Sydney Dynamics Group Seminar: Lachlan Astfalck, University of New South Wales -- Sydney Dynamics Group Seminar, Lachlan Astfalck (UNSW), Conditioning almost all stochastic processes on almost anything

Seminar : Sydney Dynamics group Seminar.  
Day/time : Wednesday, October 7 at 4:30 PM
Location : SMRI seminar room (A12 Macleay Room 301).  
Speaker : Lachlan Astfalck, University of New South Wales 

Title: Conditioning almost all stochastic processes on almost anything 

Abstract: Sampling from a stochastic process only requires running it forward; outside a
small collection of special cases, conditioning has remained the preserve of
model-specific constructions.  Once conjugacy breaks, we reach for Laplace, EP,
variational bounds, or a bespoke sampler, with a fresh derivation for every new
problem.  Borrowing the architecture of diffusion models, I'll show a general solution
for conditioning intractable stochastic processes.  Stripped of its hype and branding, a
diffusion model is simply a way to sample from an inconvenient distribution.  Both
sampling and conditioning require the score of the noised process, which in the ML
literature, would be approximated with a neural network trained on a huge dataset.  I'll
show that if the forward model can be written as a deterministic map of simple noise,
this score is available in closed form and we can do without the network; sampling and
conditioning then reduce to solving a reverse SDE.  After discretisation this covers
essentially every stochastic process in use: Gaussian, Student-t and Cauchy fields; SDEs
and SPDEs; Potts models; or whatever your simulator already produces.  Examples are
given for conditioning on observed data, censoring, shape constraints,
differential-equation constraints, rare events, and (subject to some hand-waving)
natural language.