Related papers: Machine Learning of Linear Differential Equations …
We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…
Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
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…
Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art…
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…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…
Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…
Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…
Despite significant recent advances in probabilistic meta-learning, it is common for practitioners to avoid using deep learning models due to a comparative lack of interpretability. Instead, many practitioners simply use non-meta-models…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…
Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following…
We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…
In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…
Information theoretic active learning has been widely studied for probabilistic models. For simple regression an optimal myopic policy is easily tractable. However, for other tasks and with more complex models, such as classification with…