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Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that…
For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori…
Most prognostic methods require a decent amount of data for model training. In reality, however, the amount of historical data owned by a single organization might be small or not large enough to train a reliable prognostic model. To…
Federated learning brings potential benefits of faster learning, better solutions, and a greater propensity to transfer when heterogeneous data from different parties increases diversity. However, because federated learning tasks tend to be…
In the context of a high-dimensional linear regression model, we propose the use of an empirical correlation-adaptive prior that makes use of information in the observed predictor variable matrix to adaptively address high collinearity,…
We report the application of implicit likelihood inference to the prediction of the macro-parameters of strong lensing systems with neural networks. This allows us to perform deep learning analysis of lensing systems within a well-defined…
The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational…
We introduce the concept of conjugate prior models for a given likelihood function in Bayesian spatial inversion. The conjugate class of prior models can be selection extended and still remain conjugate. We demonstrate the generality of…
Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…
This paper explores a federated learning approach that automatically selects the number of latent processes in multi-output Gaussian processes (MGPs). The MGP has seen great success as a transfer learning tool when data is generated from…
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22],…
Robust Mixture Prior (RMP) is a popular Bayesian dynamic borrowing method, which combines an informative historical distribution with a less informative component (referred as robustification component) in a mixture prior to enhance the…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
Bayesian neural networks promise calibrated uncertainty but require $O(mn)$ parameters for standard mean-field Gaussian posteriors. We argue this cost is often unnecessary, particularly when weight matrices exhibit fast singular value…
Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture…
Recent work has shown that the prior over functions induced by a deep Bayesian neural network (BNN) behaves as a Gaussian process (GP) as the width of all layers becomes large. However, many BNN applications are concerned with the BNN…
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…