Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns. However, conventional density estimators based on uniform histograms often fail to capture local variations, especially when the underlying distribution is highly nonuniform. Furthermore, the inherent discontinuity of histograms poses challenges for tasks requiring smooth derivatives, such as gradient-based optimization, clustering, and nonparametric discriminant analysis. In this work, we present a novel non-parametric approach for multivariate probability density function (PDF) estimation that utilizes minimum description length (MDL)-based binning with quantile cuts. Our approach builds upon tensor factorization techniques, leveraging the canonical polyadic decomposition (CPD) of a joint probability tensor. We demonstrate the effectiveness of our method on synthetic data and a challenging real dry bean classification dataset.

To improve the segmentation of diabetic retinopathy lesions (microaneurysms, hemorrhages, exudates, and soft exudates), we implemented a binary segmentation method specific to each type of lesion. As post-segmentation, we combined the individual model outputs into a single image to better analyze the lesion types. This approach facilitated parameter optimization and improved accuracy, effectively overcoming challenges related to dataset limitations and annotation complexity. Specific preprocessing steps included cropping and applying contrast-limited adaptive histogram equalization to the L channel of the LAB image. Additionally, we employed targeted data augmentation techniques to further refine the model's efficacy. Our methodology utilized the DeepLabv3+ model, achieving a segmentation accuracy of 99%. These findings highlight the efficacy of innovative strategies in advancing medical image analysis, particularly in the precise segmentation of diabetic retinopathy lesions. The IDRID dataset was utilized to validate and demonstrate the robustness of our approach.

In this study, we develop Neural Machine Translation (NMT) and Transformer-based transfer learning models for English-to-Igbo translation - a low-resource African language spoken by over 40 million people across Nigeria and West Africa. Our models are trained on a curated and benchmarked dataset compiled from Bible corpora, local news, Wikipedia articles, and Common Crawl, all verified by native language experts. We leverage Recurrent Neural Network (RNN) architectures, including Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU), enhanced with attention mechanisms to improve translation accuracy. To further enhance performance, we apply transfer learning using MarianNMT pre-trained models within the SimpleTransformers framework. Our RNN-based system achieves competitive results, closely matching existing English-Igbo benchmarks. With transfer learning, we observe a performance gain of +4.83 BLEU points, reaching an estimated translation accuracy of 70%. These findings highlight the effectiveness of combining RNNs with transfer learning to address the performance gap in low-resource language translation tasks.

Defeasible conditionals are a form of non-monotonic inference which enable the expression of statements like "if $ϕ$ then normally $ψ$". The KLM framework defines a semantics for the propositional case of defeasible conditionals by construction of a preference ordering over possible worlds. The pattern of reasoning induced by these semantics is characterised by consequence relations satisfying certain desirable properties of non-monotonic reasoning. In FCA, implications are used to describe dependencies between attributes. However, these implications are unsuitable to reason with erroneous data or data prone to exceptions. Until recently, the topic of non-monotonic inference in FCA has remained largely uninvestigated. In this paper, we provide a construction of the KLM framework for defeasible reasoning in FCA and show that this construction remains faithful to the principle of non-monotonic inference described in the original framework. We present an additional argument that, while remaining consistent with the original ideas around non-monotonic reasoning, the defeasible reasoning we propose in FCA offers a more contextual view on inference, providing the ability for more relevant conclusions to be drawn when compared to the propositional case.

While many models have been developed that can produce such probabilistic predictions, it is often the case that predictions are required for multiple related tasks, such that it would be desirable to have a probabilistic model that can make rapid predictions on new tasks without the need for task-specific training. Such is the case in the probabilistic meta-learning paradigm. While meta-learning has received an abundance of attention from the research community over the last decade (Finn et al., 2017; Gordon et al., 2019; Hospedales et al., 2022), the most notable class of probabilistic meta-model is, without doubt, the neural process family (NP; Garnelo et al., 2018a,b; Dubois et al., 2020). Recent advances in NPs have led them to reach astonishing heights in performance, representing the state-of-the-art in data-based approaches to weather and climate modeling (Bodnar et al., 2024; Allen et al., 2025; Ashman et al., 2024b), for example. Despite such impressive performance, industry practitioners seldom opt for deep learning models owing to their inherent lack of interpretability (Li et al., 2022), and instead prefer more traditional approaches such as kernel methods (Hofmann et al., 2008) that are easier to explain to non-technical stakeholders, even if they are incapable of meta-learning. Perhaps the most ubiquitous probabilistic model that practitioners turn to is the Gaussian process (GP; Rasmussen and Williams, 2005). With GPs, users can leverage their domain expertise to specify meaningful priors with which to bias predictions, any free parameters tend to have clear interpretations, and schemes such as automatic relevance T. Rochussen & V. Fortuin.

