# A general method for regularizing tensor decomposition methods via pseudo-data

## TL;DR

This paper introduces a versatile regularization technique for tensor decomposition methods that uses pseudo-data to improve model inference, applicable across various likelihood models and regularization goals.

## Contribution

A novel, general approach to regularize tensor decomposition methods via pseudo-data, applicable to any differentiable regularizer and likelihood model.

## Key findings

- Improves inference accuracy on synthetic and real data.
- Enables regularization for transfer learning, sparsity, and interpretability.
- Enhances orthogonality of learned parameters.

## Abstract

Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize them, and in the past regularization has mostly been performed using bespoke modifications to the algorithms, tailored for the particular form of the desired regularizer. We present a general method of regularizing tensor decomposition methods which can be used for any likelihood model that is learnable using tensor decomposition methods and any differentiable regularization function by supplementing the training data with pseudo-data. The pseudo-data is optimized to balance two terms: being as close as possible to the true data and enforcing the desired regularization. On synthetic, semi-synthetic and real data, we demonstrate that our method can improve inference accuracy and regularize for a broad range of goals including transfer learning, sparsity, interpretability, and orthogonality of the learned parameters.