Related papers: Free-Form Variational Inference for Gaussian Proce…

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…

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…

An inference method for Gaussian process augmented state-space models are presented. This class of grey-box models enables domain knowledge to be incorporated in the inference process to guarantee a minimum of performance, still they are…

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

This paper proposes approaches for the analysis of multiple changepoint models when dependency in the data is modelled through a hierarchical Gaussian Markov random field. Integrated nested Laplace approximations are used to approximate…

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and…

We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing…

The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…

Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle…

We present an R package bssm for Bayesian non-linear/non-Gaussian state space modelling. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

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…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced…