[Sds-seminars] S&DS Talk: Monday, 2/4, Yian Ma, "Bridging MCMC and Optimization", DL 220

[Dan Spielman]

*Department of Statistics and Data Science * <https://statistics.yale.edu/>
YIAN MA, University of California, Berkeley

[image:
https://statistics.yale.edu/sites/default/files/styles/user_picture_node/public/unnamed.jpg?itok=ak2oyU1C]

*Date*: Monday, February 04, 2019

*Time*: 4:00PM to 5:15PM

*Location*: Dunham Lab see map
<http://maps.google.com/?q=10+Hillhouse+Avenue%2C+Room+220%2C+New+Haven%2C+CT%2C+%2C+us>


10 Hillhouse Avenue, Room 220

New Haven, CT

Website <https://sites.google.com/view/yianma>











*Title: Bridging MCMC and Optimization*



*Information and Abstract: *

In this talk, I will discuss three ingredients of optimization theory in
the context of MCMC: Non-convexity, Acceleration, and stochasticity. I will
focus on a class of non-convex objective functions arising from mixture
models. For that class of objective functions, I will demonstrate that the
computational complexity of a simple MCMC algorithm scales linearly with
the model dimension, while optimization problems are NP-hard.

I will then study MCMC algorithms as optimization over the KL-divergence in
the space of measures. By incorporating a momentum variable, I will discuss
an algorithm which performs accelerated gradient descent over the
KL-divergence. Using optimization-like ideas, a suitable Lyapunov function
is constructed to prove that an accelerated convergence rate is obtained.

Finally, I will present a complete recipe for constructing stochastic
gradient MCMC algorithms that translates the task of finding a valid
sampler into one of  choosing two matrices. I will then describe how
stochastic gradient MCMC algorithms can be applied to applications
involving temporally correlated data, where the challenge arises from the
need to break the dependencies when considering minibatches of
observations.

*3:45 p.m.**   Pre-talk tea Dunham Lab, Suite 222, Breakroom 228*

For more details and upcoming events visit our website at
http://statistics.yale.edu/ .






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