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Bayesian model selection poses two main challenges: the specification of parameter priors for all models, and the computation of the resulting Bayes factors between models. There is now a large literature on automatic and objective…
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only…
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…
Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…
Model uncertainty is a central challenge in statistical models for binary outcomes such as logistic regression, arising when it is unclear which predictors should be included in the model. Many methods have been proposed to address this…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
A key problem in the theory of meta-learning is to understand how the task distributions influence transfer risk, the expected error of a meta-learner on a new task drawn from the unknown task distribution. In this paper, focusing on fixed…
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint…
We rigorously analyse fully-trained neural networks of arbitrary depth in the Bayesian optimal setting in the so-called proportional scaling regime where the number of training samples and width of the input and all inner layers diverge…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has…
Mixed linear regression (MLR) model is among the most exemplary statistical tools for modeling non-linear distributions using a mixture of linear models. When the additive noise in MLR model is Gaussian, Expectation-Maximization (EM)…
Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of…
Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed…
Network lasso is a method for solving a multi-task learning problem through the regularized maximum likelihood method. A characteristic of network lasso is setting a different model for each sample. The relationships among the models are…