Despite the empirical success and practical significance of (relational) knowledge distillation that matches (the relations of) features between teacher and student models, the corresponding theoretical interpretations remain limited for various knowledge distillation paradigms. In this work, we take an initial step toward a theoretical understanding of relational knowledge distillation (RKD), with a focus on semi-supervised classification problems. We start by casting RKD as spectral clustering on a population-induced graph unveiled by a teacher model. Via a notion of clustering error that quantifies the discrepancy between the predicted and ground truth clusterings, we illustrate that RKD over the population provably leads to low clustering error. Moreover, we provide a sample complexity bound for RKD with limited unlabeled samples. For semi-supervised learning, we further demonstrate the label efficiency of RKD through a general framework of cluster-aware semi-supervised learning that assumes low clustering errors. Finally, by unifying data augmentation consistency regularization into this cluster-aware framework, we show that despite the common effect of learning accurate clusterings, RKD facilitates a "global" perspective through spectral clustering, whereas consistency regularization focuses on a "local" perspective via expansion.

In recent years, significant attention in deep learning theory has been devoted to analyzing when models that interpolate their training data can still generalize well to unseen examples. Many insights have been gained from studying models with multiple layers of Gaussian random features, for which one can compute precise generalization asymptotics. However, few works have considered the effect of weight anisotropy; most assume that the random features are generated using independent and identically distributed Gaussian weights, and allow only for structure in the input data. Here, we use the replica trick from statistical physics to derive learning curves for models with many layers of structured Gaussian features. We show that allowing correlations between the rows of the first layer of features can aid generalization, while structure in later layers is generally detrimental. Our results shed light on how weight structure affects generalization in a simple class of solvable models.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

Vessel structure is one of the most important parts of the retina which physicians can detect many diseases by analysing its features. Localization of blood vessels in retina images is an important process in medical image analysis. This process is also more challenging with the presence of bright and dark lesions. In this thesis, two automated vessel localization methods to handle both healthy and unhealthy (pathological) retina images are analyzed. Each method consists of two major steps and the second step is the same in the two methods. In the first step, an algorithm is used to decrease the effect of bright lesions. In Method 1, this algorithm is based on K- Means segmentation, and in Method 2, it is based on a regularization procedure. In the second step of both methods, a multi-scale line operator is used to localize the line-shaped vascular structures and ignore the dark lesions which are generally assumed to have irregular patterns. After the introduction of the methods, a detailed quantitative and qualitative comparison of the methods with one another as well as the state-of-the-art solutions in the literature based on the segmentation results on the images of the two publicly available datasets, DRIVE and STARE, is reported. The results demonstrate that the methods are highly comparable with other solutions.

This paper presents a reputation-based threat mitigation framework that defends potential security threats in electroencephalogram (EEG) signal classification during model aggregation of Federated Learning. While EEG signal analysis has attracted attention because of the emergence of brain-computer interface (BCI) technology, it is difficult to create efficient learning models for EEG analysis because of the distributed nature of EEG data and related privacy and security concerns. To address these challenges, the proposed defending framework leverages the Federated Learning paradigm to preserve privacy by collaborative model training with localized data from dispersed sources and introduces a reputation-based mechanism to mitigate the influence of data poisoning attacks and identify compromised participants. To assess the efficiency of the proposed reputation-based federated learning defense framework, data poisoning attacks based on the risk level of training data derived by Explainable Artificial Intelligence (XAI) techniques are conducted on both publicly available EEG signal datasets and the self-established EEG signal dataset. Experimental results on the poisoned datasets show that the proposed defense methodology performs well in EEG signal classification while reducing the risks associated with security threats.

The aim of this study is clustering students according to their gamification user types and learning styles with the purpose of providing instructors with a new perspective of grouping students in case of clustering which cannot be done by hand when there are multiple scales in data. The data used consists of 251 students who were enrolled at a Turkish state university. When grouping students, K-means algorithm has been utilized as clustering algorithm. As for determining the gamification user types and learning styles of students, Gamification User Type Hexad Scale and Grasha-Riechmann Student Learning Style Scale have been used respectively. Silhouette coefficient is utilized as clustering quality measure. After fitting the algorithm in several ways, highest Silhouette coefficient obtained was 0.12 meaning that results are neutral but not satisfactory. All the statistical operations and data visualizations were made using Python programming language.

