Related papers: Stochastic Multidimensional Scaling
The optimistic gradient method is useful in addressing minimax optimization problems. Motivated by the observation that the conventional stochastic version suffers from the need for a large batch size on the order of…
This paper proposes a computationally efficient mechanism for multi-dimensional matching markets where agents report preferences over object features rather than complete utility assessments. We use Singular Value Decomposition (SVD) to…
In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
Distributed adaptive signal processing has attracted much attention in the recent decade owing to its effectiveness in many decentralized real-time applications in networked systems. Because many natural signals are highly sparse with most…
Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…
Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…
Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…
Feature selection is a crucial step in machine learning, especially for high-dimensional datasets, where irrelevant and redundant features can degrade model performance and increase computational costs. This paper proposes a novel…
Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…
Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant…
In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
The popularity of bi-level optimization (BO) in deep learning has spurred a growing interest in studying gradient-based BO algorithms. However, existing algorithms involve two coupled learning rates that can be affected by approximation…
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDEs) with random data, where the random coefficient is parametrized by means of a countable…
At present, high-dimensional global optimization problems with time-series models have received much attention from engineering fields. Since it was proposed, Bayesian optimization has quickly become a popular and promising approach for…
In this work, a unified framework for gradient-free Multidimensional Scaling (MDS) based on Coordinate Search (CS) is proposed. This family of algorithms is an instance of General Pattern Search (GPS) methods which avoid the explicit…
We propose a novel multi-scale template matching method which is robust against both scaling and rotation in unconstrained environments. The key component behind is a similarity measure referred to as scalable diversity similarity (SDS).…