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This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultrafast numerical solutions of high-dimensional…
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
We present TRACE (Transformer-based Risk Assessment for Clinical Evaluation), a novel method for clinical risk assessment based on clinical data, leveraging the self-attention mechanism for enhanced feature interaction and result…
Deep convolutional neural networks are shown to be overkill with high parametric and computational redundancy in many application scenarios, and an increasing number of works have explored model pruning to obtain lightweight and efficient…
Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…
Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…
In recent years, data-driven reinforcement learning (RL), also known as offline RL, have gained significant attention. However, the role of data sampling techniques in offline RL has been overlooked despite its potential to enhance online…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
This study proposes a Newton based multiple objective optimization algorithm for hyperparameter search. The first order differential (gradient) is calculated using finite difference method and a gradient matrix with vectorization is formed…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data.…
This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy…
We introduce a novel random projection technique for efficiently reducing the dimension of very high-dimensional tensors. Building upon classical results on Gaussian random projections and Johnson-Lindenstrauss transforms~(JLT), we propose…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…