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Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…
In precision medicine, identifying optimal sequences of decision rules, termed dynamic treatment regimes (DTRs), is an important undertaking. One approach investigators may take to infer about optimal DTRs is via Bayesian dynamic Marginal…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…
Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and…
Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…
Dupuytren disease is a fibroproliferative disorder with unknown etiology that often progresses and eventually can cause permanent contractures of the affected fingers. In this paper, we provide a computationally efficient Bayesian framework…
Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have,…
Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…
Clustering is one of the most widely used procedures in the analysis of microarray data, for example with the goal of discovering cancer subtypes based on observed heterogeneity of genetic marks between different tissues. It is well-known…
Distributed Gaussian processes (DGPs) are prominent local approximation methods to scale Gaussian processes (GPs) to large datasets. Instead of a global estimation, they train local experts by dividing the training set into subsets, thus…
This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…
Its conceptual appeal and effectiveness has made latent factor modeling an indispensable tool for multivariate analysis. Despite its popularity across many fields, there are outstanding methodological challenges that have hampered practical…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…