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On positive influence and negative dependence

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Ranjan,  Desh
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-98-1-018.pdf
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Citation

Dubhashi, D., & Ranjan, D.(1998). On positive influence and negative dependence (MPI-I-1998-1-018). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-7BAC-E
Abstract
We study two notions of negative influence namely negative regression and negative association. We show that if a set of symmetric binary random variables are negatively regressed then they are necessarily negatively associated. The proof uses a lemma that is of independent interest and shows that every binary symmetric distribution has a variable of ``positive influence''. We also show that in general the notion of negative regression is different from that of negative association.