Related papers: Semismooth Newton Coordinate Descent Algorithm for…
This paper is concerned with the computation of the high-dimensional zero-norm penalized quantile regression estimator, defined as a global minimizer of the zero-norm penalized check loss function. To seek a desirable approximation to the…
Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…
This letter proposes a deep neural network (DNN)-based neuro-adaptive sliding mode control (SMC) strategy for leader-follower tracking in multi-agent systems with higher-order, heterogeneous, nonlinear, and unknown dynamics under external…
This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…
Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…
Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in…
A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been…
Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…
Deep convolutional neural networks (CNNs) have dominated many computer vision domains because of their great power to extract good features automatically. However, many deep CNNs-based computer vison tasks suffer from lack of training data…
Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…
We propose a novel parametric dictionary learning algorithm for line spectral estimation, applicable in both single measurement vector (SMV) and multiple measurement vectors (MMV) scenarios. This algorithm, termed cubic Newtonized K-SVD…
The recent years have witnessed advances in parallel algorithms for large scale optimization problems. Notwithstanding demonstrated success, existing algorithms that parallelize over features are usually limited by divergence issues under…
Deep neural networks (DNNs) have achieved remarkable success in computer vision; however, training DNNs for satisfactory performance remains challenging and suffers from sensitivity to empirical selections of an optimization algorithm for…
A convergence analysis is developed for the regularized Newton method for training neural networks (NNs) in the overparameterized limit. As the number of hidden units tends to infinity, the NN training dynamics converge in probability to…
Deep neural networks are usually trained with stochastic gradient descent (SGD), which minimizes objective function using very rough approximations of gradient, only averaging to the real gradient. Standard approaches like momentum or ADAM…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…
In general, deep neural network (DNN) pruning methods fall into two categories: 1) Weight-based deterministic constraints, and 2) Probabilistic frameworks. While each approach has its merits and limitations there are a set of common…
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…