Prediction-based (PB) inference is increasingly used in applications where the outcome of interest is difficult to obtain, but its predictors are readily available. Unlike traditional inference, PB inference performs statistical inference using a partially observed outcome and a set of covariates by leveraging a prediction of the outcome generated from a machine learning (ML) model. Motwani and Witten (2023) recently revisited two innovative PB inference approaches for ordinary least squares. They found that the method proposed by Wang et al. (2020) yields a consistent estimator for the association of interest when the ML model perfectly captures the underlying regression function. Conversely, the prediction-powered inference (PPI) method proposed by Angelopoulos et al. (2023) yields valid inference regardless of the model's accuracy. In this paper, we study the statistical efficiency of the PPI estimator. Our analysis reveals that a more efficient estimator, proposed 25 years ago by Chen and Chen (2000), can be obtained by simply adding a weight to the PPI estimator. We also contextualize PB inference with methods from the economics and statistics literature dating back to the 1960s. Our extensive theoretical and numerical analyses indicate that the Chen and Chen (CC) estimator offers a balance between robustness to ML model specification and statistical efficiency, making it the preferred choice for use in practice.

Consider a semi-supervised setting with a labeled dataset of binary responses and predictors and an unlabeled dataset with only the predictors. Logistic regression is equivalent to an exponential tilt model in the labeled population. For semi-supervised estimation, we develop further analysis and understanding of a statistical approach using exponential tilt mixture (ETM) models and maximum nonparametric likelihood estimation, while allowing that the class proportions may differ between the unlabeled and labeled data. We derive asymptotic properties of ETM-based estimation and demonstrate improved efficiency over supervised logistic regression in a random sampling setup and an outcome-stratified sampling setup previously used. Moreover, we reconcile such efficiency improvement with the existing semiparametric efficiency theory when the class proportions in the unlabeled and labeled data are restricted to be the same. We also provide a simulation study to numerically illustrate our theoretical findings.

Reducing unexpected urban traffic congestion caused by en-route events (e.g., road closures, car crashes, etc.) often requires fast and accurate reactions to choose the best-fit traffic signals. Traditional traffic light control systems, such as SCATS and SCOOT, are not efficient as their traffic data provided by induction loops has a low update frequency (i.e., longer than 1 minute). Moreover, the traffic light signal plans used by these systems are selected from a limited set of candidate plans pre-programmed prior to unexpected events' occurrence. Recent research demonstrates that camera-based traffic light systems controlled by deep reinforcement learning (DRL) algorithms are more effective in reducing traffic congestion, in which the cameras can provide high-frequency high-resolution traffic data. However, these systems are costly to deploy in big cities due to the excessive potential upgrades required to road infrastructure. In this paper, we argue that Unmanned Aerial Vehicles (UAVs) can play a crucial role in dealing with unexpected traffic congestion because UAVs with onboard cameras can be economically deployed when and where unexpected congestion occurs. Then, we propose a system called "AVARS" that explores the potential of using UAVs to reduce unexpected urban traffic congestion using DRL-based traffic light signal control. This approach is validated on a widely used open-source traffic simulator with practical UAV settings, including its traffic monitoring ranges and battery lifetime. Our simulation results show that AVARS can effectively recover the unexpected traffic congestion in Dublin, Ireland, back to its original un-congested level within the typical battery life duration of a UAV.

In dynamic programming (DP) and reinforcement learning (RL), an agent learns to act optimally in terms of expected long-term return by sequentially interacting with its environment modeled by a Markov decision process (MDP). More generally in distributional reinforcement learning (DRL), the focus is on the whole distribution of the return, not just its expectation. Although DRL-based methods produced state-of-the-art performance in RL with function approximation, they involve additional quantities (compared to the non-distributional setting) that are still not well understood. As a first contribution, we introduce a new class of distributional operators, together with a practical DP algorithm for policy evaluation, that come with a robust MDP interpretation. Indeed, our approach reformulates through an augmented state space where each state is split into a worst-case substate and a best-case substate, whose values are maximized by safe and risky policies respectively. Finally, we derive distributional operators and DP algorithms solving a new control task: How to distinguish safe from risky optimal actions in order to break ties in the space of optimal policies?

We develop a new approach to solving classification problems, in which the labeled training data is viewed as random samples from populations with unknown distributions and we base our analysis on the theory of coherent measures of risk and risk sharing. The proposed approach aims at designing a risk-averse classifier. We stipulate that misclassification in different classes is associated with different risk. Therefore, we employ non-linear (in probability) risk functionals specific to each class. We analyze the structure of the new classifier design problem and establish its theoretical relation to the risk-neutral design problem. In particular, we show that the risk-sharing classification problem is equivalent to an implicitly defined optimization problem with unequal, implicitly defined but unknown weights for each data point. We implement our methodology in a binary classification scenario on several different data sets and carry out numerical comparison with classifiers which are obtained using the Huber loss function and other popular loss functions. In these applications, we use linear support vector machines in order to demonstrate the viability of our method.