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SUMMARY:A Poisson Process Model for Monte Carlo - Greg Flamich\, Universit
 y of Cambridge
DTSTART:20231115T110000Z
DTEND:20231115T123000Z
UID:TALK208546@talks.cam.ac.uk
CONTACT:Isaac Reid
DESCRIPTION:What is so fishy about rejection sampling\, importance samplin
 g\, and the Gumbel-max trick? It turns out that in each case\, Poisson pro
 cesses are lurking beneath the surface!\n\nPoisson processes are the most 
 fundamental point processes (“distributions over randomly placed points 
 in space”) in probability theory. As such\, they are widely used for mod
 eling discrete phenomena across mathematics (e.g.\, the occurrence of prim
 es along the integers in number theory)\, the sciences (e.g.\, neural spik
 e trains or the occurrence of earthquakes)\, and engineering (incoming cal
 ls at a call center). However\, a lesser-known fact about them is that the
 y also provide a unifying view of (non-Markov chain) Monte Carlo\, allowin
 g us to recast sampling as a search problem over Poisson processes.\n\nMy 
 talk aims to provide a brief introduction to Poisson processes and showcas
 e four operations that preserve them: restriction\, superposition\, thinni
 ng\, and mapping. Pleasingly\, all the above-mentioned sampling algorithms
  follow the same three-step recipe:\n\n1. Take a base Poisson process.\n2.
  Modify it using one of the four operations.\n3. Search over the points of
  the modified process to find our sample.\n\nIn my talk\, I will explain t
 he details of how this general recipe gives rise to rejection sampling\, t
 he Gumble-max trick\, importance sampling (and more generally\, A* samplin
 g)\, and greedy Poisson rejection sampling\; with a focus on their computa
 tional aspects\, such as numerical stability and runtime. Finally\, I will
  provide insight into how we can use them for data compression via channel
  simulation/relative entropy coding. 
LOCATION:Cambridge University Engineering Department\, CBL Seminar room BE
 4-38.
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