Fixed-Size Determinantal Point Processes Sampling For Species Phylogeny

Diala Wehbe (1, 2) , Nicolas Wicker (1) , Baydaa Al-Ayoubi (2) , Luc Moulinier (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]
3 ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie

Determinantal point processes (DPPs) are popular tools that supply useful information for repulsiveness. They provide coherent probabilistic models when negative correlations arise and also represent new algo-rithms for inference problems like sampling, marginalization and conditioning. Recently, DPPs have played an increasingly important role in machine learning and statistics, since they are used for diverse subset se-lection problems. In this paper we use k-DPP, a conditional DPP that models only sets of cardinality k, to sample a diverse subset of species from a large phylogenetic tree. The tree sampling task is important in many studies in modern bioinformatics. The results show a fast mixing sampler for k-DPP, for which a polynomial bound on the mixing time is given. This approach is applied to a real-world dataset of species,and we observe that leaves joined by a higher subtree are more likely to appear.

Mots clés: Determinantal point process; Kernel; Markov chain; Metropolis-Hasting; Mixing time; Phylogenetic tree

Domaines: Intelligence artificielle [cs.AI]

Diala Wehbe, Nicolas Wicker, Baydaa Al-Ayoubi, Luc Moulinier. Fixed-Size Determinantal Point Processes Sampling For Species Phylogeny. MathematicS In Action, 2021, ⟨10.5802/msia.13⟩. ⟨hal-03402874⟩