# Tensorized LSSVMs for Multitask Regression

arXiv: https://arxiv.org/abs/2303.02451 · HTML: https://mlsanity.com/paper/2303.02451/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 4 Mar 2023.

## Builds on (most cited first, 2 of 2)

- [Deep Multi-task Representation Learning: A Tensor Factorisation Approach](https://mlsanity.com/paper/1605.06391/) (2016)
- [Deep Multi-Task Learning via Generalized Tensor Trace Norm](https://mlsanity.com/paper/2002.04799/) (2020)

## Built on by (most cited first, 2 of 2)

- [Low-Rank Multitask Learning based on Tensorized SVMs and LSSVMs](https://mlsanity.com/paper/2308.16056/) (2023)
- [Kernel Singular Value Decomposition with Extension to Multiple Data Sources](https://mlsanity.com/paper/2610.03216/) (2026)

## Abstract (arXiv)

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient representations for such tasks, while preserving structural task-relations. In this paper, a new MTL method is proposed by leveraging low-rank tensor analysis and constructing tensorized Least Squares Support Vector Machines, namely the tLSSVM-MTL, where multilinear modelling and its nonlinear extensions can be flexibly exerted. We employ a high-order tensor for all the weights with each mode relating to an index and factorize it with CP decomposition, assigning a shared factor for all tasks and retaining task-specific latent factors along each index. Then an alternating algorithm is derived for the nonconvex optimization, where each resulting subproblem is solved by a linear system. Experimental results demonstrate promising performances of our tLSSVM-MTL.