OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

"Convex Tensor Decomposition with Performance Guarantee"
Ryota Tomioka (University of Tokyo)

Abstract:
We analyze the statistical performance of a recently proposed convex tensor
decomposition algorithm. Conventionally tensor decomposition has been
formulated as non-convex optimization problems, which hindered the
analysis of their performance. We show under some conditions that
both the performance of noisy tensor decomposition and tensor completion
can be predicted by the quantity we call the normalized rank.
Numerical experiments show that our theory can precisely predict
the scaling behavior in practice. The current analysis naturally
extends the analysis of convex low-rank matrix estimation to tensors.
We also discuss some limitations of our theory, open issues, and
possible extensions.

(OPTEC-WG2: data-driven modelling)