A. Jung

Y. SarcheshmehPour, Y. Tian, L. Zhang et al.

We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature vectors can then be fed into basic clustering methods such as k-means or Gaussian mixture model (GMM) based soft clustering. What sets our approach apart from spectral clustering is that we do not use the eigenvectors of a graph Laplacian to construct the feature vectors. Instead, we use the solutions of total variation minimization problems to construct feature vectors that reflect connectivity between data points. Our motivation is that the solutions of total variation minimization are piece-wise constant around a given set of seed nodes. These seed nodes can be obtained from domain knowledge or by simple heuristics that are based on the network structure of data. Our results indicate that our clustering methods can cope with certain graph structures that are challenging for spectral clustering methods.

S. Abdurakhmanova, Y. SarcheshmehPour, A. Jung

We present a model-agnostic federated learning method that mirrors the operation of a smart power grid: diverse local models, like energy prosumers, train independently on their own data while exchanging lightweight signals to coordinate with statistically similar peers. This coordination is governed by a graph-based regularizer that encourages connected models to produce similar predictions on a shared, public unlabeled dataset. The resulting method is a flexible instance of regularized empirical risk minimization and supports a wide variety of local models - both parametric and non-parametric - provided they can be trained via regularized loss minimization. Such training is readily supported by standard ML libraries including scikit-learn, Keras, and PyTorch.

A. Jung

A key challenge in federated learning applications is the statistical heterogeneity of local datasets. Clustered federated learning addresses this challenge by identifying clusters of local datasets that are approximately homogeneous. One recent approach to clustered federated learning is generalized total variation minimization (GTVMin). This approach requires a similarity graph which can be obtained by domain expertise or in a data-driven fashion via graph learning techniques. Under a widely applicable clustering assumption, we derive an upper bound the deviation between GTVMin solutions and their cluster-wise averages. This bound provides valuable insights into the effectiveness and robustness of GTVMin in addressing statistical heterogeneity within federated learning environments.

A. Jung

We consider the problem of federated clustering, where interconnected devices have access to private local datasets and need to jointly cluster the overall dataset without sharing their local dataset. Our focus is on hard clustering based on the k-means principle. We formulate federated k-means clustering as an instance of GTVMin. This formulation naturally lends to a federated k-means algorithm where each device updates local cluster centroids by solving a modified local k-means problem. The modification involves adding a penalty term to measure the discrepancy between the cluster centroid of neighbouring devices. Our federated k-means algorithm is privacy-friendly as it only requires sharing aggregated information among interconnected devices.

A. Jung

This book offers a hands-on introduction to building and understanding federated learning (FL) systems. FL enables multiple devices -- such as smartphones, sensors, or local computers -- to collaboratively train machine learning (ML) models, while keeping their data private and local. It is a powerful solution when data cannot or should not be centralized due to privacy, regulatory, or technical reasons. The book is designed for students, engineers, and researchers who want to learn how to design scalable, privacy preserving FL systems. Our main focus is on personalization: enabling each device to train its own model while still benefiting from collaboration with relevant devices. This is achieved by leveraging similarities between (the learning tasks associated with) devices that are encoded by the weighted edges (or links) of a federated learning network (FL network). The key idea is to represent real-world FL systems as networks of devices, where nodes correspond to device and edges represent communication links and data similarities between them. The training of personalized models for these devices can be naturally framed as a distributed optimization problem. This optimization problem is referred to as generalized total variation minimization (GTVMin) and ensures that devices with similar learning tasks learn similar model parameters. Our approach is both mathematically principled and practically motivated. While we introduce some advanced ideas from optimization theory and graph-based learning, we aim to keep the book accessible. Readers are guided through the core ideas step by step, with intuitive explanations.

Y. Sarcheshmehpour, M. Leinonen, A. Jung

This paper formulates and studies a novel algorithm for federated learning from large collections of local datasets. This algorithm capitalizes on an intrinsic network structure that relates the local datasets via an undirected "empirical" graph. We model such big data over networks using a networked linear regression model. Each local dataset has individual regression weights. The weights of close-knit sub-collections of local datasets are enforced to deviate only little. This lends naturally to a network Lasso problem which we solve using a primal-dual method. We obtain a distributed federated learning algorithm via a message passing implementation of this primal-dual method. We provide a detailed analysis of the statistical and computational properties of the resulting federated learning algorithm.

L. Zhang, G. Karakasidis, A. Odnoblyudova et al.

The successful application of machine learning (ML) methods becomes increasingly dependent on their interpretability or explainability. Designing explainable ML systems is instrumental to ensuring transparency of automated decision-making that targets humans. The explainability of ML methods is also an essential ingredient for trustworthy artificial intelligence. A key challenge in ensuring explainability is its dependence on the specific human user ("explainee"). The users of machine learning methods might have vastly different background knowledge about machine learning principles. One user might have a university degree in machine learning or related fields, while another user might have never received formal training in high-school mathematics. This paper applies information-theoretic concepts to develop a novel measure for the subjective explainability of the predictions delivered by a ML method. We construct this measure via the conditional entropy of predictions, given a user feedback. The user feedback might be obtained from user surveys or biophysical measurements. Our main contribution is the explainable empirical risk minimization (EERM) principle of learning a hypothesis that optimally balances between the subjective explainability and risk. The EERM principle is flexible and can be combined with arbitrary machine learning models. We present several practical implementations of EERM for linear models and decision trees. Numerical experiments demonstrate the application of EERM to detecting the use of inappropriate language on social media.

A. Jung, N. Vesselinova

We apply network Lasso to semi-supervised regression problems involving network structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which represents the network structure of the data. By using a simple non-parametric regression model, which is motivated by a clustering hypothesis, we provide an analysis of the estimation error incurred by network Lasso. This analysis reveals conditions on the the network structure and the available training data which guarantee network Lasso to be accurate. Remarkably, the accuracy of network Lasso is related to the existence of sufficiently large network flows over the empirical graph. Thus, our analysis reveals a connection between network Lasso and maximum flow problems.