Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of reasons. First, it comes with a rich mathematical structure to account for a wide range of non-linear geometries that has been shown to be able to capture the data geometry through empirical evidence from classical non-linear embedding. Second, many standard data analysis tools initially developed for data in Euclidean space can also be generalised efficiently to data on a symmetric Riemannian manifold. A conceptual challenge comes from the lack of guidelines for constructing a symmetric Riemannian structure on the data space itself and the lack of guidelines for modifying successful algorithms on symmetric Riemannian manifolds for data analysis to this setting. This work considers these challenges in the setting of pullback Riemannian geometry through a diffeomorphism. The first part of the paper characterises diffeomorphisms that result in proper, stable and efficient data analysis. The second part then uses these best practices to guide construction of such diffeomorphisms through deep learning. As a proof of concept, different types of pullback geometries -- among which the proposed construction -- are tested on several data analysis tasks and on several toy data sets. The numerical experiments confirm the predictions from theory, i.e., that the diffeomorphisms generating the pullback geometry need to map the data manifold into a geodesic subspace of the pulled back Riemannian manifold while preserving local isometry around the data manifold for proper, stable and efficient data analysis, and that pulling back positive curvature can be problematic in terms of stability.

Remarkable successes were made in Medical Image Classification (MIC) recently, mainly due to wide applications of convolutional neural networks (CNNs). However, adversarial examples (AEs) exhibited imperceptible similarity with raw data, raising serious concerns on network robustness. Although adversarial training (AT), in responding to malevolent AEs, was recognized as an effective approach to improve robustness, it was challenging to overcome generalization decline of networks caused by the AT. In this paper, in order to reserve high generalization while improving robustness, we proposed a dynamic perturbation-adaptive adversarial training (DPAAT) method, which placed AT in a dynamic learning environment to generate adaptive data-level perturbations and provided a dynamically updated criterion by loss information collections to handle the disadvantage of fixed perturbation sizes in conventional AT methods and the dependence on external transference. Comprehensive testing on dermatology HAM10000 dataset showed that the DPAAT not only achieved better robustness improvement and generalization preservation but also significantly enhanced mean average precision and interpretability on various CNNs, indicating its great potential as a generic adversarial training method on the MIC.

High-performing out-of-distribution (OOD) detection, both anomaly and novel class, is an important prerequisite for the practical use of classification models. In this paper, we focus on the species recognition task in images concerned with large databases, a large number of fine-grained hierarchical classes, severe class imbalance, and varying image quality. We propose a framework for combining individual OOD measures into one combined OOD (COOD) measure using a supervised model. The individual measures are several existing state-of-the-art measures and several novel OOD measures developed with novel class detection and hierarchical class structure in mind. COOD was extensively evaluated on three large-scale (500k+ images) biodiversity datasets in the context of anomaly and novel class detection. We show that COOD outperforms individual, including state-of-the-art, OOD measures by a large margin in terms of TPR@1% FPR in the majority of experiments, e.g., improving detecting ImageNet images (OOD) from 54.3% to 85.4% for the iNaturalist 2018 dataset. SHAP (feature contribution) analysis shows that different individual OOD measures are essential for various tasks, indicating that multiple OOD measures and combinations are needed to generalize. Additionally, we show that explicitly considering ID images that are incorrectly classified for the original (species) recognition task is important for constructing high-performing OOD detection methods and for practical applicability. The framework can easily be extended or adapted to other tasks and media modalities.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

One aspect of the algorithmic lens in theoretical computer science is a view on other scientific disciplines that focuses on satisfactory solutions that adhere to real-world constraints, as opposed to solutions that would be optimal ignoring such constraints. The algorithmic lens has provided a unique and important perspective on many academic fields, including molecular biology, ecology, neuroscience, quantum physics, economics, and social science. This thesis applies the algorithmic lens to Bayesian epistemology. Traditional Bayesian epistemology provides a comprehensive framework for how an individual's beliefs should evolve upon receiving new information. However, these methods typically assume an exhaustive model of such information, including the correlation structure between different pieces of evidence. In reality, individuals might lack such an exhaustive model, while still needing to form beliefs. Beyond such informational constraints, an individual may be bounded by limited computation, or by limited communication with agents that have access to information, or by the strategic behavior of such agents. Even when these restrictions prevent the formation of a *perfectly* accurate belief, arriving at a *reasonably* accurate belief remains crucial. In this thesis, we establish fundamental possibility and impossibility results about belief formation under a variety of restrictions, and lay the groundwork for further exploration.

