DeepAI AI Chat
Log In Sign Up

Optimized Algorithms to Sample Determinantal Point Processes

by   Nicolas Tremblay, et al.

In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative correlation, i.e., ones that can generate a "diverse" sample from a set of items. They are parametrized by a matrix L, called L-ensemble, that encodes the correlations between items. The standard sampling algorithm is separated in three phases: 1/ eigendecomposition of L, 2/ an eigenvector sampling phase where L's eigenvectors are sampled independently via a Bernoulli variable parametrized by their associated eigenvalue, 3/ a Gram-Schmidt-type orthogonalisation procedure of the sampled eigenvectors. In a naive implementation, the computational cost of the third step is on average O(Nμ^3) where μ is the average number of samples of the DPP. We give an algorithm which runs in O(Nμ^2) and is extremely simple to implement. If memory is a constraint, we also describe a dual variant with reduced memory costs. In addition, we discuss implementation details often missing in the literature.


page 1

page 2

page 3

page 4


A Faster Sampler for Discrete Determinantal Point Processes

Discrete Determinantal Point Processes (DPPs) have a wide array of poten...

Fast determinantal point processes via distortion-free intermediate sampling

Given a fixed n× d matrix X, where n≫ d, we study the complexity of samp...

DPPNet: Approximating Determinantal Point Processes with Deep Networks

Determinantal Point Processes (DPPs) provide an elegant and versatile wa...

Kronecker Determinantal Point Processes

Determinantal Point Processes (DPPs) are probabilistic models over all s...

Variance of Longest Run Duration in a Random Bitstring

We continue an earlier study, starting with unconstrained n-bitstrings, ...

Exact Sampling from Determinantal Point Processes

Determinantal point processes (DPPs) are an important concept in random ...

Simulation methods and error analysis for trawl processes and ambit fields

Trawl processes are continuous-time, stationary and infinitely divisible...