We study computational aspects of algorithmic replicability, a notion of stability introduced by Impagliazzo, Lei, Pitassi, and Sorrell [2022]. Motivated by a recent line of work that established strong statistical connections between replicability and other notions of learnability such as online learning, private learning, and SQ learning, we aim to understand better the computational connections between replicability and these learning paradigms. Our first result shows that there is a concept class that is efficiently replicably PAC learnable, but, under standard cryptographic assumptions, no efficient online learner exists for this class. Subsequently, we design an efficient replicable learner for PAC learning parities when the marginal distribution is far from uniform, making progress on a question posed by Impagliazzo et al. [2022]. To obtain this result, we design a replicable lifting framework inspired by Blanc, Lange, Malik, and Tan [2023] that transforms in a black-box manner efficient replicable PAC learners under the uniform marginal distribution over the Boolean hypercube to replicable PAC learners under any marginal distribution, with sample and time complexity that depends on a certain measure of the complexity of the distribution. Finally, we show that any pure DP learner can be transformed to a replicable one in time polynomial in the accuracy, confidence parameters and exponential in the representation dimension of the underlying hypothesis class.

We consider the task of retraining machine learning (ML) models when new batches of data become available. Existing methods focus largely on greedy approaches to find the best-performing model for each batch, without considering the stability of the model's structure across retraining iterations. In this study, we propose a methodology for finding sequences of ML models that are stable across retraining iterations. We develop a mixed-integer optimization formulation that is guaranteed to recover Pareto optimal models (in terms of the predictive power-stability trade-off) and an efficient polynomial-time algorithm that performs well in practice. We focus 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. Our method shows stronger stability than greedily trained models with a small, controllable sacrifice in predictive power, as evidenced through a real-world case study in a major hospital system in Connecticut.

Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees applied to well-behaved, differentiable functions, and determine the relationship between node parameters and the local gradient of the function being approximated. We find a simple estimate of the gradient which can be efficiently computed using quantities exposed by popular tree learning libraries. This allows the tools developed in the context of differentiable algorithms, like neural nets and Gaussian processes, to be deployed to tree-based models. To demonstrate this, we study measures of model sensitivity defined in terms of integrals of gradients and demonstrate how to compute them for regression trees using the proposed gradient estimates. Quantitative and qualitative numerical experiments reveal the capability of gradients estimated by regression trees to improve predictive analysis, solve tasks in uncertainty quantification, and provide interpretation of model behavior.

We present Collaborative Trees, a novel tree model designed for regression prediction, along with its bagging version, which aims to analyze complex statistical associations between features and uncover potential patterns inherent in the data. We decompose the mean decrease in impurity from the proposed tree model to analyze the additive and interaction effects of features on the response variable. Additionally, we introduce network diagrams to visually depict how each feature contributes additively to the response and how pairs of features contribute interaction effects. Through a detailed demonstration using an embryo growth dataset, we illustrate how the new statistical tools aid data analysis, both visually and numerically. Moreover, we delve into critical aspects of tree modeling, such as prediction performance, inference stability, and bias in feature importance measures, leveraging real datasets and simulation experiments for comprehensive discussions. On the theory side, we show that Collaborative Trees, built upon a ``sum of trees'' approach with our own innovative tree model regularization, exhibit characteristics akin to matching pursuit, under the assumption of high-dimensional independent binary input features (or one-hot feature groups). This newfound link sheds light on the superior capability of our tree model in estimating additive effects of features, a crucial factor for accurate interaction effect estimation.

This paper introduces the concept of Hyper-Trees and offers a new direction in applying tree-based models to time series data. Unlike conventional applications of decision trees that forecast time series directly, Hyper-Trees are designed to learn the parameters of a target time series model. Our framework leverages the gradient-based nature of boosted trees, which allows us to extend the concept of Hyper-Networks to Hyper-Trees and to induce a time-series inductive bias to tree models. By relating the parameters of a target time series model to features, Hyper-Trees address the issue of parameter non-stationarity and enable tree-based forecasts to extend beyond their training range. With our research, we aim to explore the effectiveness of Hyper-Trees across various forecasting scenarios and to extend the application of gradient boosted decision trees outside their conventional use in time series modeling.

