Related papers: Gaussian process deconvolution
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…
Generative neural network is a new category of neural networks and it has been widely utilized in applications such as content generation, unsupervised learning, segmentation and pose estimation. It typically involves massive…
Gravity inversion is a commonly applied data analysis technique in the field of geophysics. While machine learning methods have previously been explored for the problem of gravity inversion, these are deterministic approaches returning a…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…
We reconstruct the Hubble function from cosmic chronometers, supernovae, and baryon acoustic oscillations compiled data sets via the Gaussian process (GP) method and use it to draw out Horndeski theories that are fully anchored on expansion…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
This method solves the dual problem of blind deconvolution and estimation of the time waveform of noisy second-order cyclo-stationary (CS2) signals that traverse a Transfer Function (TF) en route to a sensor. We have proven that the…
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator…
Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing…
Derivatives are a key nonparametric functional in wide-ranging applications where the rate of change of an unknown function is of interest. In the Bayesian paradigm, Gaussian processes (GPs) are routinely used as a flexible prior for…
We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with…
Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors,…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
This article addresses the output regulation problem for a class of nonlinear systems using a data-driven approach. An output feedback controller is proposed that integrates a traditional control component with a data-driven learning…
Like the ordinary power spectrum, higher-order spectra (HOS) describe signal properties that are invariant under translations in time. Unlike the power spectrum, HOS retain phase information from which details of the signal waveform can be…