Related papers: The Proximity Operator of the Log-Sum Penalty

The Hardy operator is not bounded on the space of integrable functions on the positive half-line and its discrete counterpart on summable sequences. we introduce a modified Hardy operator obtained by subtracting a natural corrective term,…

Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation…

In this paper, we consider the minimization of a Tikhonov functional with an $\ell_1$ penalty for solving linear inverse problems with sparsity constraints. One of the many approaches used to solve this problem uses the Nemskii operator to…

Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $\ell_1$ to $\ell_2$ norms, $(\ell_1/\ell_2)^2$, has been introduced as a sparsity-prompting function, showing…

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…

Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…

In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within…

We determine the power of the weighted sum scalarization with respect to the computation of approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion of…

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…

This paper investigates a new approach to estimate the gradient of the conditional probability given the covariates in the binary classification framework. The proposed approach consists in fitting a localized nearest-neighbor logistic…

It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…

We consider the ill-posed operator equation $Ax=y$ with an injective and bounded linear operator $A$ mapping between $\ell^2$ and a Hilbert space $Y$, possessing the unique solution \linebreak $x^\dag=\{x^\dag_k\}_{k=1}^\infty$. For the…

The composite L0 function serves as a sparse regularizer in many applications. The algorithmic difficulty caused by the composite L0 regularization (the L0 norm composed with a linear mapping) is usually bypassed through approximating the…

The aim of this paper is twofold. First, we show that a certain concatenation of a proximity operator with an affine operator is again a proximity operator on a suitable Hilbert space. Second, we use our findings to establish so-called…

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted…

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account…

We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the…

Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…