Intro; Foreword; Preface; Acknowledgements; Contents; Contributors; Part I Notions and Concepts on Explainability and Interpretability; Considerations for Evaluation and Generalization in Interpretable Machine Learning; 1 Introduction; 2 Defining Interpretability; 3 Defining the Interpretability Need; 4 Evaluation; 5 Considerations for Generalization; 6 Conclusion: Recommendations for Researchers; References; Explanation Methods in Deep Learning: Users, Values, Concerns and Challenges; 1 Introduction; 1.1 The Components of Explainability; 1.2 Users and Laws; 1.3 Explanation and DNNs

2 Users and Their Concerns2.1 Case Study: Autonomous Driving; 3 Laws and Regulations; 4 Explanation; 5 Explanation Methods; 5.1 Desirable Properties of Explainers; 5.2 A Taxonomy for Explanation Methods; 5.2.1 Rule-Extraction Methods; 5.2.2 Attribution Methods; 5.2.3 Intrinsic Methods; 6 Addressing General Concerns; 7 Discussion; References; Part II Explainability and Interpretability in Machine Learning; Learning Functional Causal Models with Generative NeuralNetworks; 1 Introduction; 2 Problem Setting; 2.1 Notations; 2.2 Assumptions and Properties; 3 State of the Art; 3.1 Learning the CPDAG

3.1.1 Constraint-Based Methods3.1.2 Score-Based Methods; 3.1.3 Hybrid Algorithms; 3.2 Exploiting Asymmetry Between Cause and Effect; 3.2.1 The Intuition; 3.2.2 Restriction on the Class of Causal Mechanisms Considered; 3.2.3 Pairwise Methods; 3.3 Discussion; 4 Causal Generative Neural Networks; 4.1 Modeling Continuous FCMs with Generative Neural Networks; 4.1.1 Generative Model and Interventions; 4.2 Model Evaluation; 4.2.1 Scoring Metric; 4.2.2 Representational Power of CGNN; 4.3 Model Optimization; 4.3.1 Parametric (Weight) Optimization; 4.3.2 Non-parametric (Structure) Optimization

4.3.3 Identifiability of CGNN up to Markov Equivalence Classes5 Experiments; 5.1 Experimental Setting; 5.2 Learning Bivariate Causal Structures; 5.2.1 Benchmarks; 5.2.2 Baseline Approaches; 5.2.3 Hyper-Parameter Selection; 5.2.4 Empirical Results; 5.3 Identifying v-structures; 5.4 Multivariate Causal Modeling Under Causal Sufficiency Assumption; 5.4.1 Results on Artificial Graphs with Additive and Multiplicative Noises; 5.4.2 Result on Biological Data; 5.4.3 Results on Biological Real-World Data; 6 Towards Predicting Confounding Effects; 6.1 Principle; 6.2 Experimental Validation

6.2.1 Benchmarks6.2.2 Baselines; 6.2.3 Results; 7 Discussion and Perspectives; Appendix; The Maximum Mean Discrepancy (MMD) Statistic; Proofs; Table of Scores for the Experiments on Cause-Effect Pairs; Table of Scores for the Experiments on Graphs; References; Learning Interpretable Rules for Multi-Label Classification; 1 Introduction; 2 Multi-Label Classification; 2.1 Problem Definition; 2.2 Dependencies in Multi-Label Classification; 2.3 Evaluation of Multi-Label Predictions; 2.3.1 Bipartition Evaluation Functions; 2.3.2 Multi-Label Evaluation Functions; 2.3.3 Aggregation and Averaging