaces. A…
Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these…
The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…