Related papers: Bayesian Model Selection, the Marginal Likelihood,…
Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or that sample's…
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input…
Generalization in deep learning has been the topic of much recent theoretical and empirical research. Here we introduce desiderata for techniques that predict generalization errors for deep learning models in supervised learning. Such…
In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…
Interpretation of cosmological data to determine the number and values of parameters describing the universe must not rely solely on statistics but involve physical insight. When statistical techniques such as "model selection" or…
We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…
Modern machine learning usually involves predictors in the overparameterised setting (number of trained parameters greater than dataset size), and their training yields not only good performance on training data, but also good…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
We give a general recipe for derandomising PAC-Bayesian bounds using margins, with the critical ingredient being that our randomised predictions concentrate around some value. The tools we develop straightforwardly lead to margin bounds for…
We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the normalizing constant for the posterior density, obtained by integrating the product…
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we…
The marginal Bayesian predictive classifiers (mBpc) as opposed to the simultaneous Bayesian predictive classifiers (sBpc), handle each data separately and hence tacitly assumes the independence of the observations. However, due to…
Deep neural networks have been successful in diverse discriminative classification tasks, although, they are poorly calibrated often assigning high probability to misclassified predictions. Potential consequences could lead to…
We resurrect the infamous harmonic mean estimator for computing the marginal likelihood (Bayesian evidence) and solve its problematic large variance. The marginal likelihood is a key component of Bayesian model selection to evaluate model…
Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…
Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model…