Related papers: Beyond Cross-Validation: Adaptive Parameter Select…
Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In…
This paper explores the application of kernel learning methods for parameter prediction and evaluation in the Algebraic Multigrid Method (AMG), focusing on several Partial Differential Equation (PDE) problems. AMG is an efficient iterative…
In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of…
This paper presents a novel coordinate descent algorithm leveraging a combination of one-directional line search and gradient information for parameter updates for a squared error loss function. Each parameter undergoes updates determined…
We address the challenge of estimating the learning rate for adaptive gradient methods used in training deep neural networks. While several learning-rate-free approaches have been proposed, they are typically tailored for steepest descent.…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…
Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…
The performance of gradient-based optimization methods, such as standard gradient descent (GD), greatly depends on the choice of learning rate. However, it can require a non-trivial amount of user tuning effort to select an appropriate…
This paper presents a novel kernel-based generative classifier which is defined in a distortion subspace using polynomial series expansion, named Kernel-Distortion (KD) classifier. An iterative kernel selection algorithm is developed to…
We study nonparametric regression by an over-parameterized two-layer neural network trained by gradient descent (GD) in this paper. We show that, if the neural network is trained by GD with early stopping, then the trained network renders a…
We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…
We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…
Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification,…
Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the…
We study the Stein Variational Gradient Descent (SVGD) algorithm, which optimises a set of particles to approximate a target probability distribution $\pi\propto e^{-V}$ on $\mathbb{R}^d$. In the population limit, SVGD performs gradient…
Hyperparameter selection generally relies on running multiple full training trials, with selection based on validation set performance. We propose a gradient-based approach for locally adjusting hyperparameters during training of the model.…
Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative. Treating the coupled variables independently while ignoring the interaction, however, leads to an insufficient optimization…