Related papers: Mean-Field Variational Inference for Gradient Matc…
We present a theoretical analysis of the training process for a single-layer GAN fed by high-dimensional input data. The training dynamics of the proposed model at both microscopic and macroscopic scales can be exactly analyzed in the…
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
Stiff ordinary differential equations (ODEs) play an important role in many scientific and engineering applications. Often, the dependence of the solution of the ODE on additional parameters is of interest, e.g.\ when dealing with…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Gaussian processes (GP) provide a prior over functions and allow finding complex regularities in data. Gaussian processes are successfully used for classification/regression problems and dimensionality reduction. In this work we consider…
Variational Optimization forms a differentiable upper bound on an objective. We show that approaches such as Natural Evolution Strategies and Gaussian Perturbation, are special cases of Variational Optimization in which the expectations are…
Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the…
The autoencoder model uses an encoder to map data samples to a lower dimensional latent space and then a decoder to map the latent space representations back to the data space. Implicitly, it relies on the encoder to approximate the inverse…
Out-of-distribution (OOD) generalization has long been a challenging problem that remains largely unsolved. Gaussian processes (GP), as popular probabilistic model classes, especially in the small data regime, presume strong OOD…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
We implemented a gradient-based algorithm for transition state search which uses Gaussian process regression. Besides a description of the algorithm, we provide a method to find the starting point for the optimization if only the reactant…
Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…
As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable…
The estimation of unknown parameters in nonlinear partial differential equations (PDEs) offers valuable insights across a wide range of scientific domains. In this work, we focus on estimating plant root parameters in the Richards equation,…