Discovering Reliable Correlations in Categorical Data

In many scientific tasks we are interested in discovering whether there exist any correlations in our data. This raises many questions, such as how to reliably and interpretably measure correlation between a multivariate set of attributes, how to do so without having to make assumptions on distribution of the data or the type of correlation, and, how to efficiently discover the top-most reliably correlated attribute sets from data. In this paper we answer these questions for discovery tasks in categorical data. In particular, we propose a corrected-for-chance, consistent, and efficient estimator for normalized total correlation, by which we obtain a reliable, naturally interpretable, non-parametric measure for correlation over multivariate sets. For the discovery of the top-k correlated sets, we derive an effective algorithmic framework based on a tight bounding function. This framework offers exact, approximate, and heuristic search. Empirical evaluation shows that already for small sample sizes the estimator leads to low-regret optimization outcomes, while the algorithms are shown to be highly effective for both large and high-dimensional data. Through two case studies we confirm that our discovery framework identifies interesting and meaningful correlations

The Minimum Description Length Principle for Pattern Mining: A Survey

This is about the Minimum Description Length (MDL) principle applied to pattern mining. The length of this description is kept to the minimum. Mining patterns is a core task in data analysis and, beyond issues of efficient enumeration, the selection of patterns constitutes a major challenge. The MDL principle, a model selection method grounded in information theory, has been applied to pattern mining with the aim to obtain compact high-quality sets of patterns. After giving an outline of relevant concepts from information theory and coding, as well as of work on the theory behind the MDL and similar principles, we review MDL-based methods for mining various types of data and patterns. Finally, we open a discussion on some issues regarding these methods, and highlight currently active related data analysis problems