  In this paper, we address the challenge of recovering an accurate breakdown
of aggregated tensor data using disaggregation examples. This problem is
motivated by several applications. For example, given the breakdown of energy
consumption at some homes, how can we disaggregate the total energy consumed
during the same period at other homes? In order to address this challenge, we
propose GRATE, a principled method that turns the ill-posed task at hand into a
constrained tensor factorization problem. Then, this optimization problem is
tackled using an alternating least-squares algorithm. GRATE has the ability to
handle exact aggregated data as well as inexact aggregation where some
unobserved quantities contribute to the aggregated data. Special emphasis is
given to the energy disaggregation problem where the goal is to provide energy
breakdown for consumers from their monthly aggregated consumption. Experiments
on two real datasets show the efficacy of GRATE in recovering more accurate
disaggregation than state-of-the-art energy disaggregation methods.

Systems and Control;Machine Learning;Systems and Control;Optimization and Control