Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Post Hoc Explanation 1.1 Post Hoc Explanation 1.2 The Disagreement Problem 1.2 The Disagreement Problem 1.3 Encouraging Explanation Consensus 1.3 Encouraging Explanation Consensus Related Work


Pear: Post HOC Explainer Agreement Regularizer


The Efficacy of Consensus Training
4.1 Agreement Metrics
4.2 Improving Consensus Metrics
4.3 Consistency At What Cost?
4.4 Are the Explanations Still Valuable?
4.5 Consensus and Linearity
4.6 Two Loss Terms


Discussion
5.1 Future Work
5.2 Conclusion, Acknowledgements, and References Related Work Related Work Related Work Pear: Post HOC Explainer Agreement Regularizer Pear: Post HOC Explainer Agreement Regularizer Pear: Post HOC Explainer Agreement Regularizer The Efficacy of Consensus Training
4.1 Agreement Metrics
4.2 Improving Consensus Metrics
4.3 Consistency At What Cost?
4.4 Are the Explanations Still Valuable?
4.5 Consensus and Linearity
4.6 Two Loss Terms The Efficacy of Consensus Training The Efficacy of Consensus Training 4.1 Agreement Metrics 4.1 Agreement Metrics 4.2 Improving Consensus Metrics 4.2 Improving Consensus Metrics 4.3 Consistency At What Cost? 4.3 Consistency At What Cost? 4.4 Are the Explanations Still Valuable? 4.4 Are the Explanations Still Valuable? 4.5 Consensus and Linearity 4.5 Consensus and Linearity 4.6 Two Loss Terms 4.6 Two Loss Terms Discussion
5.1 Future Work
5.2 Conclusion, Acknowledgements, and References Discussion Discussion 5.1 Future Work 5.1 Future Work 5.2 Conclusion, Acknowledgements, and References 5.2 Conclusion, Acknowledgements, and References Appendix Appendix A APPENDIX A.1 Datasets In our experiments we use tabular datasets originally from OpenML and compiled into a set of benchmark datasets from the Inria-Soda team on HuggingFace [11]. We provide some details about each dataset: Bank Marketing This is a binary classification dataset with six input features and is approximately class balanced. We train on 7,933 training samples and test on the remaining 2,645 samples. Bank Marketing California Housing This is a binary classification dataset with seven input features and is approximately class balanced. We train on 15,475 training samples and test on the remaining 5,159 samples. California Housing Electricity This is a binary classification dataset with seven input features and is approximately class balanced. We train on 28,855 training samples and test on the remaining 9,619 samples. Electricity A.2 Hyperparameters Many of our hyperparameters are constant across all of our experiments. For example, all MLPs are trained with a batch size of 64, and initial learning rate of 0.0005. Also, all the MLPs we study are 3 hidden layers of 100 neurons each. We always use the AdamW optimizer [19]. The number of epochs varies from case to case. For all three datasets, we train for 30 epochs when 𝜆 ∈ {0.0, 0.25} and 50 epochs otherwise. When training linear models, we use 10 epochs and an initial learning rate of 0.1. A.3 Disagreement Metrics We define each of the six agreement metrics used in our work here. The first four metrics depend on the top-𝑘 most important features in each explanation. Let 𝑡𝑜𝑝_𝑓 𝑒𝑎𝑡𝑢𝑟𝑒𝑠(𝐸, 𝑘) represent the top-𝑘 most important features in an explanation 𝐸, let 𝑟𝑎𝑛𝑘 (𝐸, 𝑠) be the importance rank of the feature 𝑠 within explanation 𝐸, and let 𝑠𝑖𝑔𝑛(𝐸, 𝑠) be the sign (positive, negative, or zero) of the importance score of feature 𝑠 in explanation 𝐸. The next two agreement metrics depend on all features within each explanation, not just the top-𝑘. Let 𝑅 be a function that computes the ranking of features within an explanation by importance. (Note: Krishna et al. [15] specify in their paper that 𝐹 is to be a set of features specified by an end user, but in our experiments we use all features with this metric). A.4 Junk Feature Experiment Results When we add random features for the experiment in Section 4.4, we double the number of features. We do this to check whether our consensus loss damages explanation quality by placing irrelevant features in the top-𝐾 more often than models trained naturally. In Table 1, we report the percentage of the time that each explainer included one of the random features in the top-5 most important features. We observe that across the board, we do not see a systematic increase of these percentages between 𝜆 = 0.0 (a baseline MLP without our consensus loss) and 𝜆 = 0.5 (an MLP trained with our consensus loss) A.5 More Disagreement Matrices A.6 Extended Results A.7 Additional Plots Authors:
(1) Avi Schwarzschild, University of Maryland, College Park, Maryland, USA and Work completed while working at Arthur (avi1umd.edu);
(2) Max Cembalest, Arthur, New York City, New York, USA;
(3) Karthik Rao, Arthur, New York City, New York, USA;
(4) Keegan Hines, Arthur, New York City, New York, USA;
(5) John Dickerson†, Arthur, New York City, New York, USA (john@arthur.ai). Authors: Authors: (1) Avi Schwarzschild, University of Maryland, College Park, Maryland, USA and Work completed while working at Arthur (avi1umd.edu); (2) Max Cembalest, Arthur, New York City, New York, USA; (3) Karthik Rao, Arthur, New York City, New York, USA; (4) Keegan Hines, Arthur, New York City, New York, USA; (5) John Dickerson†, Arthur, New York City, New York, USA (john@arthur.ai). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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