Deep Trees for (Un)structured Data: Tractability, Performance, and Interpretability

Decision Trees have remained a popular machine learning method for tabular datasets, mainly due to their interpretability. However, they lack the expressiveness needed to handle highly nonlinear or unstructured datasets. Motivated by recent advances in tree-based machine learning (ML) techniques and first-order optimization methods, we introduce Generalized Soft Trees (GSTs), which extend soft decision trees (STs) and are capable of processing images directly. We demonstrate their advantages with respect to tractability, performance, and interpretability. We develop a tractable approach to growing GSTs, given by the DeepTree algorithm, which, in addition to new regularization terms, produces high-quality models with far fewer nodes and greater interpretability than traditional soft trees. We test the performance of our GSTs on benchmark tabular and image datasets, including MIMIC-IV, MNIST, Fashion MNIST, CIFAR-10 and Celeb-A. We show that our approach outperforms other popular tree methods (CART, Random Forests, XGBoost) in almost all of the datasets, with Convolutional Trees having a significant edge in the hardest CIFAR-10 and Fashion MNIST datasets. Finally, we explore the interpretability of our GSTs and find that even the most complex GSTs are considerably more interpretable than deep neural networks. Overall, our approach of Generalized Soft Trees provides a tractable method that is high-performing on (un)structured datasets and preserves interpretability more than traditional deep learning methods.

Binary Classification: Is Boosting stronger than Bagging?

Random Forests have been one of the most popular bagging methods in the past few decades, especially due to their success at handling tabular datasets. They have been extensively studied and compared to boosting models, like XGBoost, which are generally considered more performant. Random Forests adopt several simplistic assumptions, such that all samples and all trees that form the forest are equally important for building the final model. We introduce Enhanced Random Forests, an extension of vanilla Random Forests with extra functionalities and adaptive sample and model weighting. We develop an iterative algorithm for adapting the training sample weights, by favoring the hardest examples, and an approach for finding personalized tree weighting schemes for each new sample. Our method significantly improves upon regular Random Forests across 15 different binary classification datasets and considerably outperforms other tree methods, including XGBoost, when run with default hyperparameters, which indicates the robustness of our approach across datasets, without the need for extensive hyperparameter tuning. Our tree-weighting methodology results in enhanced or comparable performance to the uniformly weighted ensemble, and is, more importantly, leveraged to define importance scores for trees based on their contributions to classifying each new sample. This enables us to only focus on a small number of trees as the main models that define the outcome of a new sample and, thus, to partially recover interpretability, which is critically missing from both bagging and boosting methods. In binary classification problems, the proposed extensions and the corresponding results suggest the equivalence of bagging and boosting methods in performance, and the edge of bagging in interpretability by leveraging a few learners of the ensemble, which is not an option in the less explainable boosting methods.

Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMM

We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important generalization of the Matrix Completion problem, a central problem in Statistics, Operations Research and Machine Learning, that arises in applications such as recommendation systems, signal processing, system identification and image denoising. We formalize this problem as an optimization problem with an objective that balances the strength of the fit of the reconstruction to the observed entries with the ability of the reconstruction to be predictive of the side information. We derive a mixed-projection reformulation of the resulting optimization problem and present a strong semidefinite cone relaxation. We design an efficient, scalable alternating direction method of multipliers algorithm that produces high quality feasible solutions to the problem of interest. Our numerical results demonstrate that in the small rank regime ($k \leq 15$), our algorithm outputs solutions that achieve on average $79\%$ lower objective value and $90.1\%$ lower $\ell_2$ reconstruction error than the solutions returned by the experiment-wise best performing benchmark method. The runtime of our algorithm is competitive with and often superior to that of the benchmark methods. Our algorithm is able to solve problems with $n = 10000$ rows and $m = 10000$ columns in less than a minute.

Policy Trees for Prediction: Interpretable and Adaptive Model Selection for Machine Learning

As a multitude of capable machine learning (ML) models become widely available in forms such as open-source software and public APIs, central questions remain regarding their use in real-world applications, especially in high-stakes decision-making. Is there always one best model that should be used? When are the models likely to be error-prone? Should a black-box or interpretable model be used? In this work, we develop a prescriptive methodology to address these key questions, introducing a tree-based approach, Optimal Predictive-Policy Trees (OP2T), that yields interpretable policies for adaptively selecting a predictive model or ensemble, along with a parameterized option to reject making a prediction. We base our methods on learning globally optimized prescriptive trees. Our approach enables interpretable and adaptive model selection and rejection while only assuming access to model outputs. By learning policies over different feature spaces, including the model outputs, our approach works with both structured and unstructured datasets. We evaluate our approach on real-world datasets, including regression and classification tasks with both structured and unstructured data. We demonstrate that our approach provides both strong performance against baseline methods while yielding insights that help answer critical questions about which models to use, and when.

