Coupled norms have emerged as a convex method to solve coupled tensor completion. A limitation with coupled norms is that they only induce low-rankness using the multilinear rank of coupled tensors. In this paper, we introduce a new set of coupled norms known as coupled nuclear norms by constraining the CP rank of coupled tensors. We propose new coupled completion models using the coupled nuclear norms as regularizers, which can be optimized using computationally efficient optimization methods. We derive excess risk bounds for proposed coupled completion models and show that proposed norms lead to better performance. Through simulation and real-data experiments, we demonstrate that proposed norms achieve better performance for coupled completion compared to existing coupled norms.

Extensive experiments on multiple networks show that saddle-points are not the cause for generalization gap of large batch size training, and the results consistently show that large batch converges to points with noticeably higher Hessian spectrum.

Optimization is an integral part of most machine learning systems and most numerical optimization schemes rely on the computation of derivatives.

We develop a dual framework for solving the low-rank tensor completion problem.

Given the well-known hardness results in finding stationary points, recent focus has shifted in characterizing approximate stationary points.

The algorithm is derived from the variational objective in the filtering setting and consists of an optimization procedure at each time step.

We also introduce the concept of contour entropy, a formal measure of uncertainty about the location of the zero contour of a function approximated by a statistical surrogate model.

In our work, we focus on smooth convex or strongly convex problems in the interpolation regime.

In most applications, the output labels of learning problems have some structure that is crucial to consider. This includes natural language processing applications, where the output may be a sentence, a sequence of parts-of-speech tags, a parse tree, or a dependency graph.