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  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
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\begin{center}
  4:15 p.m., Tuesday, November 28, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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\begin{center}
  \textsl{Sourav Chatterjee} \\
Department of Statistics\\
University of California, Berkeley
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  \textbf{Exponential Families of Random Networks}
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\noindent                   
   
With the advent of graphical models and causal networks, random graphs are becoming increasingly  relevant in modern statistics. It is statistically natural, therefore, to study exponential families of distributions on graph space. In the first part of the talk, I will present some results about an  exponential family where the sufficient statistics are the vertex degrees. A byproduct of the investigation is a surprisingly fast and easy algorithm for computing the MLE (this is based on a joint work with Joseph Blitzstein and Persi Diaconis).

In the second part, I will consider the following toy problem as a precursor to more complex questions: What happens if the sufficient statistics are the number of edges and the number of triangles? Is it still possible to evaluate the normalizing constant (the key issue in exponential families)? I will present a new technique that gives an analytical solution to this seemingly intractable problem in a subset of the parameter space.

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