Efficient Data Representation by Selecting Prototypes with Importance Weights Prototypical examples that best summarize and compactly represent an underlying complex data distribution, communicate meaningful insights to humans in domains where simple explanations are hard to extract. In this paper, we present algorithms with strong theoretical guarantees to mine these data sets and select prototypes, a.k.a. representatives that optimally describes them. Our work notably generalizes the recent work by Kim et al. (2016) where in addition to selecting prototypes, we also associate nonnegative weights which are indicative of their importance. This extension provides a single coherent framework under which both prototypes and criticisms (i.e. outliers) can be found. Furthermore, our framework works for any symmetric positive definite kernel thus addressing one of the key open questions laid out in Kim et al. (2016). By establishing that our objective function enjoys a key property of that of weak submodularity, we present a fast ProtoDash algorithm and also derive approximation guarantees for the same. We demonstrate the efficacy of our method on diverse domains such as retail, digit recognition (MNIST) and on publicly available 40 health questionnaires obtained from the Center for Disease Control (CDC) website maintained by the US Dept. of Health. We validate the results quantitatively as well as qualitatively based on expert feedback and recently published scientific studies on public health, thus showcasing the power of our technique in providing actionability (for retail), utility (for MNIST), and insight (on CDC datasets), which arguably are the hallmarks of an effective interpretable machine learning method.

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.