Annotator disagreement is ubiquitous in natural language processing (NLP) tasks. There are multiple reasons for such disagreements, including the subjectivity of the task, difficult cases, unclear guidelines, and so on. Rather than simply aggregating labels to obtain data annotations, we instead try to directly model the diverse perspectives of the annotators, and explicitly account for annotators' idiosyncrasies in the modeling process by creating representations for each annotator (annotator embeddings) and also their annotations (annotation embeddings). In addition, we propose TID-8, The Inherent Disagreement - 8 dataset, a benchmark that consists of eight existing language understanding datasets that have inherent annotator disagreement. We test our approach on TID-8 and show that our approach helps models learn significantly better from disagreements on six different datasets in TID-8 while increasing model size by fewer than 1% parameters. By capturing the unique tendencies and subjectivity of individual annotators through embeddings, our representations prime AI models to be inclusive of diverse viewpoints.

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis. Traditional PCA, a main workhorse in dimensionality reduction, lacks the ability to capture geometrical structure information embedded in the data, and previous graph Laplacian regularizations are limited by the analysis of only a single scale. We propose a topological Principal Components Analysis (tPCA) method by the combination of persistent Laplacian (PL) technique and L$_{2,1}$ norm regularization to address multiscale and multiclass heterogeneity issues in data. We further introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique to improve the robustness of our persistent Laplacian method. The proposed kNN-PL is a new algebraic topology technique which addresses the many limitations of the traditional persistent homology. Rather than inducing filtration via the varying of a distance threshold, we introduced kNN-tPCA, where filtrations are achieved by varying the number of neighbors in a kNN network at each step, and find that this framework has significant implications for hyper-parameter tuning. We validate the efficacy of our proposed tPCA and kNN-tPCA methods on 11 diverse benchmark scRNA-seq datasets, and showcase that our methods outperform other unsupervised PCA enhancements from the literature, as well as popular Uniform Manifold Approximation (UMAP), t-Distributed Stochastic Neighbor Embedding (tSNE), and Projection Non-Negative Matrix Factorization (NMF) by significant margins.

Previous research on expert advice-taking shows that humans exhibit two contradictory behaviors: on the one hand, people tend to overvalue their own opinions undervaluing the expert opinion, and on the other, people often defer to other people's advice even if the advice itself is rather obviously wrong. In our study, we conduct an exploratory evaluation of users' AI-advice accepting behavior when evaluating the truthfulness of a health-related statement in different "advice quality" settings. We find that even feedback that is confined to just stating that "the AI thinks that the statement is false/true" results in more than half of people moving their statement veracity assessment towards the AI suggestion. The different types of advice given influence the acceptance rates, but the sheer effect of getting a suggestion is often bigger than the suggestion-type effect.

Personalization aims to characterize individual preferences and is widely applied across many fields. However, conventional personalized methods operate in a centralized manner and potentially expose the raw data when pooling individual information. In this paper, with privacy considerations, we develop a flexible and interpretable personalized framework within the paradigm of Federated Learning, called PPFL (Population Personalized Federated Learning). By leveraging canonical models to capture fundamental characteristics among the heterogeneous population and employing membership vectors to reveal clients' preferences, it models the heterogeneity as clients' varying preferences for these characteristics and provides substantial insights into client characteristics, which is lacking in existing Personalized Federated Learning (PFL) methods. Furthermore, we explore the relationship between our method and three main branches of PFL methods: multi-task PFL, clustered FL, and decoupling PFL, and demonstrate the advantages of PPFL. To solve PPFL (a non-convex constrained optimization problem), we propose a novel random block coordinate descent algorithm and present the convergence property. We conduct experiments on both pathological and practical datasets, and the results validate the effectiveness of PPFL.