Related papers: Likelihood approximations via Gaussian approximate…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
Composite likelihood usually ignores dependencies among response components, while variational approximation to likelihood ignores dependencies among parameter components. We derive a Gaussian variational approximation to the composite…
Gaussian process training decomposes into inference of the (approximate) posterior and learning of the hyperparameters. For non-Gaussian (non-conjugate) likelihoods, two common choices for approximate inference are Expectation Propagation…
Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
We investigate the use of data-driven likelihoods to bypass a key assumption made in many scientific analyses, which is that the true likelihood of the data is Gaussian. In particular, we suggest using the optimization targets of flow-based…
We present a framework for approximate Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex…