arXiv research

Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regul…

Paper proposes a working set algorithm for non-convex sparse regression with provable convergence.

Unified framework for training neural networks with non-smooth, non-convex regularizers.

New methods improve convergence in non-convex non-smooth learning problems.

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a no…

Introduces screening rules for non-convex Lasso problems.

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal Newton algorithm that is able to deal with such a situation. The algorithm consi…

Optimally shows the distance between perturbed convex functions and their Γ-regularizations.

Heavy Ball method speeds up finding global optima in non-convex problems.

This study improves graph signal denoising for vector-valued data with non-convex penalties.

We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization. This approach is particularly attractive because it escapes strict saddle points and it provides stronger convergence gu…

The paper shows regularization can't always find all optimal solutions in constrained ML.

Paper tackles non-convex inf-projection problems with stochastic optimization.

A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.

Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this problem. Our contribution consists of three parts. First, we propose the leaky capped …

Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC functions have been extensively studied, stochastic optimization that is more suitable …

Weight normalization and reparametrized gradient descent adaptively regularize weights and converge to minimum l2 norm solutions.

Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multi-task sparse feature learning algorithms are formulated a…

SAGA is a fast incremental gradient method on the finite sum problem and its effectiveness has been tested on a vast of applications. In this paper, we analyze SAGA on a class of non-strongly convex and non-convex statistical problem such as Lasso, group Lasso, Logistic regression with $\ell_1$ regularization, linear r…

Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has been demonstrated by some theoretical and experimental work that non-convex relax…

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…

New FGSPCA method captures grouping and sparse structures in PCA without prior info.

Improved bounds for MALA in non-convex sampling problems.

SGD's uncertainty quantified in non-convex learning problems.

New algorithm recovers model coefficients and supports from noisy data.

The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly time-varying, connectivity pattern. In such distributed scenario, the training prob…

MTLRRC improves MTL by robustly clustering tasks and detecting outliers.

Exact second-order optimization for deep learning reduces computational cost and improves performance.

New method smooths optimization for sparse regularization.

Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of all models. A recent area of considerable interest is to develop efficient algor…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…

In this paper, we consider the problem of learning high-dimensional tensor regression problems with low-rank structure. One of the core challenges associated with learning high-dimensional models is computation since the underlying optimization problems are often non-convex. While convex relaxations could lead to polyn…

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-conv…

Lower bounds for higher-order methods in non-convex optimization.

Trust region and cubic regularization methods have demonstrated good performance in small scale non-convex optimization, showing the ability to escape from saddle points. Each iteration of these methods involves computation of gradient, Hessian and function value in order to obtain the search direction and adjust the r…

New approach for distributed online optimization of non-convex losses with sublinear regret.

This paper improves 3D pose recovery from 2D images using non-convex regularization.

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve $ε$-approximate seco…

Deep learning with noisy gradient descent outperforms linear estimators in high dimensions.

Flexible ADMM-based algorithm for non-convex problems with convergence guarantees.

A new method solves l1-regularized optimization problems efficiently and sparsely.

We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise search to determine a locally optimal L0 solution given any L1 regularization solution. We …

Unified analysis of multi-attribute graph learning with non-convex penalties.

Paper improves stability analysis of SGD for various loss functions and data distributions.

New algorithm solves non-convex min-max problems in signal processing.

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of r…

This work explains GAN mode collapse and convergence issues via optimal transportation theory.

New rates for GLD and SGLD in infinite-dimensional spaces without dimensionality issues.