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Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…
We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges IN many practical cases, but NOT…
Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation.…
Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…
Given a reference model that includes all the available variables, projection predictive inference replaces its posterior with a constrained projection including only a subset of all variables. We extend projection predictive inference to…
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…
All discretized numerical models contain modelling errors - this reality is amplified when reduced-order models are used. The ability to accurately approximate modelling errors informs statistics on model confidence and improves…
Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this…
We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
A late time asymptotic perturbative analysis of curvature coupled complex scalar field models with accelerated cosmological expansion is carried out on the level of formal power series expansions. For this, algebraic analogues of the…
Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function…
It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…
Evolutionary symbolic regression approaches are powerful tools that can approximate an explicit mapping between input features and observation for various problems. However, ensuring that explored expressions maintain consistency with…
Inference-time scaling (ITS) in latent reasoning models typically relies on heuristic perturbations, such as dropout or fixed Gaussian noise, to generate diverse candidate trajectories. However, we show that stronger perturbations do not…
Bootstrap techniques relying on the constraints imposed by Extended Galilean Invariance (EGI), have proved to be very useful in the context of perturbation theory of the Large Scale Structure (LSS). It has been formulated in both the…
Equilibrium Propagation (EP) is a powerful and more bio-plausible alternative to conventional learning frameworks such as backpropagation. The effectiveness of EP stems from the fact that it relies only on local computations and requires…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…