BIR: A Method for Selecting the Best Interpretable Multidimensional Scaling Rotation using External Variables

Interpreting nonlinear dimensionality reduction models using external features (or external variables) is crucial in many fields, such as psychology and ecology. Multidimensional scaling (MDS) is one of the most frequently used dimensionality reduction techniques in these fields. However, the rotation invariance of the MDS objective function may make interpretation of the resulting embedding difficult. This paper analyzes how the rotation of MDS embeddings affects sparse regression models used to interpret them and proposes a method, called the Best Interpretable Rotation (BIR) method, which selects the best MDS rotation for interpreting embeddings using external information

ML + FV = ♡\heartsuit? A Survey on the Application of Machine Learning to Formal Verification

Formal Verification (FV) and Machine Learning (ML) can seem incompatible due to their opposite mathematical foundations and their use in real-life problems: FV mostly relies on discrete mathematics and aims at ensuring correctness; ML often relies on probabilistic models and consists of learning patterns from training data. In this paper, we postulate that they are complementary in practice, and explore how ML helps FV in its classical approaches: static analysis, model-checking, theorem-proving, and SAT solving. We draw a landscape of the current practice and catalog some of the most prominent uses of ML inside FV tools, thus offering a new perspective on FV techniques that can help researchers and practitioners to better locate the possible synergies. We discuss lessons learned from our work, point to possible improvements and offer visions for the future of the domain in the light of the science of software and systems modeling.Comment: 13 pages, no figures, 3 table