*Tid:* **19 september 2011 kl 15.15-16.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7.
Karta!
*Föredragshållare:*
**
Erik Aurell, Department of Computational Biology,
KTH and
Department of Information and Computer Science, Aalto University,
Helsinki.
**
**Titel:**
Recent developments on the inverse Ising problem
**Abstract**
The probability distributions over a set of binary variables
which have given single-variable marginals and given pair-wise
correlations, and which maximize entropy, from an exponential
family called the Ising model of statistical mechanics.
The (standard) Ising problem is to compute properties (marginals,
correlation functions) in such a model at given
model parameters. The inverse Ising problem is the opposite
task to infer parameter given marginals and correlation
functions. In this exponential family (sample) marginals and
(sample) pair-wise correlation functions are sufficient statistics, but
a maximum likelihood solution is not feasible in large instances
since the normalization factor (the partition function) is not easily
computable.
Various approximations which allow for fast (but not exact)
solutions have been introduced in the last decade. The competitive
evaluations of the various scheme is at this point mainly empirical,
by numerical experiments in well-controlled test examples, or in
concrete applications, but some rigorous results have also been
obtained. I will survey these developments, with an emphasis
on what my group has been working on.
This is joint work with John Hertz, Yasser Roudi, Mikko Alava,
Zeng HongLi and others.
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