**Wicher Bergsma**

http://www2.lse.ac.uk/researchAndExpertise/Experts/profile.aspx?KeyValue=w.p.bergsma@lse.ac.uk

LSE The London School of Economics and Political Science

Wednesday 14th November 2012

**Time: 4pm**

** **

B10 Basement Seminar Room

Alexandra House, 17 Queen Square, London, WC1N 3AR

**Nonparametric testing of conditional**

independence

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Random variables Y and Z are conditionally independent given X if, knowing the value of X, information about Y does not provide information about Z.

Conditional independence relations are the building blocks of graphical models, applications of which include information extraction, speech recognition, computer vision, decoding of low-density parity-check codes, modeling of gene regulatory networks, gene finding and diagnosis of diseases, and graphical models for protein structure.

The present talk discusses a new method to test conditional independence. Existing literature on the topic is usually restricted to the normal and categorical cases, but recently nonparametric testing has also received a fair amount of attention.

Our method is also nonparametric, but differs from previous ones in that it is based on the following decomposition, which gives some advantages.

Denote by $\Psi_{g,h}(x)$ the conditional covariance between g(Y) and

h(Z) given X=x.

Conditional independence of Y and Z given X holds if and only if the following two conditions hold:

CI1: For arbitrary g and h, $E\Psi_{g,h}(X)=0$.

CI2: For arbitrary g and h, $E\Psi_{g,h}(x)$ does not depend on x.

Each condition can be tested separately. However, there are some technical difficulties which we explain and for which we provide a solution.

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