arXiv research

Two new methods improve block-sparse signal recovery from noisy data.

Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the nonconvex penalized SVMs due to their nondifferentiability, nonsmoothness and nonconve…

Sign information is the key to overcoming the inevitable saturation error in compressive sensing systems, which causes information loss and results in bias. For sparse signal recovery from saturation, we propose to use a linear loss to improve the effectiveness from existing methods that utilize hard constraints/hinge …

One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing. In this paper, we propose novel algorithms based on both convex and nonconvex s…

New method improves signal reconstruction with nonconvex penalties and parameter control.

Proposes new $\ell_0$-based methods for low-rank sparse subspace clustering.

Proposes a new algorithm for online decision-making with high-dimensional data.

A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.

SCOPE fuses categorical variable levels to estimate high-dimensional linear models.

Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an l0-norm penalty. Exactly enforcing the l0-no…

New convex relaxations solve sparse regression problems efficiently.

Current online learning methods suffer issues such as lower convergence rates and limited capability to select important features compared to their offline counterparts. In this paper, a novel framework for online learning based on running averages is proposed. Many popular offline regularized methods such as Lasso, El…

The aim of this paper is to train an RBF neural network and select centers under concurrent faults. It is well known that fault tolerance is a very attractive property for neural networks. And center selection is an important procedure during the training process of an RBF neural network. In this paper, we devise two n…

In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including $\ell^0$, bridge, smoothly clipped absolute deviation, capped $\ell^1$ and mini…

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of t…

In this paper, we study the Kurdyka-Łojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with known KL exponents. In …

The paper explores nonconvex penalties for deep learning regularization.

Gradient penalty improves GAN performance by inducing a large-margin classifier.

Study examines insider trading with penalties, finding optimal penalties increase quickly for small orders.

The paper studies robust risk measures with linear penalties under uncertain distributions.

The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…

Paper introduces a new SVR model using a combined reward and penalty loss function.

New sparse penalty improves biclustering for gene expression data.

New approach avoids excess empirical risk in domain generalization.

We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…

Curvature penalties improve interpretability of KANs without sacrificing accuracy.

New method reduces bias in sparse Bayesian learning.

PPO-B improves sampling efficiency by using a logarithmic barrier method.

New nonconvex penalty smooths at origin for deep learning.

This study proves local stability of SGP μ-WGAN and shows penalizing data or sample manifold is key.

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…

Multi-group learners suffer a penalty in transductive learning.

Global minima found for multidimensional scaling with penalties.

Improved penalty-based methods for bilevel optimization with reduced complexity.

Proposes an alternative invariance penalty to address domain generalization issues.

Paper proposes efficient algorithms for designing SLOPE penalty sequences.

Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.

Survey on minimal penalty algorithms and slope heuristics.

Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical optimization of such penalties involves solving problems with l1-norms in the ob…

In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are c…

Improved online penalty selection for time series models.

In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such methods are typically computationally intensive. Recent work in the penalised optimi…

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 over the desired level of sparsity of estimators. We analyze its structural prop…

Bayesian priors and penalties are equivalent in variational inference.

Proposes using MLP for predicting optimal penalty in changepoint detection.

Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm. However, the best estimator performance is not always achieved with this penalty. The …

A new penalty-free method optimizes portfolios without quantum annealing penalties.

Study ablated data augmentation techniques and their mathematical equivalence to penalties.