Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes
This work addresses scalability for subset selection tasks in machine learning, offering a practical solution for applications like recommendation systems, though it is incremental as it builds on prior NDPP methods.
The paper tackles the scalability issue of nonsymmetric determinantal point processes (NDPPs), which have high memory and runtime costs, by developing learning and inference algorithms with linear complexity in the number of items, enabling practical use on large datasets while maintaining predictive performance.
Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection. Recent work shows that nonsymmetric DPP (NDPP) kernels have significant advantages over symmetric kernels in terms of modeling power and predictive performance. However, for an item collection of size $M$, existing NDPP learning and inference algorithms require memory quadratic in $M$ and runtime cubic (for learning) or quadratic (for inference) in $M$, making them impractical for many typical subset selection tasks. In this work, we develop a learning algorithm with space and time requirements linear in $M$ by introducing a new NDPP kernel decomposition. We also derive a linear-complexity NDPP maximum a posteriori (MAP) inference algorithm that applies not only to our new kernel but also to that of prior work. Through evaluation on real-world datasets, we show that our algorithms scale significantly better, and can match the predictive performance of prior work.