In many real-world machine learning (ML) applications (e.g. detecting broken bones in x-ray images, detecting species in camera traps), in practice models need to perform well on specific deployments (e.g. a specific hospital, a specific national park) rather than the domain broadly. However, deployments often have imbalanced, unique data distributions. Discrepancy between the training distribution and the deployment distribution can lead to suboptimal performance, highlighting the need to select deployment-specialized subsets from the available training data. We formalize dataset subset selection for specialization (DS3): given a training set drawn from a general distribution and a (potentially unlabeled) query set drawn from the desired deployment-specific distribution, the goal is to select a subset of the training data that optimizes deployment performance. We introduce DataS^3; the first dataset and benchmark designed specifically for the DS3 problem. DataS^3 encompasses diverse real-world application domains, each with a set of distinct deployments to specialize in. We conduct a comprehensive study evaluating algorithms from various families--including coresets, data filtering, and data curation--on DataS^3, and find that general-distribution methods consistently fail on deployment-specific tasks. Additionally, we demonstrate the existence of manually curated (deployment-specific) expert subsets that outperform training on all available data with accuracy gains up to 51.3 percent. Our benchmark highlights the critical role of tailored dataset curation in enhancing performance and training efficiency on deployment-specific distributions, which we posit will only become more important as global, public datasets become available across domains and ML models are deployed in the real world.

--Vision systems are increasingly deployed in critical domains such as surveillance, law enforcement, and transportation. However, their vulnerabilities to rare or unforeseen scenarios pose significant safety risks. T o address these challenges, we introduce Context-A wareness and Interpretability of Rare Occurrences (CAIRO), an ontology-based human-assistive discovery framework for failure cases (or CP - Critical Phenomena) detection and formalization. CAIRO by design incentivizes human-in-the-loop for testing and evaluation of criticality that arises from misdetections, adversarial attacks, and hallucinations in AI black-box models. Our robust analysis of object detection model(s) failures in automated driving systems (ADS) showcases scalable and interpretable ways of formalizing the observed gaps between camera perception and real-world contexts, resulting in test cases stored as explicit knowledge graphs (in OWL/XML format) amenable for sharing, downstream analysis, logical reasoning, and accountability. I NTRODUCTION Formal verification techniques are a norm in chip design, but they remain elusive in computer vision (CV) applications. The reason being CV applications are deemed open-ended, often trained on millions of data and billions of parameters to learn a few hundreds of labels. Finetuning practices are commonly used to tailor them to specific needs, but with no standard testing procedures in place providing guidance for their application to ensure fail-safe behaviors, critical systems like Autonomous V ehicles (A V) are bound to fail [1].

Diabetic retinopathy (DR) is a leading cause of blindness worldwide, underscoring the importance of early detection for effective treatment. However, automated DR classification remains challenging due to variations in image quality, class imbalance, and pixel-level similarities that hinder model training. To address these issues, we propose a robust preprocessing pipeline incorporating image cropping, Contrast-Limited Adaptive Histogram Equalization (CLAHE), and targeted data augmentation to improve model generalization and resilience. Our approach leverages the Swin Transformer, which utilizes hierarchical token processing and shifted window attention to efficiently capture fine-grained features while maintaining linear computational complexity. We validate our method on the Aptos and IDRiD datasets for multi-class DR classification, achieving accuracy rates of 89.65% and 97.40%, respectively. These results demonstrate the effectiveness of our model, particularly in detecting early-stage DR, highlighting its potential for improving automated retinal screening in clinical settings.

The process of creating educational materials is both time-consuming and demanding for educators. This research explores the potential of Large Language Models (LLMs) to streamline this task by automating the generation of extended reading materials and relevant course suggestions. Using the TED-Ed Dig Deeper sections as an initial exploration, we investigate how supplementary articles can be enriched with contextual knowledge and connected to additional learning resources. Our method begins by generating extended articles from video transcripts, leveraging LLMs to include historical insights, cultural examples, and illustrative anecdotes. A recommendation system employing semantic similarity ranking identifies related courses, followed by an LLM-based refinement process to enhance relevance. The final articles are tailored to seamlessly integrate these recommendations, ensuring they remain cohesive and informative. Experimental evaluations demonstrate that our model produces high-quality content and accurate course suggestions, assessed through metrics such as Hit Rate, semantic similarity, and coherence. Our experimental analysis highlight the nuanced differences between the generated and existing materials, underscoring the model's capacity to offer more engaging and accessible learning experiences. This study showcases how LLMs can bridge the gap between core content and supplementary learning, providing students with additional recommended resources while also assisting teachers in designing educational materials.

In the field of natural language processing (NLP), the capability to infer and reason about causality is increasingly recognized as a critical component of intelligent systems. Despite the recent advancement of large language models (LLMs) (Radford et al., 2019; Devlin et al., 2019; Brown et al., 2020; Zhang et al., 2022; OpenAI, 2023; Ignat et al., 2024, inter alia), a key question still remains: Can these models understand and reason about causality? This is a critical skill before we can trust AI agents to be integrated into decision-making systems. Moreover, even if LLMs succeed at some extent of reasoning, they still lack transparency of how their decisions are made, forming a strong need for interpretabil-ity (Luo and Specia, 2024; Räuker et al., 2023; Zou et al., 2023). T o bridge the gap, this thesis explores various facets of causal reasoning in LLMs. W e present a series of studies that collectively advance the knowledge of how well these models perform causal reasoning (Part I), how their decisions are made (Part II), how causality among learning variables influences NLP tasks (Part III), and how causality and NLP can together analyze social problems (Part IV). Below we introduce an overview of the four parts and their corresponding chapters.