This paper addresses second-order stochastic optimization for estimating the minimizer of a convex function written as an expectation. A direct recursive estimation technique for the inverse Hessian matrix using a Robbins-Monro procedure is introduced. This approach enables to drastically reduces computational complexity. Above all, it allows to develop universal stochastic Newton methods and investigate the asymptotic efficiency of the proposed approach. This work so expands the application scope of secondorder algorithms in stochastic optimization.

A multi-modal emotional speech Mandarin database including articulatory kinematics, acoustics, glottal and facial micro-expressions is designed and established, which is described in detail from the aspects of corpus design, subject selection, recording details and data processing. Where signals are labeled with discrete emotion labels (neutral, happy, pleasant, indifferent, angry, sad, grief) and dimensional emotion labels (pleasure, arousal, dominance). In this paper, the validity of dimension annotation is verified by statistical analysis of dimension annotation data. The SCL-90 scale data of annotators are verified and combined with PAD annotation data for analysis, so as to explore the internal relationship between the outlier phenomenon in annotation and the psychological state of annotators. In order to verify the speech quality and emotion discrimination of the database, this paper uses 3 basic models of SVM, CNN and DNN to calculate the recognition rate of these seven emotions. The results show that the average recognition rate of seven emotions is about 82% when using acoustic data alone. When using glottal data alone, the average recognition rate is about 72%. Using kinematics data alone, the average recognition rate also reaches 55.7%. Therefore, the database is of high quality and can be used as an important source for speech analysis research, especially for the task of multimodal emotional speech analysis.

Recent years have seen rapid development in Information Extraction, as well as its subtask, Relation Extraction. Relation Extraction is able to detect semantic relations between entities in sentences. Currently, many efficient approaches have been applied to relation extraction tasks. Supervised learning approaches especially have good performance. However, there are still many difficult challenges. One of the most serious problems is that manually labeled data is difficult to acquire. In most cases, limited data for supervised approaches equals lousy performance. Thus here, under the situation with only limited training data, we focus on how to improve the performance of our supervised baseline system with unsupervised pre-training. Feature is one of the key components in improving the supervised approaches. Traditional approaches usually apply hand-crafted features, which require expert knowledge and expensive human labor. However, this type of feature might suffer from data sparsity: when the training set size is small, the model parameters might be poorly estimated. In this thesis, we present several novel unsupervised pre-training models to learn the distributed text representation features, which are encoded with rich syntactic-semantic patterns of relation expressions. The experiments have demonstrated that this type of feature, combine with the traditional hand-crafted features, could improve the performance of the logistic classification model for relation extraction, especially on the classification of relations with only minor training instances.

We study the compatibility between the optimal statistical parity solutions and individual fairness. While individual fairness seeks to treat similar individuals similarly, optimal statistical parity aims to provide similar treatment to individuals who share relative similarity within their respective sensitive groups. The two fairness perspectives, while both desirable from a fairness perspective, often come into conflict in applications. Our goal in this work is to analyze the existence of this conflict and its potential solution. In particular, we establish sufficient (sharp) conditions for the compatibility between the optimal (post-processing) statistical parity $L^2$ learning and the ($K$-Lipschitz or $(\epsilon,\delta)$) individual fairness requirements. Furthermore, when there exists a conflict between the two, we first relax the former to the Pareto frontier (or equivalently the optimal trade-off) between $L^2$ error and statistical disparity, and then analyze the compatibility between the frontier and the individual fairness requirements. Our analysis identifies regions along the Pareto frontier that satisfy individual fairness requirements. (Lastly, we provide individual fairness guarantees for the composition of a trained model and the optimal post-processing step so that one can determine the compatibility of the post-processed model.) This provides practitioners with a valuable approach to attain Pareto optimality for statistical parity while adhering to the constraints of individual fairness.

Computer simulations (a.k.a. white-box models) are more indispensable than ever to model intricate engineering systems. However, computational models alone often fail to fully capture the complexities of reality. When physical experiments are accessible though, it is of interest to enhance the incomplete information offered by computational models. Gray-box modeling is concerned with the problem of merging information from data-driven (a.k.a. black-box) models and white-box (i.e., physics-based) models. In this paper, we propose to perform this task by using multi-fidelity surrogate models (MFSMs). A MFSM integrates information from models with varying computational fidelity into a new surrogate model. The multi-fidelity surrogate modeling framework we propose handles noise-contaminated data and is able to estimate the underlying noise-free high-fidelity function. Our methodology emphasizes on delivering precise estimates of the uncertainty in its predictions in the form of confidence and prediction intervals, by quantitatively incorporating the different types of uncertainty that affect the problem, arising from measurement noise and from lack of knowledge due to the limited experimental design budget on both the high- and low-fidelity models. Applied to gray-box modeling, our MFSM framework treats noisy experimental data as the high-fidelity and the white-box computational models as their low-fidelity counterparts. The effectiveness of our methodology is showcased through synthetic examples and a wind turbine application.

