A general method for regularizing tensor decomposition methods via pseudo-data
This provides a general solution for regularizing tensor decomposition methods, which is incremental as it builds on existing algorithms but addresses a known bottleneck in the field.
The authors tackled the lack of a general regularization method for tensor decomposition algorithms by proposing a pseudo-data approach that balances closeness to true data with regularization goals, demonstrating improved inference accuracy and applicability to various regularization objectives like sparsity and transfer learning on synthetic and real datasets.
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.