The estimation of heterogeneous treatment effects (HTEs) has become a central topic across statistics, econometrics, and machine learning, with applications ranging from personalized medicine to policy evaluation [1, 2, 3]. A growing body of work has proposed flexible estimators to capture individual-level treatment heterogeneity, including tree-based methods [2], representation-learning approaches [4, 5], and meta-learners [6, 7]. Despite this abundance of methods, determining which estimator performs best for a given application remains an open and underexplored problem [8, 9]. A reliable selection mechanism is crucial for practitioners [10], as choosing suboptimal estimators can directly affect downstream decision-making [11]. Evaluating or comparing HTE estimators is inherently difficult because the ground truth is unobservable: for each individual, only one potential outcome is realized [12], while HTEs are defined as the difference between two. Due to the fundamental unobservability of the treatment effect, comparing two HTE estimators is already challenging, and the difficulty is further exacerbated when a collection of estimators are being compared simultaneously. To our knowledge, most papers that compare multiple HTE estimators rely on ground-truth or simulated values and use them to compute metrics such as the Precision in Estimation of Heterogeneous Effect (PEHE) and the A TE [13, 14]. However, these evaluation metrics are subject to fundamental limitations: ground-truth are unavailable in real-world observational studies, and simulated values depend critically on the chosen data-generating process and offer no formal statistical guarantees. In this paper, we develop a method for accurately selecting the best heterogeneous treatment effect estimator that operates without ground-truth information and provides provable error control.

Walkability is a key component of sustainable urban development. In walkability studies, collecting detailed pedestrian infrastructure data remains challenging due to the high costs and limited scalability of traditional methods. Sidewalk delivery robots, increasingly deployed in urban environments, offer a promising solution to these limitations. This paper explores how these robots can serve as mobile data collection platforms, capturing sidewalk-level features related to walkability in a scalable, automated, and real-time manner. A sensor-equipped robot was deployed on a sidewalk network at KTH in Stockholm, completing 101 trips covering 900 segment records. From the collected data, different typologies of features are derived, including robot trip characteristics (e.g., speed, duration), sidewalk conditions (e.g., width, surface unevenness), and sidewalk utilization (e.g., pedestrian density). Their walkability-related implications were investigated with a series of analyses. The results demonstrate that pedestrian movement patterns are strongly influenced by sidewalk characteristics, with higher density, reduced width, and surface irregularity associated with slower and more variable trajectories. Notably, robot speed closely mirrors pedestrian behavior, highlighting its potential as a proxy for assessing pedestrian dynamics. The proposed framework enables continuous monitoring of sidewalk conditions and pedestrian behavior, contributing to the development of more walkable, inclusive, and responsive urban environments.

-- In this work we introduce a novel adaptive anomaly detection framework specifically designed for monitoring sequential random finite set (RFS) observations. Our approach effectively distinguishes between In-Control data (normal) and Out-Of-Control data (anomalies) by detecting deviations from the expected statistical behavior of the process. The primary contributions of this study include the development of an innovative RFS-based framework that not only learns the normal behavior of the data-generating process online but also dynamically adapts to behavioral shifts to accurately identify abnormal point patterns. T o achieve this, we introduce a new class of RFS-based posterior distributions, named Power Discounting Posteriors (PD), which facilitate adaptation to systematic changes in data while enabling anomaly detection of point pattern data through a novel predictive posterior density function. The effectiveness of the proposed approach is demonstrated by extensive qualitative and quantitative simulation experiments.

This paper introduces a hybrid framework for portfolio optimization that fuses Long Short-Term Memory (LSTM) forecasting with a Proximal Policy Optimization (PPO) reinforcement learning strategy. The proposed system leverages the predictive power of deep recurrent networks to capture temporal dependencies, while the PPO agent adaptively refines portfolio allocations in continuous action spaces, allowing the system to anticipate trends while adjusting dynamically to market shifts. Using multi-asset datasets covering U.S. and Indonesian equities, U.S. Treasuries, and major cryptocurrencies from January 2018 to December 2024, the model is evaluated against several baselines, including equal-weight, index-style, and single-model variants (LSTM-only and PPO-only). The framework's performance is benchmarked against equal-weighted, index-based, and single-model approaches (LSTM-only and PPO-only) using annualized return, volatility, Sharpe ratio, and maximum drawdown metrics, each adjusted for transaction costs. The results indicate that the hybrid architecture delivers higher returns and stronger resilience under non-stationary market regimes, suggesting its promise as a robust, AI-driven framework for dynamic portfolio optimization.