Scoring the driving performance of various drivers on a unified scale, based on how safe or economical they drive on their daily trips, is essential for the driver profile task. Connected vehicles provide the opportunity to collect real-world driving data, which is advantageous for constructing scoring models. However, the lack of pre-labeled scores impede the use of supervised regression models and the data privacy issues hinder the way of traditionally data-centralized learning on the cloud side for model training. To address them, an unsupervised scoring method is presented without the need for labels while still preserving fairness and objectiveness compared to subjective scoring strategies. Subsequently, a federated learning framework based on vehicle-cloud collaboration is proposed as a privacy-friendly alternative to centralized learning. This framework includes a consistently federated version of the scoring method to reduce the performance degradation of the global scoring model caused by the statistical heterogeneous challenge of local data. Theoretical and experimental analysis demonstrate that our federated scoring model is consistent with the utility of the centrally learned counterpart and is effective in evaluating driving performance.

Parameter prediction is essential for many applications, facilitating insightful interpretation and decision-making. However, in many real life domains, such as power systems, medicine, and engineering, it can be very expensive to acquire ground truth labels for certain datasets as they may require extensive and expensive laboratory testing. In this work, we introduce a semi-supervised learning approach based on topological projections in self-organizing maps (SOMs), which significantly reduces the required number of labeled data points to perform parameter prediction, effectively exploiting information contained in large unlabeled datasets. Our proposed method first trains SOMs on unlabeled data and then a minimal number of available labeled data points are ultimately assigned to key best matching units (BMU). The values estimated for newly-encountered data points are computed utilizing the average of the $n$ closest labeled data points in the SOM's U-matrix in tandem with a topological shortest path distance calculation scheme. Our results indicate that the proposed semi-supervised model significantly outperforms traditional regression techniques, including linear and polynomial regression, Gaussian process regression, K-nearest neighbors, as well as various deep neural network models.

This personalized approach not only enhances the efficacy of treatments but also minimizes the risk of adverse effects (Agyeman and Ofori-Asenso, 2015; Kumari et al., 2023). However, the success of precision medicine heavily relies on the interpretation of complex, multidimensional data sets, where statistical analysis plays a pivotal role (Alyass et al., 2015). The integration of statistical methodologies in precision medicine is not just a mere addition but a fundamental necessity. Advanced statistical techniques enable the extraction of meaningful insights from large-scale genomics, proteomic, and metabolomic data, which are the cornerstone of precision medicine (Wafi and Mirnezami, 2018; Pinu et al., 2019). These methodologies include, but are not limited to, predictive modeling, machine learning algorithms, and complex data visualization techniques, all of which contribute to more accurate diagnosis, prognosis, and treatment planning (Bellazzi and Zupan, 2008; Davatzikos et al., 2018; Richter and Khoshgoftaar, 2018). The heterogeneity of data sources in precision medicine, ranging from electronic health records (EHRs) to high-throughput sequencing data, presents unique challenges in data integration and interpretation (Martinez-Garcia and Hernández-Lemus, 2022). Statistical analysis serves as a bridge, merging these diverse data types into coherent, interpretable information that can guide clinical decision-making. However, the field is not without its challenges. Issues such as overfitting, handling of highdimensional data, and maintaining the balance between model complexity and interpretability are ongoing areas of research (Bolón-Canedo et al., 2015; Xu et al., 2019; Bommert, 2020; Pes, 2020; Hou and Behdinan, 2022).

Recent text-based causal methods attempt to mitigate confounding bias by including unstructured text data as proxies of confounding variables that are partially or imperfectly measured. These approaches assume analysts have supervised labels of the confounders given text for a subset of instances, a constraint that is not always feasible due to data privacy or cost. Here, we address settings in which an important confounding variable is completely unobserved. We propose a new causal inference method that splits pre-treatment text data, infers two proxies from two zero-shot models on the separate splits, and applies these proxies in the proximal g-formula. We prove that our text-based proxy method satisfies identification conditions required by the proximal g-formula while other seemingly reasonable proposals do not. We evaluate our method in synthetic and semi-synthetic settings and find that it produces estimates with low bias. This combination of proximal causal inference and zero-shot classifiers is novel (to our knowledge) and expands the set of text-specific causal methods available to practitioners.

We present a boosting-based method to learn additive Structural Equation Models (SEMs) from observational data, with a focus on the theoretical aspects of determining the causal order among variables. We introduce a family of score functions based on arbitrary regression techniques, for which we establish necessary conditions to consistently favor the true causal ordering. Our analysis reveals that boosting with early stopping meets these criteria and thus offers a consistent score function for causal orderings. To address the challenges posed by high-dimensional data sets, we adapt our approach through a component-wise gradient descent in the space of additive SEMs. Our simulation study underlines our theoretical results for lower dimensions and demonstrates that our high-dimensional adaptation is competitive with state-of-the-art methods. In addition, it exhibits robustness with respect to the choice of the hyperparameters making the procedure easy to tune.