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We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

Planning safe trajectories for autonomous vehicles is essential for operational safety but remains extremely challenging due to the complex interactions among traffic participants. Recent autonomous driving frameworks have focused on…

We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative…

Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…

Accurate wind power forecasts depend on reliable wind speed forecasts. Numerical Weather Predictions (NWPs) utilize huge amounts of computing time, but still have rather low spatial and temporal resolution. However, stochastic wind speed…

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important…

Quantifying the impacts of anthropogenic global warming requires accurate Earth system model (ESM) simulations. Statistical bias correction and downscaling can be applied to reduce errors and increase the resolution of ESMs. However,…

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…

Spatial-temporal forecasting is crucial and widely applicable in various domains such as traffic, energy, and climate. Benefiting from the abundance of unlabeled spatial-temporal data, self-supervised methods are increasingly adapted to…

Fast and efficient motion planning algorithms are crucial for many state-of-the-art robotics applications such as self-driving cars. Existing motion planning methods become ineffective as their computational complexity increases…

In recent years, interest in autonomous shipping in urban waterways has increased significantly due to the trend of keeping cars and trucks out of city centers. Classical approaches such as Frenet frame based planning and potential field…

Sampling-based Motion Planners (SMPs) have become increasingly popular as they provide collision-free path solutions regardless of obstacle geometry in a given environment. However, their computational complexity increases significantly…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial regression involving…

This letter presents a novel coarse-to-fine motion planning framework for robotic manipulation in cluttered, unmodeled environments. The system integrates a dual-camera perception setup with a B-spline-based model predictive control (MPC)…

A partially linear probit model for spatially dependent data is considered. A triangular array setting is used to cover various patterns of spatial data. Conditional spatial heteroscedasticity and non-identically distributed observations…

Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…

Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference…

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…