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# MATH 273B Advanced Techniques in Computational
Mathematics:

# Information Geometry and its Applications

# Winter 2020

##
TTh 12:30pm-1:50pm, APM 2402.

## Instructor

## Target Audience

- This course is relevant to engineers,
scientists, and mathematicians with an interest in the applications of
information geometry to data science and machine learning. The application
areas addressed will be tailored to the interests of the course
participants.

## Course Description

- Information
geometry involves the use of differential geometric tools to describe the
manifold of probability density functions, and allows one to investigate
the intrinsic properties of statistical models as opposed to their
parametric representations. In particular, we will discuss how divergence
functions, and their induced geometric structures, like the Riemannian
metric, dually flat affine connections, and curvature relate to
statistical issues like asymptotic efficiency of maximum likelihood
estimators as well as optimization algorithms on the manifold of
probability distributions.

## Announcements

- The resources below are password protected with the user name ma273b,
and the password is the first 4 digits of:

.

## References

- Information
Geometry and its Applications, Shun-ichi Amari, Applied
Mathematical Sciences, Springer 2016. ISBN: 978-4-431-55977-1.
[ Electronic Version ]
- Information
Geometry,
Nihat Ay, Jurgen Jost, Hong Van Le, Lorenz Schwachhofer, Modern Surveys
in Mathematics, Springer 2017. ISBN: 978-3-319-56477-7.
[ Electronic Version ]
- Methods of Information
Geometry,
Shun-ichi Amari, Hiroshi Nagaoka, Translations of Mathematical
Monographs, American Mathematical Society. ISBN: 978-0-8218-4302-4.
[ Electronic Version ]
- An elementary introduction to
information geometry, Frank Nielsen, arXiv:1808.08271 [cs.LG]
[ Electronic Version ]
- Optimization Algorithms on
Matrix Manifolds, P.-A. Absil, R. Mahony,
R.
Sepulchre, Princeton University Press, 2007, ISBN: 9780691132983.
[ Electronic Version ]

## Grading

- Your grade in the course is based on your written project report
(5-10 pages) and your 20-minute
project presentation during the time of the final.
- The topic of your project should be decided in consultation with the
instructor before the end of the first month of class.