In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good starting model to avoid producing non-physical solutions. Moreover, conventional optimization methods fail to quantify the uncertainty associated with the recovered solution, which is critical for decision-making processes. Bayesian inference offers an alternative approach as it directly or indirectly evaluates the posterior probability density function. For example, Markov Chain Monte Carlo (MCMC) methods generate multiple sample chains to characterize the solution's uncertainty. Despite their ability to theoretically handle any form of distribution, MCMC methods require many sampling steps; this limits their usage in high-dimensional problems with computationally intensive forward modeling, as is the FWI case. Variational Inference (VI), on the other hand, provides an approximate solution to the posterior distribution in the form of a parametric or non-parametric proposal distribution. Among the various algorithms used in VI, Stein Variational Gradient Descent (SVGD) is recognized for its ability to iteratively refine a set of samples to approximate the target distribution. However, mode and variance-collapse issues affect SVGD in high-dimensional inverse problems. This study aims to improve the performance of SVGD within the context of FWI by utilizing, for the first time, an annealed variant of SVGD and combining it with a multi-scale strategy. Additionally, we demonstrate that Principal Component Analysis (PCA) can be used to evaluate the performance of the optimization process. Clustering techniques are also employed to provide more rigorous and meaningful statistical analysis of the particles in the presence of multi-modal distributions.

Traditional clustering algorithms often focus on the most fine-grained information and achieve clustering by calculating the distance between each pair of data points or implementing other calculations based on points. This way is not inconsistent with the cognitive mechanism of "global precedence" in human brain, resulting in those methods' bad performance in efficiency, generalization ability and robustness. To address this problem, we propose a new clustering algorithm called granular-ball clustering (GBCT) via granular-ball computing. Firstly, GBCT generates a smaller number of granular-balls to represent the original data, and forms clusters according to the relationship between granular-balls, instead of the traditional point relationship. At the same time, its coarse-grained characteristics are not susceptible to noise, and the algorithm is efficient and robust; besides, as granular-balls can fit various complex data, GBCT performs much better in non-spherical data sets than other traditional clustering methods. The completely new coarse granularity representation method of GBCT and cluster formation mode can also used to improve other traditional methods.

Privacy personas capture the differences in user segments with respect to one's knowledge, behavioural patterns, level of self-efficacy, and perception of the importance of privacy protection. Modelling these differences is essential for appropriately choosing personalised communication about privacy (e.g. to increase literacy) and for defining suitable choices for privacy enhancing technologies (PETs). While various privacy personas have been derived in the literature, they group together people who differ from each other in terms of important attributes such as perceived or desired level of control, and motivation to use PET. To address this lack of granularity and comprehensiveness in describing personas, we propose eight personas that we derive by combining qualitative and quantitative analysis of the responses to an interactive educational questionnaire. We design an analysis pipeline that uses divisive hierarchical clustering and Boschloo's statistical test of homogeneity of proportions to ensure that the elicited clusters differ from each other based on a statistical measure. Additionally, we propose a new measure for calculating distances between questionnaire responses, that accounts for the type of the question (closed- vs open-ended) used to derive traits. We show that the proposed privacy personas statistically differ from each other. We statistically validate the proposed personas and also compare them with personas in the literature, showing that they provide a more granular and comprehensive understanding of user segments, which will allow to better assist users with their privacy needs.

One significant application is in nutrition science, where ML models can provide dietary recommendations, detect food quality and safety issues during production, and surveil public health and epidemiology. However, the complex and often opaque nature of these models presents challenges in understanding and trusting their predictions. To address these issues, explainability techniques have garnered considerable interest, aiming to make ML models more interpretable and transparent. Explainability can be approached from different perspectives, including local explanations that focus on individual predictions and global explanations that provide insights into the overall behavior of the model. However, there is a growing need for intermediate-level explanations that balance these two extremes, offering contextually relevant insights that are both comprehensive and specific (Sokol and Flach, 2020; Arrieta et al., 2020; Adadi and Berrada, 2018). Cohort explainability, also referred to as subgroup explainability, explains model predictions by analyzing groups of instances with shared characteristics and emerges as a promising solution to this challenge.

Natural Language Processing (NLP) is a vital computational method for addressing language processing, analysis, and generation. NLP tasks form the core of many daily applications, from automatic text correction to speech recognition. While significant research has focused on NLP tasks for the English language, less attention has been given to Modern Standard Arabic and Dialectal Arabic. Globalization has also contributed to the rise of Code-Switching (CS), where speakers mix languages within conversations and even within individual words (intra-word CS). This is especially common in Arab countries, where people often switch between dialects or between dialects and a foreign language they master. CS between Arabic and English is frequent in Egypt, especially on social media. Consequently, a significant amount of code-switched content can be found online. Such code-switched data needs to be investigated and analyzed for several NLP tasks to tackle the challenges of this multilingual phenomenon and Arabic language challenges. No work has been done before for several integral NLP tasks on Arabic-English CS data. In this work, we focus on the Named Entity Recognition (NER) task and other tasks that help propose a solution for the NER task on CS data, e.g., Language Identification. This work addresses this gap by proposing and applying state-of-the-art techniques for Modern Standard Arabic and Arabic-English NER. We have created the first annotated CS Arabic-English corpus for the NER task. Also, we apply two enhancement techniques to improve the NER tagger on CS data using CS contextual embeddings and data augmentation techniques. All methods showed improvements in the performance of the NER taggers on CS data. Finally, we propose several intra-word language identification approaches to determine the language type of a mixed text and identify whether it is a named entity or not.

