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Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
The current definition of a Bayesian credible set cannot, in general, achieve an arbitrarily preassigned credible level. This drawback is particularly acute for classification problems, where there are only a finite number of achievable…
We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to…
Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard…
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
An important aspect of Bayesian model selection is how to deal with huge model spaces, since exhaustive enumeration of all the models entertained is unfeasible and inferences have to be based on the very small proportion of models visited.…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…
Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…
The Bayesian approach provides powerful methods for variable selection. The ability to incorporate sparsity through prior beliefs and account for parameter uncertainty allows Bayesian variable selection to consistently identify which of the…