Related papers: A brief introduction to the Grey Machine Learning

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Importation of these ideas, combined with an existing rich body of…

The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their…

Modern machine learning systems based on neural networks have shown great success in learning complex data patterns while being able to make good predictions on unseen data points. However, the limited interpretability of these systems…

Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused…

Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…

Gradient-domain machine learning (GDML) is an accurate and efficient approach to learn a molecular potential and associated force field based on the kernel ridge regression algorithm. Here, we demonstrate its application to learn an…

Recent efforts in Machine Learning (ML) interpretability have focused on creating methods for explaining black-box ML models. However, these methods rely on the assumption that simple approximations, such as linear models or decision-trees,…

In multi-attribute decision-making problems where the attribute values are interval grey numbers, a simplified form based on kernels and the degree of greyness is presented. Combining fuzzy graph theory with the kernel and the degree of…

This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…

This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…

Despite classical statistical theory predicting severe overfitting, modern massively overparameterized neural networks still generalize well. This unexpected property is attributed to the network's so-called implicit bias, which describes…

Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep…

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

To learn about real world phenomena, scientists have traditionally used models with clearly interpretable elements. However, modern machine learning (ML) models, while powerful predictors, lack this direct elementwise interpretability (e.g.…