A Statistically Efficient and Scalable Method for Exploratory Analysis of HighDimensional Data Discovering associations among variables is an important data mining task. The associations can be considered as statistical dependencies among random variables, expressed as the structure of an underlying probabilistic graphical model. Current methods for graphical model structure discovery either do not scale well to datasets with large sample sizes, or suffer from high false discovery rates when the number of dimensions is much larger than the sample size. In this paper, we propose a scalable and statistically efficient approach for graphical model structure discovery for multivariate data involving continuous variables. Our approach uses a minimum message length (MML)based objective, for which we design a greedy algorithm where the best edges maximising improvements to the MMLbased score are added incrementally to the graphical model. We present extensive empirical results on synthetic data with different sample, variable, clique and inverse correlation coefficient and show that our method outperforms strong baselines in terms of both speed and the accuracy of the predicted associations among the random variables in the graphical model. We also report that our method performs significantly very well in AML, BRCA cancer data and other reallife datasets.

Discovering Reliable Correlations in Categorical Data In many scientific tasks we are interested in finding 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 data distribution or the type of correlation, and, how to search efficiently for the most correlated attribute sets. We answer these questions for discovery tasks with categorical data. In particular, we propose a correctedforchance, consistent, and efficient estimator for normalized total correlation, in order to obtain a reliable, interpretable, and nonparametric measure for correlation over multivariate sets. For the discovery of the topk 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 lowregret optimization outcomes, while the algorithms are shown to be highly effective for both large and highdimensional data. Through a case study we confirm that our discovery framework identifies interesting and meaningful correlations.