Related papers: A Bidirectional DeepParticle Method for Efficientl…

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…

Cooperative localization (CL) is an important technology for innovative services such as location-aware communication networks, modern convenience, and public safety. We consider wireless networks with mobile agents that aim to localize…

Diffusion probabilistic models (DPMs) and their extensions have emerged as competitive generative models yet confront challenges of efficient sampling. We propose a new bilateral denoising diffusion model (BDDM) that parameterizes both the…

In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…

Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…

This paper investigates the optimization of the long-standing probabilistically robust transmit beamforming problem with channel uncertainties in the multiuser multiple-input single-output (MISO) downlink transmission. This problem poses…

We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…

Trajectory prediction plays a crucial role in the autonomous driving stack by enabling autonomous vehicles to anticipate the motion of surrounding agents. Goal-based prediction models have gained traction in recent years for addressing the…

This paper presents a novel sensitivity-based distributed programming (SBDP) approach for non-convex, large-scale nonlinear programs (NLP). The algorithm relies on first-order sensitivities to cooperatively solve the central NLP in a…

The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…

Backpropagation (BP) is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, BP is considered as a de-facto choice in a variety of machine learning…

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…

We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…

Travel time tomography for the velocity structure of a medium is a highly non-linear and non-unique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but…

Discrete diffusion models are promising alternatives to autoregressive approaches for text generation, yet their decoding methods remain under-studied. Standard decoding methods for autoregressive models, such as beam search, do not…

Belief Propagation (BP) is an important message-passing algorithm for various reasoning tasks over graphical models, including solving the Constraint Optimization Problems (COPs). It has been shown that BP can achieve state-of-the-art…

We present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin discretizations of the SN transport equation. This approach is sweep-compatible: as the transport sweep is performed, a local quadratic programming (QP)…

Low-light image enhancement aims to improve the visibility of degraded images to better align with human visual perception. While diffusion-based methods have shown promising performance due to their strong generative capabilities. However,…

Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…

We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…