Related papers: Nuclear Norm Regularized Estimation of Panel Regre…
We consider convex relaxations for recovering low-rank tensors based on constrained minimization over a ball induced by the tensor nuclear norm, recently introduced in \cite{tensor_tSVD}. We build on a recent line of results that considered…
The reconstruction of low-rank matrix from its noisy observation finds its usage in many applications. It can be reformulated into a constrained nuclear norm minimization problem, where the bound $\eta$ of the constraint is explicitly given…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…
In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. Recently, many flexible machine learning methods have been developed for instrumental variable estimation. However, these methods have at least one…
We describe novel subgradient methods for a broad class of matrix optimization problems involving nuclear norm regularization. Unlike existing approaches, our method executes very cheap iterations by combining low-rank stochastic…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
We address the numerical solution of minimal norm residuals of {\it nonlinear} equations in finite dimensions. We take inspiration from the problem of finding a sparse vector solution by using greedy algorithms based on iterative residual…
We develop regularization methods to find flat minima while training deep neural networks. These minima generalize better than sharp minima, yielding models outperforming baselines on real-world test data (which may be distributed…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a…
In this article, we apply non-convex regularization methods in order to obtain stable estimation of loss development factors in insurance claims reserving. Among the non-convex regularization methods, we focus on the use of the log-adjusted…
This manuscript proposes a novel empirical Bayes technique for regularizing regression coefficients in predictive models. When predictions from a previously published model are available, this empirical Bayes method provides a natural…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
This paper considers the problem of finding a low rank matrix from observations of linear combinations of its elements. It is well known that if the problem fulfills a restricted isometry property (RIP), convex relaxations using the nuclear…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the…