From nicolas.brodu at numerimoire.net  Fri Jan 30 21:53:30 2009
From: nicolas.brodu at numerimoire.net (Nicolas Brodu)
Date: Fri, 30 Jan 2009 22:53:30 +0100
Subject: [Causality-ML] Video replay, mailing list and next talk announcement
Message-ID: <200901302253.30168.nicolas.brodu@numerimoire.net>

Dear Causality and Machine Learning group,

We have a new mailing-list! Please do not hesitate to use it and discuss the 
papers and presentations. Future events and talks will be announced to the 
list as well.

You can manage your options (ex: changing address, unsubscribing 
duplicates...) by following the links sent to you in the list welcome 
message.

The video of the last talk by Arthur Gretton is available online! You can find 
it together with other videos for most of the recent talks on the schedule 
and material page:
  http://www.afia-france.org/tiki-index.php?page=Groupe+de+lecture

The next presentation is by Kenji Fukumizu. It builds on and extends the last 
presentation:

Topic: Conditional independence with positive definite kernels
When: Friday 06/02, Tokyo 8h, Paris 0h, ET 18h (Thursday), PT 15h (Thursday)
URL: http://www.afia-france.org/tiki-index.php?page=GroupeDeLecture090206KF

Abstract:
--------
A new nonparametric methodology for dependence of random variables is 
discussed. It uses the framework of reproducing kernel Hilbert spaces (RKHS) 
defined by positive definite kernels. In this methodology, a random variable 
is mapped to a RKHS, thus random variables on the RKHS are considered. The 
basic statistics such as mean and covariance of the variables on the RKHS can 
capture all the information on the underlying probabilities by using a 
sufficiently rich function space as RKHS, which we call a characteristic 
RKHS.
  In this presentation, I focus on the characterization of conditional 
independence of variables by covariance operators. I will show that, in the 
similar fashion to the partial correlation for Gaussian variables, the 
conditional covariance operator on characteristic RKHS characterizes the 
conditional independence of arbitrary random variables. The Hilbert-Schmidt 
norm of the conditional covariance operator, thus, defines a measure of 
conditional dependence, and the empirical estimate of the norm works as a 
test statistics of conditional independence. In addition, I will show that, 
for any characteristic RKHS the Hilbert-Schmidt norm of the "normalized" 
conditional covariance operator coincides with the (conditional) mean square 
contingency in population, and thus does not depends on the choice of kernel. 
The empirical estimate gives a new kernel estimate of the mean square 
contingency.
  I will also show consistency of the estimators, and demonstrate some 
experimental results of conditional independence tests with the 
Hilbert-Schmidt norm of the normalized and unnormalized conditional 
covariance operators.
--------

If you know of potentially interested speakers or if you wish to present a 
paper, please send us a message so we can add you in the planning.

Best regards,
Nicolas Brodu