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In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured,…

We present a model-agnostic algorithm for generating post-hoc explanations and uncertainty intervals for a machine learning model when only a static sample of inputs and outputs from the model is available, rather than direct access to the…

Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…

We present a new method to visualize data ensembles by constructing structured probabilistic representations in latent spaces, i.e., lower-dimensional representations of spatial data features. Our approach transforms the spatial features of…

A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…

In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…

The variational autoencoder (VAE) is a popular deep latent variable model used to analyse high-dimensional datasets by learning a low-dimensional latent representation of the data. It simultaneously learns a generative model and an…

Bayesian optimisation in the latent space of a Variational AutoEncoder (VAE) is a powerful framework for optimisation tasks over complex structured domains, such as the space of scientifically interesting molecules. However, existing…

Geostatistical modeling of the reservoir intrinsic properties starts only with sparse data available. These estimates will depend largely on the number of wells and their location. The drilling costs are so high that they do not allow new…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…

Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate…

Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in…

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is…

Bayesian model updating facilitates the calibration of analytical models based on observations and the quantification of uncertainties in model parameters such as stiffness and mass. This process significantly enhances damage assessment and…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…

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…

Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. The central challenge is to both mitigate…

Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and…