We study the problem of nonparametric instrumental variable regression with observed covariates, which we refer to as NPIV-O. Compared with standard nonparametric instrumental variable regression (NPIV), the additional observed covariates facilitate causal identification and enables heterogeneous causal effect estimation. However, the presence of observed covariates introduces two challenges for its theoretical analysis. First, it induces a partial identity structure, which renders previous NPIV analyses - based on measures of ill-posedness, stability conditions, or link conditions - inapplicable. Second, it imposes anisotropic smoothness on the structural function. To address the first challenge, we introduce a novel Fourier measure of partial smoothing; for the second challenge, we extend the existing kernel 2SLS instrumental variable algorithm with observed covariates, termed KIV-O, to incorporate Gaussian kernel lengthscales adaptive to the anisotropic smoothness. We prove upper $L^2$-learning rates for KIV-O and the first $L^2$-minimax lower learning rates for NPIV-O. Both rates interpolate between known optimal rates of NPIV and nonparametric regression (NPR). Interestingly, we identify a gap between our upper and lower bounds, which arises from the choice of kernel lengthscales tuned to minimize a projected risk. Our theoretical analysis also applies to proximal causal inference, an emerging framework for causal effect estimation that shares the same conditional moment restriction as NPIV-O.

Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such a cost is particularly challenging when datasets live in heterogeneous spaces, often motivating practitioners to adopt Gromov-Wasserstein formulations. To address this challenge, we introduce cost-regularized unbalanced optimal transport (CR-UOT), a framework that allows the ground cost to vary while allowing mass creation and removal. We show that CR-UOT incorporates unbalanced Gromov-Wasserstein type problems through families of inner-product costs parameterized by linear transformations, enabling the matching of measures or point clouds across Euclidean spaces. We develop algorithms for such CR-UOT problems using entropic regularization and demonstrate that this approach improves the alignment of heterogeneous single-cell omics profiles, especially when many cells lack direct matches.

Cross-subject motor-imagery decoding remains a major challenge in EEG-based brain-computer interfaces due to strong subject variability and the curved geometry of covariance matrices on the symmetric positive definite (SPD) manifold. We address the zero-shot cross-subject setting, where no target-subject labels or adaptation are allowed, by introducing novel geometry-aware preprocessing modules and deep congruence networks that operate directly on SPD covariance matrices. Our preprocessing modules, DCR and RiFU, extend Riemannian Alignment by improving action separation while reducing subject-specific distortions. We further propose two manifold classifiers, SPD-DCNet and RiFUNet, which use hierarchical congruence transforms to learn discriminative, subject-invariant covariance representations. On the BCI-IV 2a benchmark, our framework improves cross-subject accuracy by 3-4% over the strongest classical baselines, demonstrating the value of geometry-aware transformations for robust EEG decoding.

The increasing use of machine learning in sensitive applications demands algorithms that simultaneously preserve data privacy and ensure fairness across potentially sensitive sub-populations. While privacy and fairness have each been extensively studied, their joint treatment remains poorly understood. Existing research often frames them as conflicting objectives, with multiple studies suggesting that strong privacy notions such as differential privacy inevitably compromise fairness. In this work, we challenge that perspective by showing that differential privacy can be integrated into a fairness-enhancing pipeline with minimal impact on fairness guarantees. We design a postprocessing algorithm, called DP2DP, that enforces both demographic parity and differential privacy. Our analysis reveals that our algorithm converges towards its demographic parity objective at essentially the same rate (up logarithmic factor) as the best non-private methods from the literature. Experiments on both synthetic and real datasets confirm our theoretical results, showing that the proposed algorithm achieves state-of-the-art accuracy/fairness/privacy trade-offs.

