相关论文: State Space representation of non-stationary Gauss…

A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…

State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are…

We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (GPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

While optimal input design for linear systems has been well-established, no systematic approach exists for nonlinear systems where robustness to extrapolation/interpolation errors is prioritized over minimizing estimated parameter variance.…

Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…

The ubiquity of multiscale interactions in complex systems is well-recognized, with development and heredity serving as a prime example of how processes at different temporal scales influence one another. This work introduces a novel…

Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…

Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…

State-space models (SSMs) have emerged as a powerful foundation for long-range sequence modeling, with the HiPPO framework showing that continuous-time projection operators can be used to derive stable, memory-efficient dynamical systems…

Computer experiments involving both qualitative and quantitative (QQ) factors have attracted increasing attention. Gaussian process (GP) models have proven effective in this context by choosing specialized covariance functions for QQ…

Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple…

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

Gaussian processes (GPs) are instrumental in modeling spatial processes, offering precise interpolation and prediction capabilities across fields such as environmental science and biology. Recently, there has been growing interest in…

We extend Neural Processes (NPs) to sequential data through Recurrent NPs or RNPs, a family of conditional state space models. RNPs model the state space with Neural Processes. Given time series observed on fast real-world time scales but…