Knowledge Distillation (KD) seeks to transfer the knowledge of a teacher, towards a student neural net. This process is often done by matching the networks' predictions (i.e., their output), but, recently several works have proposed to match the distributions of neural nets' activations (i.e., their features), a process known as \emph{distribution matching}. In this paper, we propose an unifying framework, Knowledge Distillation through Distribution Matching (KD$^{2}$M), which formalizes this strategy. Our contributions are threefold. We i) provide an overview of distribution metrics used in distribution matching, ii) benchmark on computer vision datasets, and iii) derive new theoretical results for KD.

Decentralized Multi-Source Domain Adaptation (DMSDA) is a challenging task that aims to transfer knowledge from multiple related and heterogeneous source domains to an unlabeled target domain within a decentralized framework. Our work tackles DMSDA through a fully decentralized federated approach. In particular, we extend the Federated Dataset Dictionary Learning (FedDaDiL) framework by eliminating the necessity for a central server. FedDaDiL leverages Wasserstein barycenters to model the distributional shift across multiple clients, enabling effective adaptation while preserving data privacy. By decentralizing this framework, we enhance its robustness, scalability, and privacy, removing the risk of a single point of failure. We compare our method to its federated counterpart and other benchmark algorithms, showing that our approach effectively adapts source domains to an unlabeled target domain in a fully decentralized manner.

An anomaly, or an outlier, is a data point that is significantly different from the remaining data [Aggarwal, 2017], to such an extent that it was likely generated by a different mechanism [Hawkins, 1980]. From the perspective of machine learning, Anomaly Detection (AD) wants to determine, from a set of examples, which ones are likely anomalies, typically through a score. This problem finds applications in many different fields, such as medicine Salem et al. [2013], cyber-security Siddiqui et al. [2019], and system monitoring Isermann [2006], to name a few. As reviewed in Han et al. [2022], existing techniques for AD are usually divided into unsupervised, semi-supervised and supervised approaches, with an increasing need for labeled data. In this paper, we focus on unsupervised AD, which does not need further labeling effort in constituting datasets. As discussed in Livernoche et al. [2024], the growing number of applications involving high-dimensional and complex data begs the need for non-parametric algorithms.

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation theory and the Gromov-Wasserstein distance. We offer a new probabilistic view of the classical Multidimensional Scaling (MDS) algorithm and the nonlinear dimensionality reduction algorithm, Isomap (Isometric Mapping or Isometric Feature Mapping) that extends the classical MDS, in which we use the Gromov-Wasserstein distance between the probability measure of high-dimensional data, and its low-dimensional representation. Through gradient descent, our method embeds high-dimensional data into a lower-dimensional space, providing a robust and efficient solution for analyzing complex high-dimensional datasets.

Multi-Source Domain Adaptation (MSDA) is a challenging scenario where multiple related and heterogeneous source datasets must be adapted to an unlabeled target dataset. Conventional MSDA methods often overlook that data holders may have privacy concerns, hindering direct data sharing. In response, decentralized MSDA has emerged as a promising strategy to achieve adaptation without centralizing clients' data. Our work proposes a novel approach, Decentralized Dataset Dictionary Learning, to address this challenge. Our method leverages Wasserstein barycenters to model the distributional shift across multiple clients, enabling effective adaptation while preserving data privacy. Specifically, our algorithm expresses each client's underlying distribution as a Wasserstein barycenter of public atoms, weighted by private barycentric coordinates. Our approach ensures that the barycentric coordinates remain undisclosed throughout the adaptation process. Extensive experimentation across five visual domain adaptation benchmarks demonstrates the superiority of our strategy over existing decentralized MSDA techniques. Moreover, our method exhibits enhanced robustness to client parallelism while maintaining relative resilience compared to conventional decentralized MSDA methodologies.

In this paper, we tackle Multi-Source Domain Adaptation (MSDA), a task in transfer learning where one adapts multiple heterogeneous, labeled source probability measures towards a different, unlabeled target measure. We propose a novel framework for MSDA, based on Optimal Transport (OT) and Gaussian Mixture Models (GMMs). Our framework has two key advantages. First, OT between GMMs can be solved efficiently via linear programming. Second, it provides a convenient model for supervised learning, especially classification, as components in the GMM can be associated with existing classes. Based on the GMM-OT problem, we propose a novel technique for calculating barycenters of GMMs. Based on this novel algorithm, we propose two new strategies for MSDA: GMM-WBT and GMM-DaDiL. We empirically evaluate our proposed methods on four benchmarks in image classification and fault diagnosis, showing that we improve over the prior art while being faster and involving fewer parameters.

In this paper we explore domain adaptation through optimal transport. We propose a novel approach, where we model the data distributions through Gaussian mixture models. This strategy allows us to solve continuous optimal transport through an equivalent discrete problem. The optimal transport solution gives us a matching between source and target domain mixture components. From this matching, we can map data points between domains, or transfer the labels from the source domain components towards the target domain. We experiment with 2 domain adaptation benchmarks in fault diagnosis, showing that our methods have state-of-the-art performance.

This paper seeks to solve Multi-Source Domain Adaptation (MSDA), which aims to mitigate data distribution shifts when transferring knowledge from multiple labeled source domains to an unlabeled target domain. We propose a novel MSDA framework based on dictionary learning and optimal transport. We interpret each domain in MSDA as an empirical distribution. As such, we express each domain as a Wasserstein barycenter of dictionary atoms, which are empirical distributions. We propose a novel algorithm, DaDiL, for learning via mini-batches: (i) atom distributions; (ii) a matrix of barycentric coordinates. Based on our dictionary, we propose two novel methods for MSDA: DaDil-R, based on the reconstruction of labeled samples in the target domain, and DaDiL-E, based on the ensembling of classifiers learned on atom distributions. We evaluate our methods in 3 benchmarks: Caltech-Office, Office 31, and CRWU, where we improved previous state-of-the-art by 3.15%, 2.29%, and 7.71% in classification performance. Finally, we show that interpolations in the Wasserstein hull of learned atoms provide data that can generalize to the target domain.

In this article, we propose an approach for federated domain adaptation, a setting where distributional shift exists among clients and some have unlabeled data. The proposed framework, FedDaDiL, tackles the resulting challenge through dictionary learning of empirical distributions. In our setting, clients' distributions represent particular domains, and FedDaDiL collectively trains a federated dictionary of empirical distributions. In particular, we build upon the Dataset Dictionary Learning framework by designing collaborative communication protocols and aggregation operations. The chosen protocols keep clients' data private, thus enhancing overall privacy compared to its centralized counterpart. We empirically demonstrate that our approach successfully generates labeled data on the target domain with extensive experiments on (i) Caltech-Office, (ii) TEP, and (iii) CWRU benchmarks. Furthermore, we compare our method to its centralized counterpart and other benchmarks in federated domain adaptation.

In this paper, we consider the intersection of two problems in machine learning: Multi-Source Domain Adaptation (MSDA) and Dataset Distillation (DD). On the one hand, the first considers adapting multiple heterogeneous labeled source domains to an unlabeled target domain. On the other hand, the second attacks the problem of synthesizing a small summary containing all the information about the datasets. We thus consider a new problem called MSDA-DD. To solve it, we adapt previous works in the MSDA literature, such as Wasserstein Barycenter Transport and Dataset Dictionary Learning, as well as DD method Distribution Matching. We thoroughly experiment with this novel problem on four benchmarks (Caltech-Office 10, Tennessee-Eastman Process, Continuous Stirred Tank Reactor, and Case Western Reserve University), where we show that, even with as little as 1 sample per class, one achieves state-of-the-art adaptation performance.