Nonparametric regression is one of the most extensively studied problems in past decades due to its remarkable flexibility in modeling the relationship between an input X and output Y . While numerous algorithms have been developed, the strong guarantees of learnability and generalization rely on the fact that there are a sufficient number of training samples and that the future data possess the same distribution as the training. However, training sample scarcity in the target domain of interest and distribution shifts occur frequently in practical applications and deteriorate the effectiveness of most existing algorithms both empirically and theoretically. Transfer learning has emerged as an appealing and promising paradigm for addressing these challenges by leveraging samples or pre-trained models from similar, yet not identical, source domains. In this work, we study the problem of transfer learning in the presence of the concept shifts for nonparametric regression over some specific reproducing kernel Hilbert spaces (RKHS). Specifically, we posit there are limited labeled samples from the target domain but sufficient labeled samples from a similar source domain where the concept shifted, namely, the conditional distribution of Y |X changes across domains, which implies the underlying regression function shifts.

The polynomial is fitted using weighted ordinary least-squares, giving more weight to nearby points and less weight to points farther away. The value of the regression function for the point is then obtained by evaluating the fitted local polynomial using the predictor variable value for that data point. LPR has good accuracy near the boundary and performs better than all other linear smoothers in a minimax sense [2]. The biggest advantage of this class of methods is not requiring a prior specification of a function i.e. a parameterized model. Instead, only a small number of hyperparameters need to be specified such as the type of kernel, a smoothing parameter and the degree of the local polynomial. The method is therefore suitable for modeling complex processes such as non-linear relationships, or complex dependencies for which no theoretical models exist. These two advantages, combined with the simplicity of the method, makes it one of the most attractive of the modern regression methods for applications that fit the general framework of least-squares regression but have a complex deterministic structure. Local polynomial regression incorporates the notion of proximity in two ways.

State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against it. Formulated as a min-max problem, it searches for the best solution when the training data were corrupted by the worst-case attacks. Linear models are among the simple models where vulnerabilities can be observed and are the focus of our study. In this case, adversarial training leads to a convex optimization problem which can be formulated as the minimization of a finite sum.

In epidemiology, traditional statistical methods such as logistic regression, linear regression, and other parametric models are commonly employed to investigate associations between predictors and health outcomes. However, non-parametric machine learning techniques, such as deep neural networks (DNNs), coupled with explainable AI (XAI) tools, offer new opportunities for this task. Despite their potential, these methods face challenges due to the limited availability of high-quality, high-quantity data in this field. To address these challenges, we introduce SEANN, a novel approach for informed DNNs that leverages a prevalent form of domain-specific knowledge: Pooled Effect Sizes (PES). PESs are commonly found in published Meta-Analysis studies, in different forms, and represent a quantitative form of a scientific consensus. By direct integration within the learning procedure using a custom loss, we experimentally demonstrate significant improvements in the generalizability of predictive performances and the scientific plausibility of extracted relationships compared to a domain-knowledge agnostic neural network in a scarce and noisy data setting.

Crash frequency modelling analyzes the impact of factors like traffic volume, road geometry, and environmental conditions on crash occurrences. Inaccurate predictions can distort our understanding of these factors, leading to misguided policies and wasted resources, which jeopardize traffic safety. A key challenge in crash frequency modelling is the prevalence of excessive zero observations, caused by underreporting, the low probability of crashes, and high data collection costs. These zero observations often reduce model accuracy and introduce bias, complicating safety decision making. While existing approaches, such as statistical methods, data aggregation, and resampling, attempt to address this issue, they either rely on restrictive assumptions or result in significant information loss, distorting crash data. To overcome these limitations, we propose a hybrid VAE-Diffusion neural network, designed to reduce zero observations and handle the complexities of multi-type tabular crash data (count, ordinal, nominal, and real-valued variables). We assess the synthetic data quality generated by this model through metrics like similarity, accuracy, diversity, and structural consistency, and compare its predictive performance against traditional statistical models. Our findings demonstrate that the hybrid VAE-Diffusion model outperforms baseline models across all metrics, offering a more effective approach to augmenting crash data and improving the accuracy of crash frequency predictions. This study highlights the potential of synthetic data to enhance traffic safety by improving crash frequency modelling and informing better policy decisions.

