Related papers: Regularization of Mixture Models for Robust Princi…

Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…

We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these…

We present a graph-regularized learning of Gaussian Mixture Models (GMMs) in distributed settings with heterogeneous and limited local data. The method exploits a provided similarity graph to guide parameter sharing among nodes, avoiding…

Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…

We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Multilayer graphs are appealing mathematical tools for modeling multiple types of relationship in the data. In this paper, we aim at analyzing multilayer graphs by properly combining the information provided by individual layers, while…

This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component…

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Based on the manifold hypothesis, real-world data often lie on a low-dimensional manifold, while normalizing flows as a likelihood-based generative model are incapable of finding this manifold due to their structural constraints. So, one…

We propose a supervised learning approach for predicting an underlying graph from a set of graph signals. Our approach is based on linear regression. In the linear regression model, we predict edge-weights of a graph as the output, given a…

Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…

We introduce a novel formulation for guided super-resolution. Its core is a differentiable optimisation layer that operates on a learned affinity graph. The learned graph potentials make it possible to leverage rich contextual information…