Related papers: Convex Regularization for High-Dimensional Multi-R…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a…
We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…
This paper examines reinforcement learning (RL) in infinite-horizon decision processes with almost-sure safety constraints, crucial for applications like autonomous systems, finance, and resource management. We propose a doubly-regularized…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
Reverse Unrestricted MIxed DAta Sampling (RU-MIDAS) regressions are used to model high-frequency responses by means of low-frequency variables. However, due to the periodic structure of RU-MIDAS regressions, the dimensionality grows quickly…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…
Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation…
The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that…
We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…
In this paper, we study a general framework for compressive sensing assuming the existence of the prior knowledge that $\boldsymbol{x}^*$ belongs to the union of multiple convex sets, $\boldsymbol{x}^{*} \in \bigcup_i \mathcal{C}_i$. In…
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…
Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…
A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic…