Algorithmic stability--that is, how perturbing training data influences a learned model--is fundamental to modern data analysis. In learning theory, certain forms of stability are necessary and sufficient for generalization (Bousquet and Elisseeff, 2002; Poggio et al., 2004; Shalev-Shwartz et al., 2010). In model selection, stability measures can reliably identify important features (Meinshausen and Bühlmann, 2010; Shah and Samworth, 2013; Ren et al., 2021). In scientific applications, stable methods promote reproducibility, a prerequisite for meaningful inference (Yu, 2013). In distribution-free prediction, stability is a key assumption for the validity of jackknife prediction intervals (Barber et al., 2021; Steinberger and Leeb, 2023). Anticipating various benefits of stability, Breiman (1996a,b) proposed bagging as an ensemble metaalgorithm to stabilize any base learning algorithm. Bagging, short for bootstrap aggregating, refits the base algorithm to many perturbations of the training data and averages the resulting predictions. Breiman's vision of bagging as off-the-shelf stabilizer motivates our main question: How stable is bagging on an arbitrary base algorithm, placing no assumptions on the data generating distribution? In this paper, we first answer this question for the case of base algorithms with bounded outputs and then show extensions to the unbounded case.

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem. Several iterative methods have been developed for tackling this class of problems. Alas, their convergence guarantees are either asymptotic for the upper-level objective, or the convergence rates are slow and sub-optimal. To address this issue, in this paper, we introduce a novel bilevel optimization method that locally approximates the solution set of the lower-level problem via a cutting plane, and then runs a conditional gradient update to decrease the upper-level objective. When the upper-level objective is convex, we show that our method requires ${\mathcal{O}}(\max\{1/\epsilon_f,1/\epsilon_g\})$ iterations to find a solution that is $\epsilon_f$-optimal for the upper-level objective and $\epsilon_g$-optimal for the lower-level objective. Moreover, when the upper-level objective is non-convex, our method requires ${\mathcal{O}}(\max\{1/\epsilon_f^2,1/(\epsilon_f\epsilon_g)\})$ iterations to find an $(\epsilon_f,\epsilon_g)$-optimal solution. We also prove stronger convergence guarantees under the H\"olderian error bound assumption on the lower-level problem. To the best of our knowledge, our method achieves the best-known iteration complexity for the considered class of bilevel problems.

This article presents a dataset of 10,917 news articles with hierarchical news categories collected between 1 January 2019 and 31 December 2019. We manually labeled the articles based on a hierarchical taxonomy with 17 first-level and 109 second-level categories. This dataset can be used to train machine learning models for automatically classifying news articles by topic. This dataset can be helpful for researchers working on news structuring, classification, and predicting future events based on released news.

As the availability, size and complexity of data have increased in recent years, machine learning (ML) techniques have become popular for modeling. Predictions resulting from applying ML models are often used for inference, decision-making, and downstream applications. A crucial yet often overlooked aspect of ML is uncertainty quantification, which can significantly impact how predictions from models are used and interpreted. Extreme Gradient Boosting (XGBoost) is one of the most popular ML methods given its simple implementation, fast computation, and sequential learning, which make its predictions highly accurate compared to other methods. However, techniques for uncertainty determination in ML models such as XGBoost have not yet been universally agreed among its varying applications. We propose enhancements to XGBoost whereby a modified quantile regression is used as the objective function to estimate uncertainty (QXGBoost). Specifically, we included the Huber norm in the quantile regression model to construct a differentiable approximation to the quantile regression error function. This key step allows XGBoost, which uses a gradient-based optimization algorithm, to make probabilistic predictions efficiently. QXGBoost was applied to create 90\% prediction intervals for one simulated dataset and one real-world environmental dataset of measured traffic noise. Our proposed method had comparable or better performance than the uncertainty estimates generated for regular and quantile light gradient boosting. For both the simulated and traffic noise datasets, the overall performance of the prediction intervals from QXGBoost were better than other models based on coverage width-based criterion.

Traffic congestion caused by non-recurring incidents such as vehicle crashes and debris is a key issue for Traffic Management Centers (TMCs). Clearing incidents in a timely manner is essential for improving safety and reducing delays and emissions for the traveling public. However, TMCs and other responders face a challenge in predicting the duration of incidents (until the roadway is clear), making decisions of what resources to deploy difficult. To address this problem, this research developed an analytical framework and end-to-end machine-learning solution for predicting incident duration based on information available as soon as an incident report is received. Quality predictions of incident duration can help TMCs and other responders take a proactive approach in deploying responder services such as tow trucks, maintenance crews or activating alternative routes. The predictions use a combination of classification and regression machine learning modules. The performance of the developed solution has been evaluated based on the Mean Absolute Error (MAE), or deviation from the actual incident duration as well as Area Under the Curve (AUC) and Mean Absolute Percentage Error (MAPE). The results showed that the framework significantly improved incident duration prediction compared to methods from previous research.