Catastrophe Insurance: An Adaptive Robust Optimization Approach

The escalating frequency and severity of natural disasters, exacerbated by climate change, underscore the critical role of insurance in facilitating recovery and promoting investments in risk reduction. This work introduces a novel Adaptive Robust Optimization (ARO) framework tailored for the calculation of catastrophe insurance premiums, with a case study applied to the United States National Flood Insurance Program (NFIP). To the best of our knowledge, it is the first time an ARO approach has been applied to for disaster insurance pricing. Our methodology is designed to protect against both historical and emerging risks, the latter predicted by machine learning models, thus directly incorporating amplified risks induced by climate change. Using the US flood insurance data as a case study, optimization models demonstrate effectiveness in covering losses and produce surpluses, with a smooth balance transition through parameter fine-tuning. Among tested optimization models, results show ARO models with conservative parameter values achieving low number of insolvent states with the least insurance premium charged. Overall, optimization frameworks offer versatility and generalizability, making it adaptable to a variety of natural disaster scenarios, such as wildfires, droughts, etc. This work not only advances the field of insurance premium modeling but also serves as a vital tool for policymakers and stakeholders in building resilience to the growing risks of natural catastrophes.

M3H: Multimodal Multitask Machine Learning for Healthcare

Recent breakthroughs in AI are poised to fundamentally enhance our study and understanding of healthcare. The development of an integrated many-to-many framework that leverages multiple data modality inputs for the analytical modeling of multiple medical tasks, is critical for a unified understanding of modern medicine. In this work, we introduce M3H, an explainable Multimodal Multitask Machine Learning for Healthcare framework that consolidates learning from diverse multimodal inputs across a broad spectrum of medical task categories and machine learning problem classes. The modular design of the framework ensures its generalizable data processing, task definition, and rapid model prototyping, applicable to both clinical and operational healthcare settings. We evaluate the M3H framework by validating models trained from four modalities (tabular, time-series, language, and vision) on 41 medical tasks across 4 machine learning problem classes. Our results demonstrate that M3H consistently produces multitask models that outperform canonical single-task models (by 1.1- 37.2%) across 37 disease diagnoses from 16 medical departments, three hospital operation forecasts, and one patient phenotyping task: spanning ML problem classes of supervised binary classification, multiclass classification, regression, and clustering. Additionally, the framework introduces a novel attention mechanism to balance self-exploitation (focus on learning source task), and cross-exploration (encourage learning from other tasks). Furthermore, M3H provides explainability insights on how joint learning of additional tasks impacts the learning of source task using a proposed TIM score, shedding light into the dynamics of task interdependencies. Its adaptable architecture facilitates the customization and integration, establishing it as a robust and scalable candidate solution for future AI-driven healthcare systems.

Towards Stable Machine Learning Model Retraining via Slowly Varying Sequences

Retraining machine learning models remains an important task for real-world machine learning model deployment. Existing methods focus largely on greedy approaches to find the best-performing model without considering the stability of trained model structures across different retraining evolutions. In this study, we develop a mixed integer optimization algorithm that holistically considers the problem of retraining machine learning models across different data batch updates. Our method focuses on retaining consistent analytical insights - which is important to model interpretability, ease of implementation, and fostering trust with users - by using custom-defined distance metrics that can be directly incorporated into the optimization problem. Importantly, our method shows stronger stability than greedily trained models with a small, controllable sacrifice in model performance in a real-world production case study. Finally, important analytical insights, as demonstrated using SHAP feature importance, are shown to be consistent across retraining iterations.

Adaptive Optimization for Prediction with Missing Data

When training predictive models on data with missing entries, the most widely used and versatile approach is a pipeline technique where we first impute missing entries and then compute predictions. In this paper, we view prediction with missing data as a two-stage adaptive optimization problem and propose a new class of models, adaptive linear regression models, where the regression coefficients adapt to the set of observed features. We show that some adaptive linear regression models are equivalent to learning an imputation rule and a downstream linear regression model simultaneously instead of sequentially. We leverage this joint-impute-then-regress interpretation to generalize our framework to non-linear models. In settings where data is strongly not missing at random, our methods achieve a 2-10% improvement in out-of-sample accuracy.

Universal Neurons in GPT2 Language Models

A basic question within the emerging field of mechanistic interpretability is the degree to which neural networks learn the same underlying mechanisms. In other words, are neural mechanisms universal across different models? In this work, we study the universality of individual neurons across GPT2 models trained from different initial random seeds, motivated by the hypothesis that universal neurons are likely to be interpretable. In particular, we compute pairwise correlations of neuron activations over 100 million tokens for every neuron pair across five different seeds and find that 1-5\% of neurons are universal, that is, pairs of neurons which consistently activate on the same inputs. We then study these universal neurons in detail, finding that they usually have clear interpretations and taxonomize them into a small number of neuron families. We conclude by studying patterns in neuron weights to establish several universal functional roles of neurons in simple circuits: deactivating attention heads, changing the entropy of the next token distribution, and predicting the next token to (not) be within a particular set.

Robust Regression over Averaged Uncertainty

We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least-squared regression problem. We show that this formulation surprisingly recovers ridge regression and establishes the missing link between robust optimization and the mean squared error approaches for existing regression problems. We first prove the equivalence for four uncertainty sets: ellipsoidal, box, diamond, and budget, and provide closed-form formulations of the penalty term as a function of the sample size, feature size, as well as perturbation protection strength. We then show in synthetic datasets with different levels of perturbations, a consistent improvement of the averaged formulation over the existing worst-case formulation in out-of-sample performance. Importantly, as the perturbation level increases, the improvement increases, confirming our method's advantage in high-noise environments. We report similar improvements in the out-of-sample datasets in real-world regression problems obtained from UCI datasets.