DEEP LEARNING OF DETERMINANTAL POINT PROCESSES VIA PROPER SPECTRAL SUB-GRADIENT

Determinantal point processes (DPPs) is an effective tool to deliver diversity in multiple machine learning and computer vision tasks. Under the deep learning framework, DPP is typically optimized via approximation, which is not straightforward and has some conflicts with the diversity requirement. We note, however, there have been no deep learning paradigms to optimize DPP directly since it involves matrix inversion that may result in computational instability. This fact greatly hinders the use of DPP on some specific objective functions where DPP would otherwise serve as a term to measure the feature diversity. In this paper, we devise a simple but effective algorithm to optimize the DPP term directly through expressing with L-ensemble in the spectral domain over the gram matrix, which is more flexible than learning on parametric kernels. By further taking into account additional geometric constraints, our algorithm seeks to generate valid sub-gradients of the DPP term in cases where the DPP gram matrix is not invertible (no gradients exist in this case). In this sense, our algorithm can be easily incorporated with multiple deep learning tasks. Experiments show the effectiveness of our algorithm, indicating promising performance for practical learning problems.