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Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks…

Graph kernels methods are based on an implicit embedding of graphs within a vector space of large dimension. This implicit embedding allows to apply to graphs methods which where until recently solely reserved to numerical data. Within the…

Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are…

Evaluation of generative models is mostly based on the comparison between the estimated distribution and the ground truth distribution in a certain feature space. To embed samples into informative features, previous works often use…

The graph layouts used for complex network studies have been mainly been developed to improve visualization. If we interpret the layouts in metric spaces such as Euclidean ones, however, the embedded spatial information can be a valuable…

A statistically principled way of conducting weighted network analysis is still lacking. Comparison of different populations of weighted networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the…

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…

The space of possible behaviors complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…

In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…

Convolutional neural networks (CNNs) are commonly used for image classification. Saliency methods are examples of approaches that can be used to interpret CNNs post hoc, identifying the most relevant pixels for a prediction following the…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…

Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…

An information theoretic approach inspired by quantum statistical mechanics was recently proposed as a means to optimize network models and to assess their likelihood against synthetic and real-world networks. Importantly, this method does…

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is…

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…

Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…