This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods. We show how these techniques emerge from familiar statistical foundations. The consistently Bayesian perspective prioritizes uncertainty quantification and statistical rigor essential for scientific inference in astronomy. The textbook progresses from probability theory and Bayesian inference through supervised learning including linear regression with measurement uncertainties, logistic regression, and classification. Unsupervised learning topics cover Principal Component Analysis and clustering methods. We then introduce computational techniques through sampling and Markov Chain Monte Carlo, followed by Gaussian Processes as probabilistic nonparametric methods and neural networks within the broader statistical context. Our theory-focused pedagogical approach derives each method from first principles with complete mathematical development, emphasizing statistical insight and complementing with astronomical applications. We prioritize understanding why algorithms work, when they are appropriate, and how they connect to broader statistical principles. The treatment builds toward modern techniques including neural networks through a solid foundation in classical methods and their theoretical underpinnings. This foundation enables thoughtful application of these methods to astronomical research, ensuring proper consideration of assumptions, limitations, and uncertainty propagation essential for advancing astronomical knowledge in the era of large astronomical surveys.

This work presents three different approaches to address the ArchEHR-QA 2025 Shared Task on automated patient question answering. We introduce an end-to-end prompt-based baseline and two two-step methods to divide the task, without utilizing any external knowledge. Both two step approaches first extract essential sentences from the clinical text, by prompt or similarity ranking, and then generate the final answer from these notes. Results indicate that the re-ranker based two-step system performs best, highlighting the importance of selecting the right approach for each subtask. Our best run achieved an overall score of 0.44, ranking 8th out of 30 on the leaderboard, securing the top position in overall factuality.

Decoder-only large language models have shown superior performance in the fluency-edit English Grammatical Error Correction, but their adaptation for minimal-edit English GEC is still underexplored. To improve their effectiveness in the minimal-edit approach, we explore the error rate adaptation topic and propose a novel training schedule method. Our experiments set a new state-of-the-art result for a single-model system on the BEA-test set. We also detokenize the most common English GEC datasets to match the natural way of writing text. During the process, we find that there are errors in them. Our experiments analyze whether training on detokenized datasets impacts the results and measure the impact of the usage of the datasets with corrected erroneous examples. To facilitate reproducibility, we have released the source code used to train our models.

With the growing prominence of antibody - based therapeutics, antibody engineering has gained increasing attention as a critical area of research and development. Recent progress in transformer - based protein large language models (LLMs) has demonstrated prom ising applications in protein sequence design and structural prediction. Moreover, the availability of large - scale antibody datasets such as the Observed Antibody Space (OAS) database has opened new avenues for the development of LLMs specialized for proce ssing antibody sequences . Among these, RoBERTa has demonstrated improved performance relative to BERT, while maintaining a smaller parameter count (125M) compared to the BERT - based protein model, ProtBERT (420M). This reduced model size enables more efficient deployment in antibody - related application s . However, despite the numerous advantages of the RoBERTa architecture, antibody - specific foundational models built upon it have remained inaccessible to the research community. In this study, we introduce Ab - RoBERTa, a RoBERTa - based antibody - specific LLM, which is publicly available at https://huggingface.co/mogam - ai/Ab - RoBERTa . This resource is intended to support a wide range of antibody - related research applications including paratope prediction or humanness assessment .

Deep neural networks (DNNs) rely heavily on high-quality open-source datasets (e.g., ImageNet) for their success, making dataset ownership verification (DOV) crucial for protecting public dataset copyrights. In this paper, we find existing DOV methods (implicitly) assume that the verification process is faithful, where the suspicious model will directly verify ownership by using the verification samples as input and returning their results. However, this assumption may not necessarily hold in practice and their performance may degrade sharply when subjected to intentional or unintentional perturbations. To address this limitation, we propose the first certified dataset watermark (i.e., CertDW) and CertDW-based certified dataset ownership verification method that ensures reliable verification even under malicious attacks, under certain conditions (e.g., constrained pixel-level perturbation). Specifically, inspired by conformal prediction, we introduce two statistical measures, including principal probability (PP) and watermark robustness (WR), to assess model prediction stability on benign and watermarked samples under noise perturbations. We prove there exists a provable lower bound between PP and WR, enabling ownership verification when a suspicious model's WR value significantly exceeds the PP values of multiple benign models trained on watermark-free datasets. If the number of PP values smaller than WR exceeds a threshold, the suspicious model is regarded as having been trained on the protected dataset. Extensive experiments on benchmark datasets verify the effectiveness of our CertDW method and its resistance to potential adaptive attacks. Our codes are at \href{https://github.com/NcepuQiaoTing/CertDW}{GitHub}.

Researchers in urban and regional studies increasingly deal with spatial data that reflects geographic location and spatial relationships. As a framework for dealing with the unique nature of spatial data, various spatial regression models have been introduced. In this article, a novel model-based gradient boosting algorithm for spatial regression models with autoregressive disturbances is proposed. Due to the modular nature, the approach provides an alternative estimation procedure which is feasible even in high-dimensional settings where established quasi-maximum likelihood or generalized method of moments estimators do not yield unique solutions. The approach additionally enables data-driven variable and model selection in low- as well as high-dimensional settings. Since the bias-variance trade-off is also controlled in the algorithm, implicit regularization is imposed which improves prediction accuracy on out-of-sample spatial data. Detailed simulation studies regarding the performance of estimation, prediction and variable selection in low- and high-dimensional settings confirm proper functionality of the proposed methodology. To illustrative the functionality of the model-based gradient boosting algorithm, a case study is presented where the life expectancy in German districts is modeled incorporating a potential spatial dependence structure.

