We present an approach for mining differentially private redescriptions. Applying differential privacy to pattern mining approaches such as redescription mining is less straightforward than with numerical methods, in part because local patterns are more susceptible to the kind of noise inherent to differential privacy, and in part because the typically combinatorial algorithms require many operations and become computationally unaffordable when overloaded with privacy preserving procedures. Our solution, and the two algorithms we provide, address both the computational bottlenecks as well as the issues with noise. They might also provide inspiration for other differentially private pattern mining algorithms. Extensive experiments on real-world data validate the usefulness of our algorithms.
Pattern condensed representations are an important concept in inductive databases. They aim at summarizing the information contained in a set of patterns. This paper is not an exhaustive survey of the 20 years of proposals on condensed representations but rather a general overview. We propose a simple formalism modeling a large part of the exact and approximate condensed representations. Through this modeling, we show that many of the condensed representations are based on the same foundations, we highlight the compression and generalization sides of the condensed representations and we describe several trends. Finally, we discuss the current extents of the work on condensed representations within pattern mining.
While most rule learning methods focus on categorical targets for tasks including classification and subgroup discovery, rule learning for numeric targets are under-studied, especially using probabilistic rules: the only existing probabilistic rule list method for numeric targets, named SSD ++ , is based on Gaussian parametric models. To extend this method, we adopt an adaptive histogram model to estimate the probability distribution of the target variable. We formalize the rule list learning as a model selection problem, which we tackle with the minimum description length principle. We demonstrate that our method produces rule lists with better predictive performance than SSD ++ .
A core idea of inductive databases was the creation of systems that can be queried declaratively for patterns and models. A natural question during the development of inductive databases was how such systems would work for one of the most popular models in machine learning, the decision tree. In our first work on this topic, in 2007, we introduced DL8, an algorithm that showed how to calculate optimal decision trees from itemset patterns. Driven by an interest in imposing additional requirements on predictive models, such requirements of interpretability and fairness, in recent years the calculation of optimal decision trees has gained a lot of interest again. In this context, we proposed an extension of DL8, DL8.5, which obtained better performance than competitor systems. This abstract describes how research on inductive databases led to these recent systems and provides an overview of these systems.
At the occasion of the 20th anniversary of the KDID workshop, I share the tale of how the inductive databases concept has inspired our work on MiningZinc, a constraint-based language for pattern mining; and how even today it influences how we are building a next-generation modeling library for constraint solving.
