In the past decades, most work in the area of data analysis and machine learning was focused on optimizing predictive models and getting better results than what was possible with existing models. To what extent the metrics with which such improvements were measured were accurately capturing the intended goal, whether the numerical differences in the resulting values were significant, or whether uncertainty played a role in this study and if it should have been taken into account, was of secondary importance. Whereas probability theory, be it frequentist or Bayesian, used to be the gold standard in science before the advent of the supercomputer, it was quickly replaced in favor of black box models and sheer computing power because of their ability to handle large data sets. This evolution sadly happened at the expense of interpretability and trustworthiness. However, while people are still trying to improve the predictive power of their models, the community is starting to realize that for many applications it is not so much the exact prediction that is of importance, but rather the variability or uncertainty. The work in this dissertation tries to further the quest for a world where everyone is aware of uncertainty, of how important it is and how to embrace it instead of fearing it. A specific, though general, framework that allows anyone to obtain accurate uncertainty estimates is singled out and analysed. Certain aspects and applications of the framework -- dubbed `conformal prediction' -- are studied in detail. Whereas many approaches to uncertainty quantification make strong assumptions about the data, conformal prediction is, at the time of writing, the only framework that deserves the title `distribution-free'. No parametric assumptions have to be made and the nonparametric results also hold without having to resort to the law of large numbers in the asymptotic regime.

Decentralized learning is appealing as it enables the scalable usage of large amounts of distributed data and resources (without resorting to any central entity), while promoting privacy since every user minimizes the direct exposure of their data. Yet, without additional precautions, curious users can still leverage models obtained from their peers to violate privacy. In this paper, we propose Decor, a variant of decentralized SGD with differential privacy (DP) guarantees. Essentially, in Decor, users securely exchange randomness seeds in one communication round to generate pairwise-canceling correlated Gaussian noises, which are injected to protect local models at every communication round. We theoretically and empirically show that, for arbitrary connected graphs, Decor matches the central DP optimal privacy-utility trade-off. We do so under SecLDP, our new relaxation of local DP, which protects all user communications against an external eavesdropper and curious users, assuming that every pair of connected users shares a secret, i.e., an information hidden to all others. The main theoretical challenge is to control the accumulation of non-canceling correlated noise due to network sparsity. We also propose a companion SecLDP privacy accountant for public use.

Automatic differentiation (see, for example, Ref.[1]) has revolutionized machine learning, permitting the routine application of gradient descent algorithms to fit to data models of essentially unlimited complexity. The same technology can be used to take the derivative of these models with respect to their inputs without the need to explicitly calculate the derivatives [2]. A potentially useful application of this capability is approximating the probability density function (pdf), f(x | θ), given an accurate neural network model of the associated conditional cumulative distribution function (cdf), F (x | θ), using the fact that F (x | θ) f(x | θ) =, (1) x where θ are the parameters of the data-generation mechanism, which we distinguish from the parameters w of the neural network model. This paper explores this possibility in the context of simulation-based frequentist inference [3-7]. Equation (1) furnishes an approximation of the pdf f(x | θ) whether x is a function of the underlying observations D only or if x = λ(D; θ) is a test statistic that depends on D as well as on the parameters θ. Moreover, computing the derivative of the cdf using autograd to obtain the pdf is exact; autograd does not use finite difference approximations.

We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of jointly Gaussian data, we prove that the optimal ellipsoid is centered around the conditional mean and shaped as the conditional covariance matrix. In more practical cases, we propose a differentiable optimization approach for approximately computing the optimal ellipsoids using a neural network with proper calibration. Compared to existing methods, our network requires less storage and less computations in inference time, leading to accurate yet smaller ellipsoids. We demonstrate these advantages on four real-world localization datasets.

A novel approach is given to overcome the computational challenges of the full-matrix Adaptive Gradient algorithm (Full AdaGrad) in stochastic optimization. By developing a recursive method that estimates the inverse of the square root of the covariance of the gradient, alongside a streaming variant for parameter updates, the study offers efficient and practical algorithms for large-scale applications. This innovative strategy significantly reduces the complexity and resource demands typically associated with full-matrix methods, enabling more effective optimization processes. Moreover, the convergence rates of the proposed estimators and their asymptotic efficiency are given. Their effectiveness is demonstrated through numerical studies.

To reduce the communication overhead caused by parallel training of multiple clients, various federated learning (FL) techniques use random client sampling. Nonetheless, ensuring the efficacy of random sampling and determining the optimal number of clients to sample in federated recommender systems (FRSs) remains challenging due to the isolated nature of each user as a separate client. This challenge is exacerbated in models where public and private features can be separated, and FL allows communication of only public features (item gradients). In this study, we establish sample complexity bounds that dictate the ideal number of clients required for improved communication efficiency and retained accuracy in such models. In line with our theoretical findings, we empirically demonstrate that RS-FairFRS reduces communication cost (~47%). Second, we demonstrate the presence of class imbalance among clients that raises a substantial equity concern for FRSs. Unlike centralized machine learning, clients in FRS can not share raw data, including sensitive attributes. For this, we introduce RS-FairFRS, first fairness under unawareness FRS built upon random sampling based FRS. While random sampling improves communication efficiency, we propose a novel two-phase dual-fair update technique to achieve fairness without revealing protected attributes of active clients participating in training. Our results on real-world datasets and different sensitive features illustrate a significant reduction in demographic bias (~approx40\%), offering a promising path to achieving fairness and communication efficiency in FRSs without compromising the overall accuracy of FRS.

