Related papers: Towards Expressive Priors for Bayesian Neural Netw…

Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson…

Bayesian approaches for learning deep neural networks (BNN) have been received much attention and successfully applied to various applications. Particularly, BNNs have the merit of having better generalization ability as well as better…

We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal…

This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…

Feed-forward neural networks (NN) are a staple machine learning method widely used in many areas of science and technology. While even a single-hidden layer NN is a universal approximator, its expressive power is limited by the use of…

Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset,…

We perform accurate numerical experiments with fully-connected (FC) one-hidden layer neural networks trained with a discretized Langevin dynamics on the MNIST and CIFAR10 datasets. Our goal is to empirically determine the regimes of…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning…

The Gleason groups serve as the primary histological grading system for prostate cancer, providing crucial insights into the cancer's potential for growth and metastasis. In clinical practice, pathologists determine the Gleason groups based…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

Variational inference provides approximations to the computationally intractable posterior distribution in Bayesian networks. A prominent medical application of noisy-or Bayesian network is to infer potential diseases given observed…

Function-space priors in Bayesian Neural Networks (BNNs) provide a more intuitive approach to embedding beliefs directly into the model's output, thereby enhancing regularization, uncertainty quantification, and risk-aware decision-making.…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…

We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…