We explore extensions and applications of the regret minimization framework introduced by~\cite{design} for solving optimal experimental design problems. Specifically, we incorporate the entropy regularizer into this framework, leading to a novel sample selection objective and a provable sample complexity bound that guarantees a $(1+\epsilon)$-near optimal solution. We further extend the method to handle regularized optimal design settings. As an application, we use our algorithm to select a small set of representative samples from image classification datasets without relying on label information. To evaluate the quality of the selected samples, we train a logistic regression model and compare performance against several baseline sampling strategies. Experimental results on MNIST, CIFAR-10, and a 50-class subset of ImageNet show that our approach consistently outperforms competing methods in most cases.

Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid geometric assumptions or rely on flexible but computationally expensive approaches that do not explicitly optimize prediction set volume. We propose an optimization-driven framework based on a novel loss function that directly learns minimum-volume covering sets while ensuring valid coverage. This formulation naturally induces a new nonconformity score for conformal prediction, which adapts to the residual distribution and covariates. Our approach optimizes over prediction sets defined by arbitrary norm balls, including single and multi-norm formulations. Additionally, by jointly optimizing both the predictive model and predictive uncertainty, we obtain prediction sets that are tight, informative, and computationally efficient, as demonstrated in our experiments on real-world datasets.

Continual learning, which aims to learn multiple tasks sequentially, has gained extensive attention. However, most existing work focuses on empirical studies, and the theoretical aspect remains under-explored. Recently, a few investigations have considered the theory of continual learning only for linear regressions, establishes the results based on the strict independent and identically distributed (i.i.d.) assumption and the persistent excitation on the feature data that may be difficult to verify or guarantee in practice. To overcome this fundamental limitation, in this paper, we provide a general and comprehensive theoretical analysis for continual learning of regression models. By utilizing the stochastic Lyapunov function and martingale estimation techniques, we establish the almost sure convergence results of continual learning under a general data condition for the first time. Additionally, without any excitation condition imposed on the data, the convergence rates for the forgetting and regret metrics are provided.

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable efforts have been devoted to the learning problem of such systems, i.e., estimating data labels and identifying model parameters, most existing investigations employ the offline algorithm, impose the strict independent and identically distributed (i.i.d.) or persistent excitation (PE) conditions on the regressor data, and provide local convergence results only. In this paper, we investigate the recursive estimation and data clustering problems for a class of stochastic MLRs with two components. To address this inherently nonconvex optimization problem, we propose a novel two-step recursive identification algorithm to estimate the true parameters, where the direction vector and the scaling coefficient of the unknown parameters are estimated by the least squares and the expectation-maximization (EM) principles, respectively. Under a general data condition, which is much weaker than the traditional i.i.d. and PE conditions, we establish the global convergence and the convergence rate of the proposed identification algorithm for the first time. Furthermore, we prove that, without any excitation condition on the regressor data, the data clustering performance including the cumulative mis-classification error and the within-cluster error can be optimal asymptotically. Finally, we provide a numerical example to illustrate the performance of the proposed learning algorithm.

As current group contribution (GC) methods are mostly proposed for a wide size-range of molecules, applying them to property prediction of small refrigerant molecules could lead to unacceptable errors. In this sense, for the design of novel refrigerants and refrigeration systems, tailoring GC-based models specifically fitted to refrigerant molecules is of great interest. In this work, databases of potential refrigerant molecules are first collected, focusing on five key properties related to the operational efficiency of refrigeration systems, namely normal boiling point, critical temperature, critical pressure, enthalpy of vaporization, and acentric factor. Based on tailored small-molecule groups, the GC method is combined with machine learning (ML) to model these performance-related properties. Following the development of GC-ML models, their performance is analyzed to highlight the potential group-to-property contributions. Additionally, the refrigerant property databases are extended internally and externally, based on which examples are presented to highlight the significance of the developed models.

