Related papers: Gaussian Processes on Cellular Complexes
In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation and the solution of these equations. We begin by examining…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a…
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too…
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…
Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on…
Convolutional neural networks (CNNs) have achieved superior accuracy in many visual related tasks. However, the inference process through intermediate layers is opaque, making it difficult to interpret such networks or develop trust in…
Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…
Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by…
The research work outlined in the present note highlights the essential role played by the simulation procedures implemented by us on CINECA supercomputers to complement the mathematical investigations carried within our group over the past…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…
We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning…
Gaussian graphical models are widely used to represent conditional dependence among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities…
This article shortly introduces Gaussian processes (GP) as a new approach for modelling time series in the field of blazar physics. In the second part of the paper, recent results from an application of GP modelling to the multi-wavelength…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…
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…
Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present…