Explaining Groups of Points in Low-Dimensional Representations
A common workflow in data exploration is to learn a low-dimensional representation of the data, identify groups of points in that representation, and examine the differences between the groups to determine what they represent. We treat this workflow as an interpretable machine learning problem by leveraging the model that learned the low-dimensional representation to help identify the key differences between the groups. To solve this problem, we introduce a new type of explanation, a Global Counterfactual Explanation (GCE), and our algorithm, Transitive Global Translations (TGT), for computing GCEs. TGT identifies the differences between each pair of groups using compressed sensing but constrains those pairwise differences to be consistent among all of the groups. Empirically, we demonstrate that TGT is able to identify explanations that accurately explain the model while being relatively sparse, and that these explanations match real patterns in the data.
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We were able to reproduce their results using their code, yielding mostly similar results. TGT generally outperforms DBM, especially when explanations use few features. TGT is consistent in terms of the features to which it attributes cluster differences, across different sparsity levels. TGT matches real patterns in data. When extending the types of functions used for explanations, performance did not improve significantly, suggesting translations make for adequate explanations. However, the scaling extension shows promising performance on the modified synthetic data to recover the original signal.
The results presented in [1] were reproducible, both by using the provided code and our own implementation. Our additional experiments have highlighted several limitations of the explanatory algorithm in question: the algorithm severely relies on the shape and variance of the clusters present in the data (and, if applicable, the method used to label these clusters), and highly non-linear dimensionality reduction algorithms perform worse in terms of explainability.