Social media platforms hold valuable insights, yet extracting essential information can be challenging. Traditional top-down approaches often struggle to capture critical signals in rapidly changing events. As global events evolve swiftly, social media narratives, including instances of disinformation, become significant sources of insights. To address the need for an inductive strategy, we explore a niche social media platform GAB and an established messaging service Telegram, to develop methodologies applicable on a broader scale. This study investigates narrative evolution on these platforms using quantitative corpus-based discourse analysis techniques. Our approach is a novel mode to study multiple social media domains to distil key information which may be obscured otherwise, allowing for useful and actionable insights. The paper details the technical and methodological aspects of gathering and preprocessing GAB and Telegram data for a keyness (Log Ratio) metric analysis, identifying crucial nouns and verbs for deeper exploration. Empirically, this approach is applied to a case study of a well defined event that had global impact: the 2023 Wagner mutiny. The main findings are: (1) the time line can be deconstructed to provide useful data features allowing for improved interpretation; (2) a methodology is applied which provides a basis for generalization. The key contribution is an approach, that in some cases, provides the ability to capture the dynamic narrative shifts over time with elevated confidence. The approach can augment near-real-time assessment of key social movements, allowing for informed governance choices. This research is important because it lays out a useful methodology for time series relevant info-culling, which can enable proactive modes for positive social engagement.

Process mining in healthcare presents a range of challenges when working with different types of data within the healthcare domain. There is high diversity considering the variety of data collected from healthcare processes: operational processes given by claims data, a collection of events during surgery, data related to pre-operative and post-operative care, and high-level data collections based on regular ambulant visits with no apparent events. In this case study, a data set from the last category is analyzed. We apply process-mining techniques on sparse patient heart failure data and investigate whether an information gain towards several research questions is achievable. Here, available data are transformed into an event log format, and process discovery and conformance checking are applied. Additionally, patients are split into different cohorts based on comorbidities, such as diabetes and chronic kidney disease, and multiple statistics are compared between the cohorts. Conclusively, we apply decision mining to determine whether a patient will have a cardiovascular outcome and whether a patient will die.

Graphs are ubiquitous in social networks and biochemistry, where Graph Neural Networks (GNN) are the state-of-the-art models for prediction. Graphs can be evolving and it is vital to formally model and understand how a trained GNN responds to graph evolution. We propose a smooth parameterization of the GNN predicted distributions using axiomatic attribution, where the distributions are on a low-dimensional manifold within a high-dimensional embedding space. We exploit the differential geometric viewpoint to model distributional evolution as smooth curves on the manifold. We reparameterize families of curves on the manifold and design a convex optimization problem to find a unique curve that concisely approximates the distributional evolution for human interpretation. Extensive experiments on node classification, link prediction, and graph classification tasks with evolving graphs demonstrate the better sparsity, faithfulness, and intuitiveness of the proposed method over the state-of-the-art methods. Graph neural networks (GNN) are now the state-of-the-art method for graph representation in many applications, such as social network modeling Kipf & Welling (2017) and molecule property prediction Wu et al. (2017), pose estimation in computer vision Yang et al. (2021), smart cities Ye et al. (2020), fraud detection Wang et al. (2019), and recommendation systems Ying et al. (2018). A GNN outputs a probability distribution Pr(Y |G; θ) of Y, the class random variable of a node (node classification), a link (link prediction), or a graph (graph classification), using trained parameters θ.

A recent research trend involves treating database index structures as Machine Learning (ML) models. In this domain, single or multiple ML models are trained to learn the mapping from keys to positions inside a data set. This class of indexes is known as "Learned Indexes." Learned indexes have demonstrated improved search performance and reduced space requirements for one-dimensional data. The concept of one-dimensional learned indexes has naturally been extended to multi-dimensional (e.g., spatial) data, leading to the development of "Learned Multi-dimensional Indexes". This survey focuses on learned multi-dimensional index structures. Specifically, it reviews the current state of this research area, explains the core concepts behind each proposed method, and classifies these methods based on several well-defined criteria. We present a taxonomy that classifies and categorizes each learned multi-dimensional index, and survey the existing literature on learned multi-dimensional indexes according to this taxonomy. Additionally, we present a timeline to illustrate the evolution of research on learned indexes. Finally, we highlight several open challenges and future research directions in this emerging and highly active field.

Although there is not an ideal biotype for all production systems, the adequate biotype should be determined according to the objectives that have been established for the herd, along with the production system being practiced [9]. This is not without consequences. For instance, larger animals usually have higher nutritional and general maintenance requirements [7]. Among the methods used to evaluate beef cattle, the EPMURAS methodology synthesized by Koury Filho [11], Koury Filho et al. [13] is one of the most utilized in Brazil. It consists in a visual assessment of body structure, precocity, muscularity, sheath, racial aspects, angulation and sexuality.