Related papers: A Tutorial on Bayesian Nonparametric Models

Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…

We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…

A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture…

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…

The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian…

Parametric Bayesian modeling offers a powerful and flexible toolbox for machine learning. Yet the model, however detailed, may still be wrong, and this can make inferences untrustworthy. In this paper we introduce a new class of…

Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…

High-throughput scientific studies involving no clear a'priori hypothesis are common. For example, a large-scale genomic study of a disease may examine thousands of genes without hypothesizing that any specific gene is responsible for the…

We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…

This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…

In this paper, we present an infinite hierarchical non-parametric Bayesian model to extract the hidden factors over observed data, where the number of hidden factors for each layer is unknown and can be potentially infinite. Moreover, the…

Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density.…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in…