相关论文: Optimal singular value shrinkage for operator norm…
We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…
This paper studies receiver design in single-input multiple-output (SIMO) slow fading channels with imperfect channel state information (CSI) at the receiver only. Using generalized mutual information (GMI) as achievable rate, we study the…
We consider the Schrodinger operator a given domain. Our goal is to study some optimization problems where an optimal (non-negative) potential V has to be determined in some suitable admissible classes and for some suitable optimization…
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as sparsity, group sparsity, low-rank and sharp edges. It is also the basis for…
In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage…
The wavelet shrinkage denoising approach is able to maintain local regularity of a signal while suppressing noise. However, the conventional wavelet shrinkage based methods are not time-scale adaptive to track the local time-scale…
Logistic models are commonly used for binary classification tasks. The success of such models has often been attributed to their connection to maximum-likelihood estimators. It has been shown that gradient descent algorithm, when applied on…
We study properties and algorithms of a minimization problem of the maximum generalized eigenvalue of symmetric-matrix-valued affine functions, which is nonsmooth and quasiconvex, and has application to eigenfrequency optimization of truss…
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
Classic zeroth-order optimization approaches typically optimize for a smoothed version of the original function, i.e., the expected objective under randomly perturbed model parameters. This can be interpreted as encouraging the loss values…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
We consider the estimation of the $p$-variate normal mean of $X\sim N_p(\theta,I)$ under the quadratic loss function. We investigate the decision theoretic properties of debiased shrinkage estimator, the estimator which shrinks towards the…
This paper is focused on the definition, analysis and numerical solution of a new optimization variant (OPT) of the shear strength reduction (SSR) problem with applications to slope stability problems. This new variant is derived on the…
The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…
Recently, flat-minima optimizers, which seek to find parameters in low-loss neighborhoods, have been shown to improve a neural network's generalization performance over stochastic and adaptive gradient-based optimizers. Two methods have…
Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored,…