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Graph convolutional network (GCN) based approaches have achieved significant progress for solving complex, graph-structured problems. GCNs incorporate the graph structure information and the node (or edge) features through message passing…

Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

The low-degree polynomial framework has emerged as a powerful tool for providing evidence of statistical-computational gaps in high-dimensional inference. For detection problems, the standard approach bounds the low-degree advantage through…

Deep learning, a rebranding of deep neural network research works, has achieved a remarkable success in recent years. With multiple hidden layers, deep learning models aim at computing the hierarchical feature representations of the…

Geometric constraints between feature matches are critical in 3D point cloud registration problems. Existing approaches typically model unordered matches as a consistency graph and sample consistent matches to generate hypotheses. However,…

Genome-wide gene expression profiles, as measured with microarrays or RNA-Seq experiments, have revolutionized biological and biomedical research by providing a quantitative measure of the entire mRNA transcriptome. Typically, researchers…

Conjoint experiments randomize multidimensional profiles, offering a powerful design for recovering structural preference parameters -- including marginal rates of substitution, willingness to pay, and the distribution of preferences across…

Deep learning is typically performed by learning a neural network solely from data in the form of input-output pairs ignoring available domain knowledge. In this work, the Constraint Guided Gradient Descent (CGGD) framework is proposed that…

We propose a new method, called a deep-genetic algorithm (deep-GA), to accelerate the performance of the so-called deep-BSDE method, which is a deep learning algorithm to solve high dimensional partial differential equations through their…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

Many statistical problems involve optimization over a discrete parameter space having an unknown dimension. In such settings, gradient-based methods often fail due to the non-differentiability of the objective function or a non-convex or…

While deep generative models (DGMs) have gained popularity, their susceptibility to biases and other inefficiencies that lead to undesirable outcomes remains an issue. With their growing complexity, there is a critical need for early…

We present a new $hp$-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements,…

Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that focuses on learning…

Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

Heterogeneity is often natural in many contemporary applications involving massive data. While posing new challenges to effective learning, it can play a crucial role in powering meaningful scientific discoveries through the understanding…

Deep learning is mainly based on utilizing gradient-based optimization for training Deep Neural Network (DNN) models. Although robust and widely used, gradient-based optimization algorithms are prone to getting stuck in local minima. In…

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…

We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge…