Interpretable Machine Learning based on Functional ANOVA Framework: Algorithms and Comparisons

In the early days of machine learning (ML), the emphasis was on developing complex algorithms to achieve best predictive performance. To understand and explain the model results, one had to rely on post hoc explainability techniques, which are known to have limitations. Recently, with the recognition that interpretability is just as important, researchers are compromising on small increases in predictive performance to develop algorithms that are inherently interpretable. While doing so, the ML community has rediscovered the use of low-order functional ANOVA (fANOVA) models that have been known in the statistical literature for some time. This paper starts with a description of challenges with post hoc explainability and reviews the fANOVA framework with a focus on main effects and second-order interactions. This is followed by an overview of two recently developed techniques: Explainable Boosting Machines or EBM (Lou et al., 2013) and GAMI-Net (Yang et al., 2021b). The paper proposes a new algorithm, called GAMI-Lin-T, that also uses trees like EBM, but it does linear fits instead of piecewise constants within the partitions. There are many other differences, including the development of a new interaction filtering algorithm. Finally, the paper uses simulated and real datasets to compare selected ML algorithms. The results show that GAMI-Lin-T and GAMI-Net have comparable performances, and both are generally better than EBM.

Enhancing Robustness of Gradient-Boosted Decision Trees through One-Hot Encoding and Regularization

Gradient-boosted decision trees (GBDT) are widely used and highly effective machine learning approach for tabular data modeling. However, their complex structure may lead to low robustness against small covariate perturbation in unseen data. In this study, we apply one-hot encoding to convert a GBDT model into a linear framework, through encoding of each tree leaf to one dummy variable. This allows for the use of linear regression techniques, plus a novel risk decomposition for assessing the robustness of a GBDT model against covariate perturbations. We propose to enhance the robustness of GBDT models by refitting their linear regression forms with $L_1$ or $L_2$ regularization. Theoretical results are obtained about the effect of regularization on the model performance and robustness. It is demonstrated through numerical experiments that the proposed regularization approach can enhance the robustness of the one-hot-encoded GBDT models.

PiML Toolbox for Interpretable Machine Learning Model Development and Validation

PiML (read $\pi$-ML, /`pai.`em.`el/) is an integrated and open-access Python toolbox for interpretable machine learning model development and model diagnostics. It is designed with machine learning workflows in both low-code and high-code modes, including data pipeline, model training, model interpretation and explanation, and model diagnostics and comparison. The toolbox supports a growing list of interpretable models (e.g. GAM, GAMI-Net, XGB2) with inherent local and/or global interpretability. It also supports model-agnostic explainability tools (e.g. PFI, PDP, LIME, SHAP) and a powerful suite of model-agnostic diagnostics (e.g. weakness, uncertainty, robustness, fairness). Integration of PiML models and tests to existing MLOps platforms for quality assurance are enabled by flexible high-code APIs. Furthermore, PiML toolbox comes with a comprehensive user guide and hands-on examples, including the applications for model development and validation in banking. The project is available at https://github.com/SelfExplainML/PiML-Toolbox.

Explaining Adverse Actions in Credit Decisions Using Shapley Decomposition

When a financial institution declines an application for credit, an adverse action (AA) is said to occur. The applicant is then entitled to an explanation for the negative decision. This paper focuses on credit decisions based on a predictive model for probability of default and proposes a methodology for AA explanation. The problem involves identifying the important predictors responsible for the negative decision and is straightforward when the underlying model is additive. However, it becomes non-trivial even for linear models with interactions. We consider models with low-order interactions and develop a simple and intuitive approach based on first principles. We then show how the methodology generalizes to the well-known Shapely decomposition and the recently proposed concept of Baseline Shapley (B-Shap). Unlike other Shapley techniques in the literature for local interpretability of machine learning results, B-Shap is computationally tractable since it involves just function evaluations. An illustrative case study is used to demonstrate the usefulness of the method. The paper also discusses situations with highly correlated predictors and desirable properties of fitted models in the credit-lending context, such as monotonicity and continuity.

Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verification

Although neural networks (NNs) with ReLU activation functions have found success in a wide range of applications, their adoption in risk-sensitive settings has been limited by the concerns on robustness and interpretability. Previous works to examine robustness and to improve interpretability partially exploited the piecewise linear function form of ReLU NNs. In this paper, we explore the unique topological structure that ReLU NNs create in the input space, identifying the adjacency among the partitioned local polytopes and developing a traversing algorithm based on this adjacency. Our polytope traversing algorithm can be adapted to verify a wide range of network properties related to robustness and interpretability, providing an unified approach to examine the network behavior. As the traversing algorithm explicitly visits all local polytopes, it returns a clear and full picture of the network behavior within the traversed region. The time and space complexity of the traversing algorithm is determined by the number of a ReLU NN's partitioning hyperplanes passing through the traversing region.

Designing Inherently Interpretable Machine Learning Models

Interpretable machine learning (IML) becomes increasingly important in highly regulated industry sectors related to the health and safety or fundamental rights of human beings. In general, the inherently IML models should be adopted because of their transparency and explainability, while black-box models with model-agnostic explainability can be more difficult to defend under regulatory scrutiny. For assessing inherent interpretability of a machine learning model, we propose a qualitative template based on feature effects and model architecture constraints. It provides the design principles for high-performance IML model development, with examples given by reviewing our recent works on ExNN, GAMI-Net, SIMTree, and the Aletheia toolkit for local linear interpretability of deep ReLU networks. We further demonstrate how to design an interpretable ReLU DNN model with evaluation of conceptual soundness for a real case study of predicting credit default in home lending. We hope that this work will provide a practical guide of developing inherently IML models in high risk applications in banking industry, as well as other sectors.

Supervised Linear Dimension-Reduction Methods: Review, Extensions, and Comparisons

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input variable that contains maximal variation and preserves as much information as possible. PCA has also been used in prediction models where the original, high-dimensional space of predictors is reduced to a smaller, more manageable, set before conducting regression analysis. However, this approach does not incorporate information in the response during the dimension-reduction stage and hence can have poor predictive performance. To address this concern, several supervised linear dimension-reduction techniques have been proposed in the literature. This paper reviews selected techniques, extends some of them, and compares their performance through simulations. Two of these techniques, partial least squares (PLS) and least-squares PCA (LSPCA), consistently outperform the others in this study.

Self-interpretable Convolutional Neural Networks for Text Classification

Deep learning models for natural language processing (NLP) are inherently complex and often viewed as black box in nature. This paper develops an approach for interpreting convolutional neural networks for text classification problems by exploiting the local-linear models inherent in ReLU-DNNs. The CNN model combines the word embedding through convolutional layers, filters them using max-pooling, and optimizes using a ReLU-DNN for classification. To get an overall self-interpretable model, the system of local linear models from the ReLU DNN are mapped back through the max-pool filter to the appropriate n-grams. Our results on experimental datasets demonstrate that our proposed technique produce parsimonious models that are self-interpretable and have comparable performance with respect to a more complex CNN model. We also study the impact of the complexity of the convolutional layers and the classification layers on the model performance.