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Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly…

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

Several studies on heritability in twins aim at understanding the different contribution of environmental and genetic factors to specific traits. Considering the National Merit Twin Study, our purpose is to correctly analyse the influence…

Understanding probabilistic dependencies among variables is central to analyzing complex systems. Traditional structure learning methods often require extensive observational data or are limited by manual, error-prone incorporation of…

Bayesian causal discovery benefits from prior information elicited from domain experts, and in heterogeneous domains any prior knowledge would be badly needed. However, so far prior elicitation approaches have assumed a single causal graph…

We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…

Combining Bayesian nonparametrics and a forward model selection strategy, we construct parsimonious Bayesian deep networks (PBDNs) that infer capacity-regularized network architectures from the data and require neither cross-validation nor…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

In this paper we examine the problem of inference in Bayesian Networks with discrete random variables that have very large or even unbounded domains. For example, in a domain where we are trying to identify a person, we may have variables…

Neural networks (NNs) are primarily developed within the frequentist statistical framework. Nevertheless, frequentist NNs lack the capability to provide uncertainties in the predictions, and hence their robustness can not be adequately…

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…

The aim of this work is to enable inference of deep networks that retain high accuracy for the least possible model complexity, with the latter deduced from the data during inference. To this end, we revisit deep networks that comprise…

We propose a Bayesian framework for fine-tuning large diffusion models with a novel network structure called Bayesian Power Steering (BPS). We clarify the meaning behind adaptation from a \textit{large probability space} to a \textit{small…

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…

Contagion processes are strongly linked to the network structures on which they propagate, and learning these structures is essential for understanding and intervention on complex network processes such as epidemics and (mis)information…

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete…

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…