Nonparametric estimation of continuous DPPs with kernel methods

Authors: Michaël Fanuel, Rémi Bardenet

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental 6 Empirical evaluation
Researcher Affiliation Academia Michaël Fanuel and Rémi Bardenet Université de Lille, CNRS, Centrale Lille UMR 9189 CRISt AL, F-59000 Lille, France {michael.fanuel, remi.bardenet}@univ-lille.fr
Pseudocode Yes Algorithm 1 Estimation of the integral kernel a(x, y) of the DPP likelihood kernel A. and Algorithm 2 Estimation of the integral kernel k(x, y) of the DPP correlation kernel K = A(A + I) 1.
Open Source Code Yes Our code is freely available1. 1https://github.com/mrfanuel/Learning Continuous DPPs.jl
Open Datasets No We draw samples3 from this continuous DPP in the window X = [0, 1]2. This is simulated data, not a pre-existing publicly available dataset.
Dataset Splits No The paper describes generating 's i.i.d. samples of a DPP' and 'sample a set of points I = {x i : 1 i n} i.i.d. from the ambient probability measure µ' but does not specify traditional train/validation/test dataset splits.
Hardware Specification No The paper mentions that compute details are in supplementary material, but the provided text does not contain specific hardware details like GPU/CPU models or memory.
Software Dependencies No The paper mentions using 'the R package spatstat [Baddeley et al., 2015]' but does not provide specific version numbers for software dependencies used in their implementation.
Experiment Setup Yes We consider an L-ensemble with correlation kernel k(x, y) = ρ exp( x y 2 2/α2) defined on Rd with α = 0.05. For the estimation, we use a Gaussian kernel k H(x, y) = exp x y 2 2/(2σ2) with σ > 0. The computation of the correlation kernel always uses p = 1000 uniform samples. Iteration (14) is run until the precision threshold tol = 10 5 is achieved. For stability, we add 10 10 to the diagonal of the Gram matrix K. The remaining parameter values are given in captions. (e.g., σ = 0.1 and λ = 0.1, ρ = 50 and ρ = 100)