Abstract
Data Mining explanatory models must deal with relevance: how values of different data items are relevant to the values of other data items. But to be able to construct explanatory models, and in particular causal explanatory models, we must do so by first understanding irrelevance and exactly how irrelevance plays a role in explanatory models. The reason is that the conditional irrelevance or conditional no influence relation defines the boundaries of the ballpark within which an explanatory model lives.
This paper reviews the theory of no influence in the mathematical relation data structure. We discuss the relationship this theory has to graphical models and we define a coefficient of no influence and give a method for the estimation of its p-value.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Phillip Dawid, A.: Conditional independence in statistical theory. Journal of the Royal Statistical Society Serial B 41, 1–31 (1979)
Fagin, R.: A new normal form for relational databases. ACM Transactions on Database Systems 2(3), 262–278 (1977)
Fagin, R., Vardi, M.: The theory of data dependencies - a survey. Proceedings of Symposia in Applied Mathematics 34, 19–71 (1986)
Galles, D., Pearl, J.: Axioms of causal relevance. Artificial Intelligence 97, 9–43 (1997)
Hausman, D., Woodward, J.: Independence, invariance, and the causal markov condition. British Journal of Philosophy 50, 521–583 (1999)
Lauritzen, S.: Graphical Models. Oxford University Press, New York (1996)
Pearl, J., Paz, A.: On the logic of representing dependencies by graphs. In: Proceedings 1986 Canadian AI Conference, Montreal, Canada, pp. 94–98 (1986)
Shafer, G., Shenoy, P., Mellouli, K.: Propagating belief functions in qualitative markov trees. International Journal of Approximate Reasoning, 349–400 (1987)
Spohn, W.: Stochastic independence, causal independence, and shieldability. Journal of Philosophical Logic 9, 73–99 (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Haralick, R.M., Liu, L., Misshula, E. (2013). Relation Decomposition: The Theory. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2013. Lecture Notes in Computer Science(), vol 7988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39712-7_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-39712-7_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39711-0
Online ISBN: 978-3-642-39712-7
eBook Packages: Computer ScienceComputer Science (R0)