Testing the Significance of Attribute Interactions |
---|

Aleks Jakulin - University of LjubljanaIvan Bratko - University of Ljubljana |

Attribute interactions are the irreducible dependencies between attributes.Interactions underlie feature relevance and selection, the structure of jointprobability and classification models: if and only if the attributes interact,they should be connected. While the issue of 2-way interactions, especially ofthose between an attribute and the label, has already been addressed, weintroduce an operational definition of a generalized n-way interaction byhighlighting two models: the reductionistic part-to-whole approximation, wherethe model of the whole is reconstructed from models of the parts, and theholistic reference model, where the whole is modelled directly. An interactionis deemed significant if these two models are significantly different. In thispaper, we propose the Kirkwood superposition approximation for constructingpart-to-whole approximations. To model data, we do not assume a particularstructure of interactions, but instead construct the model by testing for thepresence of interactions. The resulting map of significant interactions is agraphical model learned from the data. We confirm that the P-values computedwith the assumption of the asymptotic chi-squared distribution closely matchthose obtained with the bootstrap. |