Predicting air traffic congestion and flow management is essential for airlines and Air Navigation Service Providers (ANSP) to enhance operational efficiency. Accurate estimates of future airport capacity and airspace density are vital for better airspace management, reducing air traffic controller workload and fuel consumption, ultimately promoting sustainable aviation. While existing literature has addressed these challenges, data management and query processing remain complex due to the vast volume of high-rate air traffic data. Many analytics use cases require a common pre-processing infrastructure, as ad-hoc approaches are insufficient. Additionally, linear prediction models often fall short, necessitating more advanced techniques. This paper presents a data processing and predictive services architecture that ingests large, uncorrelated, and noisy streaming data to forecast future airspace system states. The system continuously collects raw data, periodically compresses it, and stores it in NoSQL databases for efficient query processing. For prediction, the system learns from historical traffic by extracting key features such as airport arrival and departure events, sector boundary crossings, weather parameters, and other air traffic data. These features are input into various regression models, including linear, non-linear, and ensemble models, with the best-performing model selected for predictions. We evaluate this infrastructure across three prediction use cases in the US National Airspace System (NAS) and a segment of European airspace, using extensive real operations data, confirming that our system can predict future system states efficiently and accurately.

The linear regression (LR) method offers the advantage that optimal parameters can be calculated relatively easily, although its representation capability is limited than that of the deep learning technique. To improve deep reinforcement learning, the Least Squares Deep Q Network (LS-DQN) method was proposed by Levine et al., which combines Deep Q Network (DQN) with LR method. However, the LS-DQN method assumes that the actions are discrete. In this study, we propose the Double Least Squares Deep Deterministic Policy Gradient (DLS-DDPG) method to address this limitation. This method combines the LR method with the Deep Deterministic Policy Gradient (DDPG) technique, one of the representative deep reinforcement learning algorithms for continuous action cases. Numerical experiments conducted in MuJoCo environments showed that the LR update improved performance at least in some tasks, although there are difficulties such as the inability to make the regularization terms small.

Whether large language models (LLMs) process language similarly to humans has been the subject of much theoretical and practical debate. We examine this question through the lens of the production-interpretation distinction found in human sentence processing and evaluate the extent to which instruction-tuned LLMs replicate this distinction. Using an empirically documented asymmetry between production and interpretation in humans for implicit causality verbs as a testbed, we find that some LLMs do quantitatively and qualitatively reflect human-like asymmetries between production and interpretation. We demonstrate that whether this behavior holds depends upon both model size - with larger models more likely to reflect human-like patterns and the choice of meta-linguistic prompts used to elicit the behavior.

The partitioning of data for estimation and calibration critically impacts the performance of propensity score based estimators like inverse probability weighting (IPW) and double/debiased machine learning (DML) frameworks. We extend recent advances in calibration techniques for propensity score estimation, improving the robustness of propensity scores in challenging settings such as limited overlap, small sample sizes, or unbalanced data. Our contributions are twofold: First, we provide a theoretical analysis of the properties of calibrated estimators in the context of DML. To this end, we refine existing calibration frameworks for propensity score models, with a particular emphasis on the role of sample-splitting schemes in ensuring valid causal inference. Second, through extensive simulations, we show that calibration reduces variance of inverse-based propensity score estimators while also mitigating bias in IPW, even in small-sample regimes. Notably, calibration improves stability for flexible learners (e.g., gradient boosting) while preserving the doubly robust properties of DML. A key insight is that, even when methods perform well without calibration, incorporating a calibration step does not degrade performance, provided that an appropriate sample-splitting approach is chosen.

This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and regression coefficients to vary across study areas. Unlike standard approaches in the literature, in which bandwidth and regression parameters are estimated separately for each focal point on the basis of different criteria, our model uses a single objective function for the integrated estimation of regression and bandwidth parameters across all focal points, based on the regression likelihood function and variance modeling. The proposed model further integrates a procedure to select a single subset of independent variables for all focal points, whereas existing approaches may return heterogeneous subsets across focal points. We then propose an alternative direction method to solve the nonconvex mathematical model and show that it converges to a partial minimum. The computational experiment indicates that the proposed algorithm provides competitive explanatory power with stable spatially varying patterns, with the ability to select the best subset and account for additional constraints.