In recent years, scientists have increasingly employed statistical and machine learning methods to uncover the governing equations of dynamical systems, particularly differential equations, from observational data [1-5]. Data-driven methods offer several advantages over traditional approaches that rely on first principles and expert knowledge. These methods can reveal patterns and relationships in the data that may not be apparent from first principles, providing new insights into complex systems [6, 7]. They are also adept at working with noisy or incomplete data commonly encountered in real-world applications, employing techniques from machine learning to enhance the robustness of discoveries [8-11]. Furthermore, by reducing the need for manual intervention and domain expertise, data-driven methods can significantly streamline the discovery process [12]. Data-driven discovery in dynamical systems has evolved from early parameter estimation using spline approximation and system reconstruction [13, 14], to leveraging statistical methods such as least squares [15-17], mixed-effects models [18, 19], and Bayesian approaches [2, 20] for parameter estimation in ordinary and partial differential equations (ODEs and PDEs). The advent of high-performance computing has further propelled symbolic regression, enabling the discovery of governing equations from data in physics and engineering [1, 21-23]. A notable development in this field is the Sparse Identification of Nonlinear Dynamics (SINDy) approach [3, 4], which constructs an extensive library of potential terms and employs the Sequential Threshold Ridge Regression (STRidge) algorithm [4] to select significant terms iteratively.

Age-related language patterns play a crucial role in understanding linguistic differences and developing age-appropriate communication strategies. However, the lack of comprehensive and diverse datasets has hindered the progress of research in this area. To address this issue, we present TextAge, a curated text dataset that maps sentences to the age and age group of the producer, as well as an underage (under 13) label. TextAge covers a wide range of ages and includes both spoken and written data from various sources such as CHILDES, Meta, Poki Poems-by-kids, JUSThink, and the TV show "Survivor." The dataset undergoes extensive cleaning and preprocessing to ensure data quality and consistency. We demonstrate the utility of TextAge through two applications: Underage Detection and Generational Classification. For Underage Detection, we train a Naive Bayes classifier, fine-tuned RoBERTa, and XLNet models to differentiate between language patterns of minors and young-adults and over. For Generational Classification, the models classify language patterns into different age groups (kids, teens, twenties, etc.). The models excel at classifying the "kids" group but struggle with older age groups, particularly "fifties," "sixties," and "seventies," likely due to limited data samples and less pronounced linguistic differences. TextAge offers a valuable resource for studying age-related language patterns and developing age-sensitive language models. The dataset's diverse composition and the promising results of the classification tasks highlight its potential for various applications, such as content moderation, targeted advertising, and age-appropriate communication. Future work aims to expand the dataset further and explore advanced modeling techniques to improve performance on older age groups.

The need for the maintenance of railway track systems have been increasing. Traditional methods that are currently being used are either inaccurate, labor and time intensive, or does not enable continuous monitoring of the system. As a result, in-service train vibrations have been shown to be a cheaper alternative for monitoring of railway track systems. In this paper, a method is proposed to detect different maintenance needs of railway track systems using a single pass of train direction. The DR-Train dataset that is publicly available was used. Results show that by using a simple classifier such as the k-nearest neighbor (k-NN) algorithm, the signal energy features of the acceleration data can achieve 76\% accuracy on two types of maintenance needs, tamping and surfacing. The results show that the transverse direction is able to more accurately detect maintenance needs, and triaxial accelerometer can give further information on the maintenance needs. Furthermore, this paper demonstrates the use of multi-label classification to detect multiple types of maintenance needs simultaneously. The results show multi-label classification performs only slightly worse than the simple binary classification (72\% accuracy) and that this can be a simple method that can easily be deployed in areas that have a history of many maintenance issues.

The escalation in urban private car ownership has worsened the urban parking predicament, necessitating effective parking availability prediction for urban planning and management. However, the existing prediction methods suffer from low prediction accuracy with the lack of spatial-temporal correlation features related to parking volume, and neglect of flow patterns and correlations between similar parking lots within certain areas. To address these challenges, this study proposes a parking availability prediction framework integrating spatial-temporal deep learning with multi-source data fusion, encompassing traffic demand data from multiple sources (e.g., metro, bus, taxi services), and parking lot data. The framework is based on the Transformer as the spatial-temporal deep learning model and leverages K-means clustering to establish parking cluster zones, extracting and integrating traffic demand characteristics from various transportation modes (i.e., metro, bus, online ride-hailing, and taxi) connected to parking lots. Real-world empirical data was used to verify the effectiveness of the proposed method compared with different machine learning, deep learning, and traditional statistical models for predicting parking availability. Experimental results reveal that, with the proposed pipeline, the developed Transformer model outperforms other models in terms of various metrics, e.g., Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). By fusing multi-source demanding data with spatial-temporal deep learning techniques, this approach offers the potential to develop parking availability prediction systems that furnish more accurate and timely information to both drivers and urban planners, thereby fostering more efficient and sustainable urban mobility.