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Trajectory representation learning (TRL) maps trajectories to vectors that can be used for many downstream tasks. Existing TRL methods use either grid trajectories, capturing movement in free space, or road trajectories, capturing movement…

We introduce a new pattern recognition algorithm for track finding in High Energy Physics Experiments based on an extension of the Hough Transform to multiple dimensions. A remarkable property of this algorithm is that the execution time is…

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…

The successes achieved by deep neural networks in computer vision tasks have led in recent years to the emergence of a new research area dubbed Multi-Dimensional Encoding (MDE). Methods belonging to this family aim to transform tabular data…

Decision Transformer (DT) is an innovative algorithm leveraging recent advances of the transformer architecture in reinforcement learning (RL). However, a notable limitation of DT is its reliance on recalling trajectories from datasets,…

In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…

Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…

Trace alignment algorithms have been used in process mining for discovering the consensus treatment procedures and process deviations. Different alignment algorithms, however, may produce very different results. No widely-adopted method…

The rate-distortion curve captures the fundamental tradeoff between compression length and resolution in lossy data compression. However, it conceals the underlying dynamics of optimal source encodings or test channels. We argue that these…

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…

Trajectories represent the mobility of moving objects and thus is of great value in data mining applications. However, trajectory data is enormous in volume, so it is expensive to store and process the raw data directly. Trajectories are…

Network-centric multitarget tracking under communication constraints is considered, where dimension-reduced track estimates are exchanged. Previous work on target tracking in this subfield has focused on fusion aspects only and derived…

Tree tensor networks (TTNs) provide a compact and structured representation of high-dimensional data, making them valuable in various areas of computational mathematics and physics. In this paper, we present a rigorous mathematical…

In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

Motivated by customer loyalty plans and scholarship programs, we study tie-breaker designs which are hybrids of randomized controlled trials (RCTs) and regression discontinuity designs (RDDs). We quantify the statistical efficiency of a…

Tensor network methods are a conceptually elegant framework for encoding complicated datasets, where high-order tensors are approximated as networks of low-order tensors. In practice, however, the numeric implementation of tensor network…