  Tensor methods have become a promising tool to solve high-dimensional
problems in the big data era. By exploiting possible low-rank tensor
factorization, many high-dimensional model-based or data-driven problems can be
solved to facilitate decision making or machine learning. In this paper, we
summarize the recent applications of tensor computation in obtaining compact
models for uncertainty quantification and deep learning. In uncertainty
analysis where obtaining data samples is expensive, we show how tensor methods
can significantly reduce the simulation or measurement cost. To enable the
deployment of deep learning on resource-constrained hardware platforms, tensor
methods can be used to significantly compress an over-parameterized neural
network model or directly train a small-size model from scratch via
optimization or statistical techniques. Recent Bayesian tensorized neural
networks can automatically determine their tensor ranks in the training
process.