We provide necessary and sufficient conditions for the uniqueness of the k-means set of a probability distribution. This uniqueness problem is related to the choice of k: depending on the underlying distribution, some values of this parameter could lead to multiple sets of k-means, which hampers the interpretation of the results and/or the stability of the algorithms. We give a general assessment on consistency of the empirical k-means adapted to the setting of non-uniqueness and determine the asymptotic distribution of the within cluster sum of squares (WCSS). We also provide statistical characterizations of k-means uniqueness in terms of the asymptotic behavior of the empirical WCSS. As a consequence, we derive a bootstrap test for uniqueness of the set of k-means. The results are illustrated with examples of different types of non-uniqueness and we check by simulations the performance of the proposed methodology.

Temporal graph clustering is a complex task that involves discovering meaningful structures in dynamic graphs where relationships and entities change over time. Existing methods typically require centralized data collection, which poses significant privacy and communication challenges. In this work, we introduce a novel Federated Temporal Graph Clustering (FTGC) framework that enables decentralized training of graph neural networks (GNNs) across multiple clients, ensuring data privacy throughout the process. Our approach incorporates a temporal aggregation mechanism to effectively capture the evolution of graph structures over time and a federated optimization strategy to collaboratively learn high-quality clustering representations. By preserving data privacy and reducing communication overhead, our framework achieves competitive performance on temporal graph datasets, making it a promising solution for privacy-sensitive, real-world applications involving dynamic data.

Data summarization tasks are often modeled as $k$-clustering problems, where the goal is to choose $k$ data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to minimize the maximum distance between any data point and its nearest center, which is formalized as the $k$-center problem. While in some applications all data points can be chosen as centers, in the general setting, centers must be chosen from a predefined subset of points, referred as facilities or suppliers; this is known as the $k$-supplier problem. In this work, we focus on fair data summarization modeled as the fair $k$-supplier problem, where data consists of several groups, and a minimum number of centers must be selected from each group while minimizing the $k$-supplier objective. The groups can be disjoint or overlapping, leading to two distinct problem variants each with different computational complexity. We present $3$-approximation algorithms for both variants, improving the previously known factor of $5$. For disjoint groups, our algorithm runs in polynomial time, while for overlapping groups, we present a fixed-parameter tractable algorithm, where the exponential runtime depends only on the number of groups and centers. We show that these approximation factors match the theoretical lower bounds, assuming standard complexity theory conjectures. Finally, using an open-source implementation, we demonstrate the scalability of our algorithms on large synthetic datasets and assess the price of fairness on real-world data, comparing solution quality with and without fairness constraints.

Recent advances in Retrieval-Augmented Generation (RAG) systems have popularized semantic chunking, which aims to improve retrieval performance by dividing documents into semantically coherent segments. Despite its growing adoption, the actual benefits over simpler fixed-size chunking, where documents are split into consecutive, fixed-size segments, remain unclear. This study systematically evaluates the effectiveness of semantic chunking using three common retrieval-related tasks: document retrieval, evidence retrieval, and retrieval-based answer generation. The results show that the computational costs associated with semantic chunking are not justified by consistent performance gains. These findings challenge the previous assumptions about semantic chunking and highlight the need for more efficient chunking strategies in RAG systems.

Large Language Models (LLMs) rely on the contextual information embedded in examples/demonstrations to perform in-context learning (ICL). To mitigate the risk of LLMs potentially leaking private information contained in examples in the prompt, we introduce a novel data-adaptive differentially private algorithm called AdaDPSyn to generate synthetic examples from the private dataset and then use these synthetic examples to perform ICL. The objective of AdaDPSyn is to adaptively adjust the noise level in the data synthesis mechanism according to the inherent statistical properties of the data, thereby preserving high ICL accuracy while maintaining formal differential privacy guarantees. A key innovation in AdaDPSyn is the Precision-Focused Iterative Radius Reduction technique, which dynamically refines the aggregation radius - the scope of data grouping for noise addition - based on patterns observed in data clustering, thereby minimizing the amount of additive noise. We conduct extensive experiments on standard benchmarks and compare AdaDPSyn with DP few-shot generation algorithm (Tang et al., 2023). The experiments demonstrate that AdaDPSyn not only outperforms DP few-shot generation, but also maintains high accuracy levels close to those of non-private baselines, providing an effective solution for ICL with privacy protection.