Inspired by the concept of active learning, we propose active inference$\unicode{x2013}$a methodology for statistical inference with machine-learning-assisted data collection. Assuming a budget on the number of labels that can be collected, the methodology uses a machine learning model to identify which data points would be most beneficial to label, thus effectively utilizing the budget. It operates on a simple yet powerful intuition: prioritize the collection of labels for data points where the model exhibits uncertainty, and rely on the model's predictions where it is confident. Active inference constructs provably valid confidence intervals and hypothesis tests while leveraging any black-box machine learning model and handling any data distribution. The key point is that it achieves the same level of accuracy with far fewer samples than existing baselines relying on non-adaptively-collected data. This means that for the same number of collected samples, active inference enables smaller confidence intervals and more powerful p-values. We evaluate active inference on datasets from public opinion research, census analysis, and proteomics.

Transformer-based models have demonstrated remarkable in-context learning capabilities, prompting extensive research into its underlying mechanisms. Recent studies have suggested that Transformers can implement first-order optimization algorithms for in-context learning and even second order ones for the case of linear regression. In this work, we study whether Transformers can perform higher order optimization methods, beyond the case of linear regression. We establish that linear attention Transformers with ReLU layers can approximate second order optimization algorithms for the task of logistic regression and achieve $\epsilon$ error with only a logarithmic to the error more layers. As a by-product we demonstrate the ability of even linear attention-only Transformers in implementing a single step of Newton's iteration for matrix inversion with merely two layers. These results suggest the ability of the Transformer architecture to implement complex algorithms, beyond gradient descent.

The transportation sector remains a major contributor to greenhouse gas emissions. The understanding of energy-efficient driving behaviors and utilization of energy-efficient driving strategies are essential to reduce vehicles' fuel consumption. However, there is no comprehensive investigation into energy-efficient driving behaviors and strategies. Furthermore, many state-of-the-art AI models have been applied for the analysis of eco-friendly driving styles, but no overview is available. To fill the gap, this paper conducts a thorough literature review on ecological driving behaviors and styles and analyzes the driving factors influencing energy consumption and state-of-the-art methodologies. With a thorough scoping review process, the methodological and related data are compared. The results show that the factors that impact driving behaviors can be summarized into eleven features including speed, acceleration, deceleration, pedal, and so on. This paper finds that supervised/unsupervised learning algorithms and reinforcement learning frameworks have been popularly used to model the vehicle's energy consumption with multi-dimensional data. Furthermore, the literature shows that the driving data are collected from either simulators or real-world experiments, and the real-world data are mainly stored and transmitted by meters, controller area networks, onboard data services, smartphones, and additional sensors installed in the vehicle. Based on driving behavior factors, driver characteristics, and safety rules, this paper recommends nine energy-efficient driving styles including four guidelines for the drivers' selection and adjustment of the vehicle parameters, three recommendations for the energy-efficient driving styles in different driving scenarios, and two subjective suggestions for different types of drivers and employers.

This book aims to provide a working introduction to the emerging fusion of modern statistical inference - aka machine learning (ML) or artificial intelligence (AI) - and causal inference methods. The book is aimed at upper level undergraduates and master's-level students as well as doctoral students focusing on applied empirical research. A sufficient background for the core material is one semester of introductory econometrics and one semester of machine learning. We hope the book is also useful to empirical researchers looking to apply modern methods in their work. The book provides an overview of key ideas in both predictive inference and causal inference and shows how predictive tools are key ingredients to answering many causal questions.

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of their applications. Based on the solution of a constrained optimization problem, we propose "prediction rigidities" as a method to obtain uncertainties of arbitrary pre-trained regressors. We establish a strong connection between our framework and Bayesian inference, and we develop a last-layer approximation that allows the new method to be applied to neural networks. This extension affords cheap uncertainties without any modification to the neural network itself or its training procedure. We show the effectiveness of our method on a wide range of regression tasks, ranging from simple toy models to applications in chemistry and meteorology.

Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical spaces, a few recent works have proposed hyperbolic prototypes for classification. Such approaches enable effective learning in low-dimensional output spaces and can exploit hierarchical relations amongst classes, but require privileged information about class labels to position the hyperbolic prototypes. In this work, we propose Hyperbolic Busemann Learning. The main idea behind our approach is to position prototypes on the ideal boundary of the Poincaré ball, which does not require prior label knowledge. To be able to compute proximities to ideal prototypes, we introduce the penalised Busemann loss. We provide theory supporting the use of ideal prototypes and the proposed loss by proving its equivalence to logistic regression in the one-dimensional case. Empirically, we show that our approach provides a natural interpretation of classification confidence, while outperforming recent hyperspherical and hyperbolic prototype approaches.

These appendices provide supplementary details and results of BAST. Appendix A contains additional details on Bayesian estimation and prediction. Supplementary simulation details and results including hyperparameter tuning and computation time can be found in Appendix B. Finally, Appendix C provides the proof of Proposition 1. Appendix A.1 Estimation This appendix provides details on the Markov chain Monte Carlo (MCMC) algorithm discussed in Section 3.1. This probability specification works well in our experiments, but one can modify it if desired. Appendix A.2 Prediction in Two-dimensional Constrained Domains In this subsection we provide details on specifying the neighbor set N To sample the cluster membership of u, we need to determine the cluster memberships for vertices on the domain boundary, which can be done by, for instance, assigning a boundary vertex to the same cluster as its nearest vertex in S with respect to the graph distance in the CDT mesh (when the number of vertices in the CDT graph is large, we expect this to well approximate the geodesic distance).

Nonparametric regression on complex domains has been a challenging task as most existing methods, such as ensemble models based on binary decision trees, are not designed to account for intrinsic geometries and domain boundaries. This article proposes a Bayesian additive regression spanning trees (BAST) model for nonparametric regression on manifolds, with an emphasis on complex constrained domains or irregularly shaped spaces embedded in Euclidean spaces. Our model is built upon a random spanning tree manifold partition model as each weak learner, which is capable of capturing any irregularly shaped spatially contiguous partitions while respecting intrinsic geometries and domain boundary constraints.

In a basketball game, scoring efficiency holds significant importance due to the numerous offensive possessions per game. Enhancing scoring efficiency necessitates effective collaboration among players with diverse playing styles. In previous studies, basketball lineups have been analyzed, but their playing style compatibility has not been quantitatively examined. The purpose of this study is to analyze more specifically the impact of playing style compatibility on scoring efficiency, focusing only on offense. This study employs two methods to capture the playing styles of players on offense: shooting style clustering using tracking data, and offensive role clustering based on annotated playtypes and advanced statistics. For the former, interpretable hand-crafted shot features and Wasserstein distances between shooting style distributions were utilized. For the latter, soft clustering was applied to playtype data for the first time. Subsequently, based on the lineup information derived from these two clusterings, machine learning models Bayesian models that predict statistics representing scoring efficiency were trained and interpreted. These approaches provide insights into which combinations of five players tend to be effective and which combinations of two players tend to produce good effects.

Music popularity prediction has garnered significant attention in both industry and academia, fuelled by the rise of data-driven algorithms and streaming platforms like Spotify. This study aims to explore the predictive power of various machine learning models in forecasting song popularity using a dataset comprising 30,000 songs spanning different genres from 1957 to 2020. Methods: We employ Ordinary Least Squares (OLS), Multivariate Adaptive Regression Splines (MARS), Random Forest, and XGBoost algorithms to analyse song characteristics and their impact on popularity. Results: Ordinary Least Squares (OLS) regression analysis reveals genre as the primary influencer of popularity, with notable trends over time. MARS modelling highlights the complex relationship between variables, particularly with features like instrumentalness and duration. Random Forest and XGBoost models underscore the importance of genre, especially EDM, in predicting popularity. Despite variations in performance, Random Forest emerges as the most effective model, improving prediction accuracy by 7.1% compared to average scores. Despite the importance of genre, predicting song popularity remains challenging, as observed variations in music-related features suggest complex interactions between genre and other factors. Consequently, while certain characteristics like loudness and song duration may impact popularity scores, accurately predicting song success remains elusive.