Society's capacity for algorithmic problem-solving has never been greater. Artificial Intelligence is now applied across more domains than ever, a consequence of powerful abstractions, abundant data, and accessible software. As capabilities have expanded, so have risks, with models often deployed without fully understanding their potential impacts. Interpretable and interactive machine learning aims to make complex models more transparent and controllable, enhancing user agency. This review synthesizes key principles from the growing literature in this field. We first introduce precise vocabulary for discussing interpretability, like the distinction between glass box and explainable algorithms. We then explore connections to classical statistical and design principles, like parsimony and the gulfs of interaction. Basic explainability techniques -- including learned embeddings, integrated gradients, and concept bottlenecks -- are illustrated with a simple case study. We also review criteria for objectively evaluating interpretability approaches. Throughout, we underscore the importance of considering audience goals when designing interactive algorithmic systems. Finally, we outline open challenges and discuss the potential role of data science in addressing them. Code to reproduce all examples can be found at https://go.wisc.edu/3k1ewe.

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that provides such guarantees. By introducing a novel change-of-measure inequality, we are able to tightly bound the model loss in terms of the deviation of the treatment propensities over the population, which we show can be empirically limited. Our theory is fully rigorous and holds even in the face of hidden confounding and violations of positivity. We demonstrate our bounds on semi-synthetic and real data, showcasing their remarkable tightness and practical utility.

A decision tree looks like a simple computational graph without cycles, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision trees in the language of computational graph. We explicitly parameterize the test phase, traversal phase and prediction phase of decision trees based on the bitvectors of non-terminal nodes. As shown later, the decision tree is a shallow binary network in some sense. Especially, we introduce the bitvector matrix to implement the tree traversal in numerical approach, where the core is to convert the logical `AND' operation to arithmetic operations. And we apply this numerical representation to extend and unify diverse decision trees in concept.

Machine Learning (ML) algorithms are generally designed for scenarios in which all data is stored in one data center, where the training is performed. However, in many applications, e.g., in the healthcare domain, the training data is distributed among several entities, e.g., different hospitals or patients' mobile devices/sensors. At the same time, transferring the data to a central location for learning is certainly not an option, due to privacy concerns and legal issues, and in certain cases, because of the communication and computation overheads. Federated Learning (FL) is the state-of-the-art collaborative ML approach for training an ML model across multiple parties holding local data samples, without sharing them. However, enabling learning from distributed data over such edge Internet of Things (IoT) systems (e.g., mobile-health and wearable technologies, involving sensitive personal/medical data) in a privacy-preserving fashion presents a major challenge mainly due to their stringent resource constraints, i.e., limited computing capacity, communication bandwidth, memory storage, and battery lifetime. In this paper, we propose a privacy-preserving edge FL framework for resource-constrained mobile-health and wearable technologies over the IoT infrastructure. We evaluate our proposed framework extensively and provide the implementation of our technique on Amazon's AWS cloud platform based on the seizure detection application in epilepsy monitoring using wearable technologies.

This work investigates how tutoring discourse interacts with students' proximal knowledge to explain and predict students' learning outcomes. Our work is conducted in the context of high-dosage human tutoring where 9th-grade students (N = 1080) attended small group tutorials and individually practiced problems on an Intelligent Tutoring System (ITS). We analyzed whether tutors' talk moves and students' performance on the ITS predicted scores on math learning assessments. We trained Random Forest Classifiers (RFCs) to distinguish high and low assessment scores based on tutor talk moves, student's ITS performance metrics, and their combination. A decision tree was extracted from each RFC to yield an interpretable model. We found AUCs of 0.63 for talk moves, 0.66 for ITS, and 0.77 for their combination, suggesting interactivity among the two feature sources. Specifically, the best decision tree emerged from combining the tutor talk moves that encouraged rigorous thinking and students' ITS mastery. In essence, tutor talk that encouraged mathematical reasoning predicted achievement for students who demonstrated high mastery on the ITS, whereas tutors' revoicing of students' mathematical ideas and contributions was predictive for students with low ITS mastery. Implications for practice are discussed.