Related papers: Efficient Approximations for the Marginal Likeliho…
Laplace approximation is a very useful tool in Bayesian inference and it claims a nearly Gaussian behavior of the posterior. \cite{SpLaplace2022} established some rather accurate finite sample results about the quality of Laplace…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
We investigate methods for parameter learning from incomplete data that is not missing at random. Likelihood-based methods then require the optimization of a profile likelihood that takes all possible missingness mechanisms into account.…
Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…
We propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first…
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…
The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…
In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured,…
With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter to have likelihood functions that elude analytical formulations. Even…
Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…
This chapter will appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). The conceptual and methodological framework that underpins approximate Bayesian computation (ABC) is targetted primarily towards problems in…
Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are related to the Expectation-Maximisation (EM)…
We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…
This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…
Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empirical performance deteriorates. We propose a simple parametric…
Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an…
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…
Bayesian model selection commonly relies on Laplace approximation or the Bayesian Information Criterion (BIC), which assume that the effective model dimension equals the number of parameters. Singular learning theory replaces this…
Data augmentation is often used to incorporate inductive biases into models. Traditionally, these are hand-crafted and tuned with cross validation. The Bayesian paradigm for model selection provides a path towards end-to-end learning of…