Jakob Bach

Jakob Bach

Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example, users might be interested in finding alternative feature sets with similar prediction quality, offering different explanations of the data. In this article, we introduce alternative feature selection and formalize it as an optimization problem. In particular, we define alternatives via constraints and enable users to control the number and dissimilarity of alternatives. We consider sequential as well as simultaneous search for alternatives. Next, we discuss how to integrate conventional feature-selection methods as objectives. In particular, we describe solver-based search methods to tackle the optimization problem. Further, we analyze the complexity of this optimization problem and prove NP-hardness. Additionally, we show that a constant-factor approximation exists under certain conditions and propose corresponding heuristic search methods. Finally, we evaluate alternative feature selection in comprehensive experiments with 30 binary-classification datasets. We observe that alternative feature sets may indeed have high prediction quality, and we analyze factors influencing this outcome.

Jakob Bach

Subgroup-discovery methods allow users to obtain simple descriptions of interesting regions in a dataset. Using constraints in subgroup discovery can enhance interpretability even further. In this article, we focus on two types of constraints: First, we limit the number of features used in subgroup descriptions, making the latter sparse. Second, we propose the novel optimization problem of finding alternative subgroup descriptions, which cover a similar set of data objects as a given subgroup but use different features. We describe how to integrate both constraint types into heuristic subgroup-discovery methods. Further, we propose a novel Satisfiability Modulo Theories (SMT) formulation of subgroup discovery as a white-box optimization problem, which allows solver-based search for subgroups and is open to a variety of constraint types. Additionally, we prove that both constraint types lead to an NP-hard optimization problem. Finally, we employ 27 binary-classification datasets to compare algorithmic and solver-based search for unconstrained and constrained subgroup discovery. We observe that heuristic search methods often yield high-quality subgroups within a short runtime, also in scenarios with constraints.