Related papers: High-Dimensional Simulation Optimization via Brown…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
Brownian dynamics of colloidal particles on complex surfaces has found important applications in diverse physical, chemical and biological processes. However, current Brownian dynamics simulation algorithms mostly work for relatively simple…
We present a sampling strategy suitable for optimization problems characterized by high-dimensional design spaces and noisy outputs. Such outputs can arise, for example, in time-averaged objectives that depend on chaotic states. The…
Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of…
We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense…
In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a…
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…
Simulation offers a simple and flexible way to estimate the power of a clinical trial when analytic formulae are not available. The computational burden of using simulation has, however, restricted its application to only the simplest of…
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be…
This paper investigates the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through an $\ell_0$ cardinality constraint. While branch-and-bound (BnB) frameworks can certify optimality…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…
Modern large scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as…