The principle of DEPENDENCY LENGTH MINIMIZATION, which seeks to keep syntactically related words close in a sentence, is thought to universally shape the structure of human languages for effective communication. However, the extent to which dependency length minimization is applied in human language systems is not yet fully understood. Preverbally, the placement of long-before-short constituents and postverbally, short-before-long constituents are known to minimize overall dependency length of a sentence. In this study, we test the hypothesis that placing only the shortest preverbal constituent next to the main-verb explains word order preferences in Hindi (a SOV language) as opposed to the global minimization of dependency length. We characterize this approach as a least-effort strategy because it is a cost-effective way to shorten all dependencies between the verb and its preverbal dependencies. As such, this approach is consistent with the bounded-rationality perspective according to which decision making is governed by "fast but frugal" heuristics rather than by a search for optimal solutions. Consistent with this idea, our results indicate that actual corpus sentences in the Hindi-Urdu Treebank corpus are better explained by the least effort strategy than by global minimization of dependency lengths. Additionally, for the task of distinguishing corpus sentences from counterfactual variants, we find that the dependency length and constituent length of the constituent closest to the main verb are much better predictors of whether a sentence appeared in the corpus than total dependency length. Overall, our findings suggest that cognitive resource constraints play a crucial role in shaping natural languages.

Differentially private (DP) mechanisms protect individual-level information by introducing randomness into the statistical analysis procedure. Despite the availability of numerous DP tools, there remains a lack of general techniques for conducting statistical inference under DP. We examine a DP bootstrap procedure that releases multiple private bootstrap estimates to infer the sampling distribution and construct confidence intervals (CIs). Our privacy analysis presents new results on the privacy cost of a single DP bootstrap estimate, applicable to any DP mechanisms, and identifies some misapplications of the bootstrap in the existing literature. Using the Gaussian-DP (GDP) framework (Dong et al.,2022), we show that the release of $B$ DP bootstrap estimates from mechanisms satisfying $(\mu/\sqrt{(2-2/\mathrm{e})B})$-GDP asymptotically satisfies $\mu$-GDP as $B$ goes to infinity. Moreover, we use deconvolution with the DP bootstrap estimates to accurately infer the sampling distribution, which is novel in DP. We derive CIs from our density estimate for tasks such as population mean estimation, logistic regression, and quantile regression, and we compare them to existing methods using simulations and real-world experiments on 2016 Canada Census data. Our private CIs achieve the nominal coverage level and offer the first approach to private inference for quantile regression.

Recent work has shown that sparse graphs containing many triangles cannot be reproduced using a finite-dimensional representation of the nodes, in which link probabilities are inner products. Here, we show that such graphs can be reproduced using an infinite-dimensional inner product model, where the node representations lie on a low-dimensional manifold. Recovering a global representation of the manifold is impossible in a sparse regime. However, we can zoom in on local neighbourhoods, where a lower-dimensional representation is possible. As our constructions allow the points to be uniformly distributed on the manifold, we find evidence against the common perception that triangles imply community structure.

We propose to adopt statistical regression as the projection operator to enable data-driven learning of the operators in the Mori--Zwanzig formalism. We present a principled method to extract the Markov and memory operators for any regression models. We show that the choice of linear regression results in a recently proposed data-driven learning algorithm based on Mori's projection operator, which is a higher-order approximate Koopman learning method. We show that more expressive nonlinear regression models naturally fill in the gap between the highly idealized and computationally efficient Mori's projection operator and the most optimal yet computationally infeasible Zwanzig's projection operator. We performed numerical experiments and extracted the operators for an array of regression-based projections, including linear, polynomial, spline, and neural-network-based regressions, showing a progressive improvement as the complexity of the regression model increased. Our proposition provides a general framework to extract memory-dependent corrections and can be readily applied to an array of data-driven learning methods for stationary dynamical systems in the literature.

The quality of air is closely linked with the life quality of humans, plantations, and wildlife. It needs to be monitored and preserved continuously. Transportations, industries, construction sites, generators, fireworks, and waste burning have a major percentage in degrading the air quality. These sources are required to be used in a safe and controlled manner. Using traditional laboratory analysis or installing bulk and expensive models every few miles is no longer efficient. Smart devices are needed for collecting and analyzing air data. The quality of air depends on various factors, including location, traffic, and time. Recent researches are using machine learning algorithms, big data technologies, and the Internet of Things to propose a stable and efficient model for the stated purpose. This review paper focuses on studying and compiling recent research in this field and emphasizes the Data sources, Monitoring, and Forecasting models. The main objective of this paper is to provide the astuteness of the researches happening to improve the various aspects of air polluting models. Further, it casts light on the various research issues and challenges also.