From ghamburg at tti-c.org  Fri Nov  2 12:50:20 2007
From: ghamburg at tti-c.org (Gary Hamburg)
Date: Fri Nov  2 12:45:01 2007
Subject: [TTIC Colloquium] Mark Newman
Message-ID: <002e01c81d81$3816bca0$a2bf8780@ghamburg5566PD1>

 

This talk is sponsored by the University of Chicago and TTI-C.  The contact
for this event is Steve Smale (834-2510) smale@tti-c.org.  It will be held
on Friday, November 9, in 251 Ryerson from 2:30 pm to 3:30 pm.

 

The large-scale structure of real-world networks.

 

Mark Newman

Department of Physics and Center for the Study of Complex Systems

University of Michigan

 

Many systems take the form of networks: the Internet, the World Wide Web,
social networks, citation networks, metabolic networks, food webs, and
neural networks are just a few examples.  In this talk I will show some
recent empirical data for these and other networks and discuss how we can
discover and understand their large-scale structure and its implications.

 

The problem is that many networks are too large to visualize in their
entirety, so to understand what they "look lie" we need algorithmic or
statistical techniques to pick useful patterns out of large network data
sets.  I will describe recent work on several methods that attempt to detect
structural features such as clustering and hierarchy using spectral and
other techniques.  I will give a variety of illustrative applications
throughout the talk.

 

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From ghamburg at tti-c.org  Mon Nov 19 15:30:08 2007
From: ghamburg at tti-c.org (Gary Hamburg)
Date: Mon Nov 19 15:23:40 2007
Subject: [TTIC Colloquium] Amir Globerson: "Message Passing and Inference -
	A Dual Perspective" at TTI-C
Message-ID: <003701c82af3$5c299e30$a2bf8780@ghamburg5566PD1>

WHAT:
Amir Globerson: "Message Passing and Inference - A Dual Perspective"

WHEN:
Mon Nov 26 12:30pm - Mon Nov 26 1:30pm

WHERE:
TTI-C conference room

ABSSTRACT:
Graphical models are a powerful tool for representing distributions over
complex multivariate objects such as images or documents. Although graphical
models have been used with considerable success in many domains, such as
machine vision and signal processing, it is theoretically NP hard to infer
even simple model properties, such as the marginals over single variables,
or the most likely assignment. This difficulty has been addressed in
practice by designing approximate inference algorithms (such as belief
propagation) that often work well in practice, although with relatively weak
theoretical guarantees.

In this work we use the notion of convex duality to design a class of
message passing algorithms that solve convex variational formulations of
inference problems. Specifically, we use the geometric and linear
programming duals of two variational approximations, and show that
coordinate ascent on these duals yields a convergent message passing
algorithm.

We illustrate the performance of our new algorithms on various problems, and
show that they converge in cases where message passing algorithms such as
max product do not.

Host: Nati Srebro

Contact host at nati@tti-c.org to be placed on the speaker's schedule.

From ghamburg at tti-c.org  Mon Nov 26 09:32:52 2007
From: ghamburg at tti-c.org (Gary Hamburg)
Date: Mon Nov 26 09:26:05 2007
Subject: [TTIC Colloquium] Alexander Razborov - TTI-C Talk
Message-ID: <001701c83041$9c21fde0$a2bf8780@ghamburg5566PD1>

When:   Tuesday, November 27, 2007 @ 10:00 AM
 
Where:  TTI-C Conference Room
 
Who:    Alexander Razborov - Institute for Advanced Study, Princeton NJ.
 
Topic:  The Sign-Rank of $AC^0$
 
 
 
The sign-rank of a matrix $M$ with $\pm 1$ entries is the smallest
rank of a real matrix $A$ such that $M_{ij}=sign(A_{ij})$ for all
$i,j$. We exhibit a $2^n\times 2^n$ matrix $M$ computable by depth 2
circuits of polynomial size whose sign-rank is exponential in $n$. Our
result has the following immediate applications.
 
1. In the context of communication complexity alternations can be more
powerful than unbounded-error probabilism. This solves a long-standing
open problem asked in the seminal paper by Babai, Frankl and Simon
(1986).
 
2. Exponential lower bounds on the dimension complexity of the class
of all DNF formulas. Our bound almost matches the upper bound proved
by Klivans and Servedio (2001) and provides apparently the first
unconditional exponential lower bound for PAC learning of DNF formulas
in a reasonable model.
 
3. The first exponential lower bound on the size of
thershold-of-majority circuits computing a function in $AC^0$.
 
Joint work with Alexander Sherstov (U. of Texas)
 

 

 

 

 

 

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From ghamburg at tti-c.org  Mon Nov 26 10:01:23 2007
From: ghamburg at tti-c.org (Gary Hamburg)
Date: Mon Nov 26 09:54:35 2007
Subject: [TTIC Colloquium] Amir Globerson - TTI-C Talk - Reminder
Message-ID: <003801c83045$97c18d20$a2bf8780@ghamburg5566PD1>

WHAT:

Amir Globerson: "Message Passing and Inference - A Dual Perspective"

 

WHEN:

Mon Nov 26 12:30pm - Mon Nov 26 1:30pm

 

WHERE:

TTI-C conference room

 

ABSSTRACT:

Graphical models are a powerful tool for representing distributions over
complex multivariate objects such as images or documents. Although graphical
models have been used with considerable success in many domains, such as
machine vision and signal processing, it is theoretically NP hard to infer
even simple model properties, such as the marginals over single variables,
or the most likely assignment. This difficulty has been addressed in
practice by designing approximate inference algorithms (such as belief
propagation) that often work well in practice, although with relatively weak
theoretical guarantees.

 

In this work we use the notion of convex duality to design a class of
message passing algorithms that solve convex variational formulations of
inference problems. Specifically, we use the geometric and linear
programming duals of two variational approximations, and show that
coordinate ascent on these duals yields a convergent message passing
algorithm.

 

We illustrate the performance of our new algorithms on various problems, and
show that they converge in cases where message passing algorithms such as
max product do not.

 

Host: Nati Srebro

 

Contact host at nati@tti-c.org to be placed on the speaker's schedule.

 

 

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