Tensor networks, weighted automata, and ANOVA-driven modeling

Low-rank tensor decompositions can be extremely insightful when a model has high degrees of interaction between its inputs (in the ANOVA sense). Thanks to certain connections between tensor networks and weighted automata, we can now design efficient algorithms that measure and control the interplay between input variables. This can be done using any of a wide range of sensitivity metrics: effective dimensions, dimension distribution, Sobol indices and arbitrary aggregations thereof, and more. We will review those techniques and discuss how they open up new possibilities for informed modeling, optimization, and visualization of high-dimensional tensors.