We consider the product of determinantal point processes (DPPs), a point process whose probability mass is proportional to the product of principal minors of multiple matrices as a natural, promising generalization of DPPs.
We consider determinantal point processes (DPPs) constrained by spanning trees.
The task is regarded as predictive optimization, but existing predictive optimization methods have not been extended to handling multiple domains.
A $k$-submodular function is a generalization of a submodular function, where the input consists of $k$ disjoint subsets, instead of a single subset, of the domain. Many machine learning problems, including influence maximization with $k$ kinds of topics and sensor placement with $k$ kinds of sensors, can be naturally modeled as the problem of maximizing monotone $k$-submodular functions. In this paper, we give constant-factor approximation algorithms for maximizing monotone $k$-submodular functions subject to several size constraints. The running time of our algorithms are almost linear in the domain size. We experimentally demonstrate that our algorithms outperform baseline algorithms in terms of the solution quality.