Related papers: Modeling Latent Neural Dynamics with Gaussian Proc…
Modern datasets in neuroscience enable unprecedented inquiries into the relationship between complex behaviors and the activity of many simultaneously recorded neurons. While latent variable models can successfully extract low-dimensional…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
Gaussian process latent variable models (GPLVM) are a flexible and non-linear approach to dimensionality reduction, extending classical Gaussian processes to an unsupervised learning context. The Bayesian incarnation of the GPLVM Titsias…
We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes…
Convolutional dictionary learning (CDL), the problem of estimating shift-invariant templates from data, is typically conducted in the absence of a prior/structure on the templates. In data-scarce or low signal-to-noise ratio (SNR) regimes,…
Observations from dynamical systems often exhibit irregularities, such as censoring, where values are recorded only if they fall within a certain range. Censoring is ubiquitous in practice, due to saturating sensors, limit-of-detection…
Modeling the structure and events of the physical world constitutes a fundamental objective of neural networks. Among the diverse approaches, Graph Network Simulators (GNS) have emerged as the leading method for modeling physical phenomena,…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We introduce a…
The combination of new recording techniques in neuroscience and powerful inference methods recently held the promise to recover useful effective models, at the single neuron or network level, directly from observed data. The value of a…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…
Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…
Most environmental phenomena, such as wind profiles, ozone concentration and sunlight distribution under a forest canopy, exhibit nonstationary dynamics i.e. phenomenon variation change depending on the location and time of occurrence.…
Time series datasets are often composed of a variety of sequences from the same domain, but from different entities, such as individuals, products, or organizations. We are interested in how time series models can be specialized to…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice,…