Related papers: Learning signals defined on graphs with optimal tr…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…

Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions,…

The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into…

Through sequential construction of posteriors on observing data online, Bayes' theorem provides a natural framework for continual learning. We develop Variational Auto-Regressive Gaussian Processes (VAR-GPs), a principled posterior updating…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

This paper addresses graph learning in Gaussian Graphical Models (GGMs). In this context, data matrices often come with auxiliary metadata (e.g., textual descriptions associated with each node) that is usually ignored in traditional graph…

Gaussian graphical models provide a powerful framework for uncovering conditional dependence relationships between sets of nodes; they have found applications in a wide variety of fields including sensor and communication networks, physics,…

Many score-based active learning methods have been successfully applied to graph-structured data, aiming to reduce the number of labels and achieve better performance of graph neural networks based on predefined score functions. However,…

Efficient signal representation is essential for the functioning of living and artificial systems operating under resource constraints. A widely recognized framework for deriving such representations is the information bottleneck method,…

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix…

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…

Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

We study the problem of causal discovery through targeted interventions. Starting from few observational measurements, we follow a Bayesian active learning approach to perform those experiments which, in expectation with respect to the…

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

In the machine learning domain, active learning is an iterative data selection algorithm for maximizing information acquisition and improving model performance with limited training samples. It is very useful, especially for the industrial…