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We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…

Parametric images provide insight into the spatial distribution of physiological parameters, but they are often extremely noisy, due to low SNR of tomographic data. Direct estimation from projections allows accurate noise modeling,…

The safe application of reinforcement learning (RL) requires generalization from limited training data to unseen scenarios. Yet, fulfilling tasks under changing circumstances is a key challenge in RL. Current state-of-the-art approaches for…

Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…

In order to enhance the performance of image recognition, a sparsity augmented probabilistic collaborative representation based classification (SA-ProCRC) method is presented. The proposed method obtains the dense coefficient through…

High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…

Sparse shrunk additive models and sparse random feature models have been developed separately as methods to learn low-order functions, where there are few interactions between variables, but neither offers computational efficiency. On the…

This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Runge-Kutta method with repeated randomized low-rank…

Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been…

Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent…

We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model…

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Context information plays an indispensable role in the success of semantic segmentation. Recently, non-local self-attention based methods are proved to be effective for context information collection. Since the desired context consists of…

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…

We propose the Selective Densification method for fast motion planning through configuration space. We create a sequence of roadmaps by iteratively adding configurations. We organize these roadmaps into layers and add edges between…

In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…

Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more…

Real-time path planning in constrained environments remains a fundamental challenge for autonomous systems. Traditional classical planners, while effective under perfect perception assumptions, are often sensitive to real-world perception…