Estimating mutual information (MI) between two continuous random variables X and Y allows to capture non-linear dependencies between them, non-parametrically. As such, MI estimation lies at the core of many data science applications. Yet, robustly estimating MI for high-dimensional X and Y is still an open research question. In this paper, we formulate this problem through the lens of manifold learning. That is, we leverage the common assumption that the information of X and Y is captured by a low-dimensional manifold embedded in the observed high-dimensional space and transfer it to MI estimation. As an extension to state-of-the-art kNN estimators, we propose to determine the k-nearest neighbors via geodesic distances on this manifold rather than from the ambient space, which allows us to estimate MI even in the high-dimensional setting. An empirical evaluation of our method, G-KSG, against the state-of-the-art shows that it yields good estimations of MI in classical benchmark and manifold tasks, even for high dimensional datasets, which none of the existing methods can provide.

Pattern set mining has been successful in discovering small sets of highly informative and useful patterns from data. To find good models, existing methods heuristically explore the twice-exponential search space over all possible pattern sets in a combinatorial way, by which they are limited to data over at most hundreds of features, as well as likely to get stuck in local minima. Here, we propose a gradient based optimization approach that allows us to efficiently discover high-quality pattern sets from data of millions of rows and hundreds of thousands of features.

Pattern mining is one of the core topics of data mining. We consider the problem of mining a succinct set of patterns that together explain the data in terms of mutual exclusivity and co-occurence. That is, we extend the traditional pattern languages beyond conjunctions, enabling us to capture more complex relationships, such as replacable sub-components or antagonists in biological pathways.