Subjectively Interesting Subgroup Discovery on Real-valued Targets

Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the fact that there are exponentially many variable combinations to potentially consider, and there are infinitely many if we consider weighted combinations, even for linear combinations. Hence, an obvious question is whether we can automate the search for interesting patterns and visualizations. In this paper, we consider the setting where a user wants to learn as efficiently as possible about real-valued attributes. For example, to understand the distribution of crime rates in different geographic areas in terms of other (numerical, ordinal and/or categorical) variables that describe the areas. We introduce a method to find subgroups in the data that are maximally informative (in the formal Information Theoretic sense) with respect to a single or set of real-valued target attributes. The subgroup descriptions are in terms of a succinct set of arbitrarily-typed other attributes. The approach is based on the Subjective Interestingness framework FORSIED to enable the use of prior knowledge when finding most informative non-redundant patterns, and hence the method also supports iterative data mining.Comment: 12 pages, 10 figures, 2 tables, conference submissio

Bie. Maximum entropy modelling for assessing results on real-valued data

Abstract-Statistical assessment of the results of data mining is increasingly recognised as a core task in the knowledge discovery process. It is of key importance in practice, as results that might seem interesting at first glance can often be explained by well-known basic properties of the data. In pattern mining, for instance, such trivial results can be so overwhelming in number that filtering them out is a necessity in order to identify the truly interesting patterns. In this paper, we propose an approach for assessing results on real-valued rectangular databases. More specifically, using our analytical model we are able to statistically assess whether or not a discovered structure may be the trivial result of the row and column marginal distributions in the database. Our main approach is to use the Maximum Entropy principle to fit a background model to the data while respecting its marginal distributions. To find these distributions, we employ an MDL based histogram estimator, and we fit these in our model using efficient convex optimization techniques. Subsequently, our model can be used to calculate probabilities directly, as well as to efficiently sample data with the purpose of assessing results by means of empirical hypothesis testing. Notably, our approach is efficient, parameter-free, and naturally deals with missing values. As such, it represents a well-founded alternative to swap randomisation