Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel K that can be seen, in a discrete setting, as a matrix storing the similarity between points. The main exact algorithm to sample DPPs uses the spectral decomposition of K, a computation that becomes costly when dealing with a high number of points. Here we present an alternative exact algorithm to sample in discrete spaces that avoids the eigenvalues and the eigenvectors computation. The method used here is innovative, and numerical experiments show competitive results with respect to the initial algorithm.

中文翻译：

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没有特征分解的行列式点过程的精确采样

行列式点过程 (DPP) 可以对排斥进行建模：它们提供了不同的点集。斥力编码在内核中ķ在离散设置中，可以将其视为存储点之间相似性的矩阵。采样 DPP 的主要精确算法使用ķ，在处理大量点时变得昂贵的计算。在这里，我们提出了一种替代的精确算法来在离散空间中进行采样，从而避免了特征值和特征向量的计算。这里使用的方法是创新的，数值实验显示了与初始算法相比具有竞争力的结果。