4 citations · 7 across the 14 of their papers we have counts for
15 papers
Tail bounds for Multivariate Random Tensor Means
Shih-Yu Chang
In our recent research endeavors, we have delved into the realm of tail bounds problems concerning bivariate random tensor means. In this context, tensors are treated as finite-dim…
Random Tensor Inequalities and Tail bounds for Bivariate Random Tensor Means, Part II
Shih-Yu Chang
This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider…
Random Tensor Inequalities and Tail bounds for Bivariate Random Tensor Means, Part I
Shih-Yu Chang
In this work, we apply the concept about operator connection to consider bivariate random tensor means. We first extend classical Markov and Chebyshev inequalities from a random va…
Tail Bounds for Tensor-valued Random Process
Shih-Yu Chang
To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining m…
Random Multiple Operator Integrals
Shih-Yu Chang
The introduction of Schur multipliers into the context of Double Operator Integrals (DOIs) was proposed by V. V. Peller in 1985. This work extends theorem on Schur multipliers from…
Geometric Approach For Majorizing Measures on Hadamard Manifolds
Shih-Yu Chang
Gaussian processes can be treated as subsets of a standard Hilbert space, however, the volume size relation between the underlying index space of random processes and its convex hu…
Geometric Approach For Majorizing Measures
Shih-Yu Chang
Gaussian processes can be considered as subsets of a standard Hilbert space, but the geometric understanding that would relate the size of a set with the size of its convex hull is…
Random Parametrization Double Tensors Integrals and Their Applications
Shih Yu Chang
In this work, we extend double tensor integrals (DTI) from our previous work to parametrization double tensors integrals (PDTI) by applying integral kernel transform bounds to uppe…
Random Double Tensors Integrals
Shih Yu Chang
In this work, we try to build a theory for random double tensor integrals (DTI). We begin with the definition of DTI and discuss how randomness structure is built upon DTI. Then, t…
Generalized Hanson-Wright Inequality for Random Tensors
Shih Yu Chang
The Hanson-Wright inequality is an upper bound for tails of real quadratic forms in independent random variables. In this work, we extend the Hanson-Wright inequality for the Ky Fa…
Generalized T-product Tensor Bernstein Bounds
Shih Yu Chang, Yimin Wei
Since Kilmer et al. introduced the new multiplication method between two third-order tensors around 2008 and third-order tensors with such multiplication structure are also called…
T product Tensors Part I: Inequalities
Shih Yu Chang, Yimin Wei
The T product operation between two three order tensors was invented around 2011 and it arises from many applications, such as signal processing, image feature extraction, machine…
General Tail Bounds for Random Tensors Summation: Majorization Approach
Shih Yu Chang
In recent years, tensors have been applied to different applications in science and engineering fields. In order to establish theory about tail bounds of the tensors summation beha…
Convenient tail bounds for sums of random tensors
Shih Yu Chang
This work prepares new probability bounds for sums of random, independent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenval…
Sherman-Morrison-Woodbury Identity for Tensors
Shih Yu Chang
In linear algebra, the sherman-morrison-woodbury identity says that the inverse of a rank- correction of some matrix can be computed by doing a rank-k correction to the inverse…