Abstract:
Motivated by the potential of Artificial Intelligence (AI) in high-cost and safety-critical
applications, and recently also by the increasing presence of AI in our everyday lives, Trustworthy AI has grown in prominence as a broad area of research encompassing topics such as interpretability, robustness, verifiable safety, fairness, privacy, accountability, and more. This has created a tension between simple, transparent models with inherent trust-related benefits and complex, black-box models with unparalleled performance on many tasks. Towards closing this gap, we propose and study an uncertain interpretation of numerical data and apply it to tree-based models, resulting in a novel kind of fuzzy decision tree called Kernel Density Decision Trees (KDDTs) with improved performance, enhanced trustworthy qualities, and increased utility, enabling the use of these trees in broader applications. We group the contributions of this thesis into three pillars.

The first pillar is robustness and verification. The uncertain interpretation, by accounting for uncertainty in the data, and more generally as a kind of regularization on the function represented by a model, can improve the model with respect to various notions of robustness. We demonstrate its ability to improve robustness to noisy features and noisy labels, both of which are common in real-world data. Next, we show how efficiently verifiable adversarial robustness is achievable through the theory of randomized smoothing. Finally, we discuss the related topic of verification and propose the first verification algorithm for fuzzy decision trees.

The second pillar is interpretability. While decision trees are widely considered to be interpretable, good performance from tree-based models is often limited to tabular data and demands both feature engineering, which increases design effort, and ensemble methods, which severely diminish interpretability compared to single-tree models. By leveraging the efficient fitting and differentiability of KDDTs, we propose a system of learning parameterized feature transformations for decision trees. By choosing interpretable feature classes and applying sparsity regularization,we can obtain compact single-tree models with competitive performance. We demonstrate application to tabular, time series, and simple image data.

The third pillar is pragmatic advancements. Semi-supervised Learning (SSL) is motivated by the expense of labeling and learns from a mix of labeled and unlabeled data. SSL for trees is generally limited to black-box wrapper methods, for which trees are not well-suited. We propose as an alternative a novel intrinsic SSL method based on our uncertain interpretation of data. Federated Learning (FL) is motivated by data sharing limitations and learns from distributed data by communicating models. We introduce a new FL algorithm based on function space regularization, which borrows concepts and methods from our formalism of uncertain interpretation. Unlike prior FL methods, it supports non-parametric models and has convergence guarantees under mild assumptions. Finally, we show how our FL algorithm also provides a simple utility for ensemble merging.

Thesis Committee Members:
Artur Dubrawski, Chair
Jeff Schneider
Tom Mitchell
Gilles Clermont, University of Pittsburgh

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