Tensor Linear Regression: Degeneracy and Solution

Triangular Solution of Linear Systems in Tensor Product Format1

This paper presents an algorithm to solve linear systems expressed by a matrix stored in a tensor product format. The proposed solution is based on a LU decomposition of the matrix keeping the tensor product structure. It is shown that the complexity of the decomposition is negligible and the backward and forward substitutions are no more complex than two standard vector-matrices multiplication...

Triangular Solution of Linear Systems in Tensor Produ t Format

Interval linear regression

‎In this paper‎, ‎we have studied the analysis an interval linear regression model for fuzzy data‎. ‎In section one‎, ‎we have introduced the concepts required in this thesis and then we illustrated linear regression fuzzy sets and some primary definitions‎. ‎In section two‎, ‎we have introduced various methods of interval linear regression analysis‎. ‎In section three‎, ‎we have implemented nu...

Solution of Linear Programming and Non-Linear Regression Problems Using Linear M-Estimation Methods

This Ph.D. thesis is devoted to algorithms for two optimization problems, and their implementation. The algorithms are based on solving linear M-estimation problems. First, an algorithm for the non-linear M-estimation problem is considered. The main idea of the algorithm is to linearize the residual function in each iteration and thus calculate the iteration step by solving a linear M-estimatio...

Tensor Contraction&Regression Networks

To date, most convolutional neural network architectures output predictions by flattening 3rd-order activation tensors, and applying fully-connected output layers. This approach has two drawbacks: (i) we lose rich, multi-modal structure during the flattening process and (ii) fully-connected layers require many parameters. We present the first attempt to circumvent these issues by expressing the...