The double descent phenomenon challenges traditional statistical learning theory by revealing scenarios where larger models do not necessarily lead to reduced performance on unseen data. While this counterintuitive behavior has been observed in a variety of classical machine learning models, particularly modern neural network architectures, it remains elusive within the context of quantum machine learning. In this work, we analytically demonstrate that quantum learning models can exhibit double descent behavior by drawing on insights from linear regression and random matrix theory. Additionally, our numerical experiments on quantum kernel methods across different real-world datasets and system sizes further confirm the existence of a test error peak, a characteristic feature of double descent. Our findings provide evidence that quantum models can operate in the modern, overparameterized regime without experiencing overfitting, thereby opening pathways to improved learning performance beyond traditional statistical learning theory.

We study the canonical problem of linear regression under (\varepsilon,\delta) -differential privacy when the datapoints are sampled i.i.d. We provide the first provably efficient -- both computationally and statistically -- method for this problem, assuming standard assumptions on the data distribution. Our algorithm is a variant of the popular differentially private stochastic gradient descent (DP-SGD) algorithm with two key innovations: a full-batch gradient descent to improve sample complexity and a novel adaptive clipping to guarantee robustness. Our method requires only linear time in input size, and still matches the information theoretical optimal sample complexity up to a data distribution dependent condition number factor. Interestingly, the same algorithm, when applied to a setting where there is no adversarial corruption, still improves upon the existing state-of-the-art and achieves a near optimal sample complexity.

Bayesian Additive Regression Trees [BART, Chipman et al., 2010] have gained significant popularity due to their remarkable predictive performance and ability to quantify uncertainty. However, standard decision tree models rely on recursive data splits at each decision node, using deterministic decision rules based on a single univariate feature. This approach limits their ability to effectively capture complex decision boundaries, particularly in scenarios involving multiple features, such as spatial domains, or when transitions are either sharp or smoothly varying. In this paper, we introduce a novel probabilistic additive decision tree model that employs a soft split rule. This method enables highly flexible splits that leverage both univariate and multivariate features, while also respecting the geometric properties of the feature domain. Notably, the probabilistic split rule adapts dynamically across decision nodes, allowing the model to account for varying levels of smoothness in the regression function. We demonstrate the utility of the proposed model through comparisons with existing tree-based models on synthetic datasets and a New York City education dataset.

Meta learning has demonstrated tremendous success in few-shot learning with limited supervised data. In those settings, the meta model is usually overparameterized. While the conventional statistical learning theory suggests that overparameterized models tend to overfit, empirical evidence reveals that overparameterized meta learning methods still work well -- a phenomenon often called benign overfitting.'' To understand this phenomenon, we focus on the meta learning settings with a challenging bilevel structure that we term the gradient-based meta learning, and analyze its generalization performance under an overparameterized meta linear regression model. While our analysis uses the relatively tractable linear models, our theory contributes to understanding the delicate interplay among data heterogeneity, model adaptation and benign overfitting in gradient-based meta learning tasks.

The present study examines the effectiveness of applying Artificial Intelligence methods in an automotive production environment to predict unknown lead times in a non-cycle-controlled production area. Data structures are analyzed to identify contextual features and then preprocessed using one-hot encoding. Methods selection focuses on supervised machine learning techniques. In supervised learning methods, regression and classification methods are evaluated. Continuous regression based on target size distribution is not feasible. Classification methods analysis shows that Ensemble Learning and Support Vector Machines are the most suitable. Preliminary study results indicate that gradient boosting algorithms LightGBM, XGBoost, and CatBoost yield the best results. After further testing and extensive hyperparameter optimization, the final method choice is the LightGBM algorithm. Depending on feature availability and prediction interval granularity, relative prediction accuracies of up to 90% can be achieved. Further tests highlight the importance of periodic retraining of AI models to accurately represent complex production processes using the database. The research demonstrates that AI methods can be effectively applied to highly variable production data, adding business value by providing an additional metric for various control tasks while outperforming current non AI-based systems.