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SUMMARY:Learning Directed Acyclic Graphs (DAGs) With Continuous Optimizati
 on - Dr Pingfan Song\, University of Cambridge
DTSTART:20231108T110000Z
DTEND:20231108T123000Z
UID:TALK208207@talks.cam.ac.uk
CONTACT:Isaac Reid
DESCRIPTION:Estimating the structure of directed acyclic graphs (DAGs) is 
 a challenging problem since the search space of DAGs is combinatorial and 
 scales super-exponentially with the number of nodes. Traditional approache
 s rely on various local heuristics for enforcing the acyclicity constraint
 . \n\nRecent advancements have introduced a fundamentally different strate
 gy that formulates DAG learning as a purely continuous optimisation proble
 m over real matrices. This is achieved by capitalising on innovative\, dif
 ferentiable acyclicity characterization functions of DAGs. By eliminating 
 the need for combinatorial constraints\, it offers efficient solutions thr
 ough standard numerical algorithms. Notably\, this strategy exhibits sever
 al advantages\, including the detection of large cycles\, improved gradien
 t behaviour\, and faster runtime performance.\n\nThis talk will introduce 
 a few representative acyclicity characterisation\, e.g. trace of matrix ex
 ponential function proposed in the No-Tears paper (which is based on the i
 dea that powers of an adjacency matrix contain information about walks and
  cycles)\, and log-determinant (log-det) function introduced in the DAGMA 
 paper (which leverages the nilpotency property of DAGs and the property of
  M-matrices.) These works open possibilities for more effective and effici
 ent DAG learning.\n\nReading suggestions:\nZheng\, Xun\, Bryon Aragam\, Pr
 adeep K. Ravikumar\, and Eric P. Xing. "Dags with no tears: Continuous opt
 imization for structure learning." Advances in neural information processi
 ng systems 31 (2018).\nBello\, Kevin\, Bryon Aragam\, and Pradeep Ravikuma
 r. "Dagma: Learning dags via m-matrices and a log-determinant acyclicity c
 haracterization." Advances in Neural Information Processing Systems 35 (20
 22): 8226-8239.\n
LOCATION:Cambridge University Engineering Department\, CBL Seminar room BE
 4-38.
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