Evaluating anomaly detection in multivariate time series (MTS) requires careful consideration of temporal dependencies, particularly when detecting subsequence anomalies common in fault detection scenarios. While time series cross-validation (TSCV) techniques aim to preserve temporal ordering during model evaluation, their impact on classifier performance remains underexplored. This study systematically investigates the effect of TSCV strategy on the precision-recall characteristics of classifiers trained to detect fault-like anomalies in MTS datasets. We compare walk-forward (WF) and sliding window (SW) methods across a range of validation partition configurations and classifier types, including shallow learners and deep learning (DL) classifiers. Results show that SW consistently yields higher median AUC-PR scores and reduced fold-to-fold performance variance, particularly for deep architectures sensitive to localized temporal continuity. Furthermore, we find that classifier generalization is sensitive to the number and structure of temporal partitions, with overlapping windows preserving fault signatures more effectively at lower fold counts. A classifier-level stratified analysis reveals that certain algorithms, such as random forests (RF), maintain stable performance across validation schemes, whereas others exhibit marked sensitivity. This study demonstrates that TSCV design in benchmarking anomaly detection models on streaming time series and provide guidance for selecting evaluation strategies in temporally structured learning environments.

Given trajectory data, a domain-specific study area, and a user-defined threshold, we aim to find anomalous trajectories indicative of possible GPS spoofing (e.g., fake trajectory). The problem is societally important to curb illegal activities in international waters, such as unauthorized fishing and illicit oil transfers. The problem is challenging due to advances in AI generated in deep fakes generation (e.g., additive noise, fake trajectories) and lack of adequate amount of labeled samples for ground-truth verification. Recent literature shows promising results for anomalous trajectory detection using generative models despite data sparsity. However, they do not consider fine-scale spatiotemporal dependencies and prior physical knowledge, resulting in higher false-positive rates. To address these limitations, we propose a physics-informed diffusion model that integrates kinematic constraints to identify trajectories that do not adhere to physical laws. Experimental results on real-world datasets in the maritime and urban domains show that the proposed framework results in higher prediction accuracy and lower estimation error rate for anomaly detection and trajectory generation methods, respectively. Our implementation is available at https://github.com/arunshar/Physics-Informed-Diffusion-Probabilistic-Model.

We propose Network Automatic Relevance Determination (NARD), an extension of ARD for linearly probabilistic models, to simultaneously model sparse relationships between inputs $X \in \mathbb R^{d \times N}$ and outputs $Y \in \mathbb R^{m \times N}$, while capturing the correlation structure among the $Y$. NARD employs a matrix normal prior which contains a sparsity-inducing parameter to identify and discard irrelevant features, thereby promoting sparsity in the model. Algorithmically, it iteratively updates both the precision matrix and the relationship between $Y$ and the refined inputs. To mitigate the computational inefficiencies of the $\mathcal O(m^3 + d^3)$ cost per iteration, we introduce Sequential NARD, which evaluates features sequentially, and a Surrogate Function Method, leveraging an efficient approximation of the marginal likelihood and simplifying the calculation of determinant and inverse of an intermediate matrix. Combining the Sequential update with the Surrogate Function method further reduces computational costs. The computational complexity per iteration for these three methods is reduced to $\mathcal O(m^3+p^3)$, $\mathcal O(m^3 + d^2)$, $\mathcal O(m^3+p^2)$, respectively, where $p \ll d$ is the final number of features in the model. Our methods demonstrate significant improvements in computational efficiency with comparable performance on both synthetic and real-world datasets.

Causal discovery (CD) plays a pivotal role in understanding the mechanisms underlying complex systems. While recent algorithms can detect spurious associations and latent confounding, many struggle to recover fairness-relevant pathways in realistic, noisy settings. Large Language Models (LLMs), with their access to broad semantic knowledge, offer a promising complement to statistical CD approaches, particularly in domains where metadata provides meaningful relational cues. Ensuring fairness in machine learning requires understanding how sensitive attributes causally influence outcomes, yet CD methods often introduce spurious or biased pathways. We propose a hybrid LLM-based framework for CD that extends a breadth-first search (BFS) strategy with active learning and dynamic scoring. Variable pairs are prioritized for LLM-based querying using a composite score based on mutual information, partial correlation, and LLM confidence, improving discovery efficiency and robustness. To evaluate fairness sensitivity, we construct a semi-synthetic benchmark from the UCI Adult dataset, embedding a domain-informed causal graph with injected noise, label corruption, and latent confounding. We assess how well CD methods recover both global structure and fairness-critical paths. Our results show that LLM-guided methods, including the proposed method, demonstrate competitive or superior performance in recovering such pathways under noisy conditions. We highlight when dynamic scoring and active querying are most beneficial and discuss implications for bias auditing in real-world datasets.