Uniform deconvolution for Poisson Point Processes
Authors: Anna Bonnet, Claire Lacour, Franck Picard, Vincent Rivoirard
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The empirical performance of our estimator is then studied by simulations and competed with a deconvolution method based on Gaussian errors. Finally we provide an illustration of our procedure on experimental data in Genomics, where the purpose is to study the spatial repartition of replication starting points and sequence motifs along chromosomes in humans (Picard et al., 2014). |
| Researcher Affiliation | Academia | Anna Bonnet EMAIL LPSM, Sorbonne Universit e, UMR CNRS 8001, 75005 Paris, France ... Claire Lacour EMAIL Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, LAMA UMR8050, F-77447 Marne-la-Vall ee, France ... Franck Picard EMAIL LBMC, Univ. Lyon, ENS de Lyon, UCBL, CNRS UMR 5239, INSERM U1210, 46 all ee d Italie, Site Jacques Monod, 69007 Lyon, France ... Vincent Rivoirard EMAIL CEREMADE, CNRS, UMR 7534, Universit e Paris-Dauphine, PSL University, 75016 Paris, France |
| Pseudocode | No | The paper describes mathematical procedures and estimation methods in Section 3 'Estimation procedure' and Section 3.4 'Bandwidth selection' but does not present them in a structured pseudocode or algorithm block. |
| Open Source Code | Yes | The code is available at https://github.com/Anna Bonnet/Poisson Deconvolution. |
| Open Datasets | Yes | Finally we provide an illustration of our procedure on experimental data in Genomics, where the purpose is to study the spatial repartition of replication starting points and sequence motifs along chromosomes in humans (Picard et al., 2014). ... We considered the spatial distribution of G-quadruplexes (Zheng et al., 2020) along all replication origins (Picard et al., 2014), by considering the initiation peak as the reference position (Figure 5). |
| Dataset Splits | No | For each set (f X, n, a), we present the median performance over 30 replicates. ... The estimation of the intensity of human replication origins along chromosome 16 (N+ = 874)... The paper describes generating data for simulations and analyzing a genomic dataset, but it does not specify explicit training/test/validation splits for machine learning experiments. |
| Hardware Specification | Yes | The computations were run on 16 cores of a server Intel Xeon E5-4620 2.20GHz . |
| Software Dependencies | No | The code, implemented in R, is parallelized and uses the Rcpp package in order to reduce the computational cost. ... competed with a deconvolution procedure for Gaussian noise (Delaigle and Gijbels, 2004), available in the f DKDE R-package. The paper mentions software used (R, Rcpp, fDKDE R-package) but does not provide specific version numbers for these dependencies. |
| Experiment Setup | Yes | We consider different shapes for the Poisson process intensity to challenge our estimator in different scenarii, by first generating Poisson processes on [0, 1] based on the Beta probability distribution function, with funisym = Beta(2, 2) (unimodal symmetric), fbisym = 0.5 Beta(2, 6) + 0.5 Beta(6, 2) (bimodal symmetric), fbiasym = 0.5 Beta(2, 20) + 0.5 Beta(2, 2) (bimodal assymmetric). We also generate Poisson processes with Laplace distribution intensity (location 5, scale 0.5) to consider a sharp form and a different support. In this case, we consider that T = 10. We consider a uniform convolution model with increasing noise (a {0.05, 0.1} for Beta, a {0.5, 1, 2, 3} for Laplace) and Poisson processes with increasing number of occurrences (n {500, 1000}). For each set (f X, n, a), we present the median performance over 30 replicates. ... Our procedure is computed with an Epanechnikov kernel, that is K(u) = 0.75(1 u2)1|u| 1. ... We propose to investigate if we could find a universal value of parameter η... For a grid of η in [ 1; 1], we compare the mean squared errors (MSE) of estimators calibrated with different values of η... |