Statistical inference from data generated by multi-armed bandit (MAB) algorithms is challenging due to their adaptive, non-i.i.d. nature. A classical manifestation is that sample averages of arm rewards under bandit sampling may fail to satisfy a central limit theorem. Lai and Wei's stability condition provides a sufficient, and essentially necessary criterion, for asymptotic normality in bandit problems. While the celebrated Upper Confidence Bound (UCB) algorithm satisfies this stability condition, it is not minimax optimal, raising the question of whether minimax optimality and statistical stability can be achieved simultaneously. In this paper, we analyze the stability properties of a broad class of bandit algorithms that are based on the optimism principle. We establish general structural conditions under which such algorithms violate the Lai-Wei stability criterion. As a consequence, we show that widely used minimax-optimal UCB-style algorithms, including MOSS, Anytime-MOSS, Vanilla-MOSS, ADA-UCB, OC-UCB, KL-MOSS, KL-UCB++, KL-UCB-SWITCH, and Anytime KL-UCB-SWITCH, are unstable. We further complement our theoretical results with numerical simulations demonstrating that, in all these cases, the sample means fail to exhibit asymptotic normality. Overall, our findings suggest a fundamental tension between stability and minimax optimal regret, raising the question of whether it is possible to design bandit algorithms that achieve both. Understanding whether such simultaneously stable and minimax optimal strategies exist remains an important open direction.

Abstract--Time series anomaly detection is widely used in IoT and cyber-physical systems, yet its evaluation remains challenging due to diverse application objectives and heterogeneous metric assumptions. This study introduces a problem-oriented framework that reinterprets existing metrics based on the specific evaluation challenges they are designed to address, rather than their mathematical forms or output structures. We categorize over twenty commonly used metrics into six dimensions: (1) basic accuracy-driven evaluation, (2) timeliness-aware reward mechanisms, (3) tolerance to labeling imprecision, (4) penalties reflecting human-audit cost, (5) robustness against random or inflated scores, and (6) parameter-free comparability for cross-dataset benchmark-ing. Comprehensive experiments are conducted to examine metric behavior under genuine, random, and oracle detection scenarios. By comparing their resulting score distributions, we quantify each metric's discriminative ability--its capability to distinguish meaningful detections from random noise. The results show that while most event-level metrics exhibit strong separability, several widely used metrics (e.g., NAB, Point-Adjust) demonstrate limited resistance to random-score inflation. These findings reveal that metric suitability must be inherently task-dependent and aligned with the operational objectives of IoT applications. The proposed framework offers a unified analytical perspective for understanding existing metrics and provides practical guidance for selecting or developing more context-aware, robust, and fair evaluation methodologies for time series anomaly detection. He emergence of the Internet of Things (IoT) has accelerated digital transformation across numerous domains. Its defining characteristic lies in the large-scale deployment of intelligent and heterogeneous devices--such as sensors, actuators, and RFID systems--that are interconnected via the Internet to enable autonomous communication without human intervention [1]. Currently, more than 12 billion IoT devices are in operation, and this number is projected to reach 125 billion by 2030 [2]. Consequently, the volume of data generated by these devices continues to soar, with an expected total of 79.4 ZB by 2025 [3]. In industrial contexts, the integration of IoT technologies has driven the ongoing Industry 4.0 revolution, emphasizing connectivity, automation, and intelligence. Kaixiang Y ang, Jiarong Liu, Y upeng Song, and Y ujue Zhou are with the School of Artificial Intelligence, Y unnan University, Kunming 650091, China. Shuanghua Y ang is with Beijing Normal University - Hong Kong Baptist University, Zhuhai 519087, China. This work was supported in part by the Y unnan Fundamental Research Projects under Grant 202401AU070151, and in part by the Y unnan Provincial Science and Technology Talent and Platform Plan under Grant 202505AF350053.