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The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…

We develop a hierarchical Bayesian dynamic game for competitive inventory and pricing under incomplete information. Two firms repeatedly choose order quantities and prices while facing two layers of uncertainty: unknown market demand and…

The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each…

Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…

We describe a limitation in the expressiveness of the predictive uncertainty estimate given by mean-field variational inference (MFVI), a popular approximate inference method for Bayesian neural networks. In particular, MFVI fails to give…

Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…

We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized…

We focus on using the predictive uncertainty signal calculated by Bayesian neural networks to guide learning in the self-same task the model is being trained on. Not opting for costly Monte Carlo sampling of weights, we propagate the…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

The Intensive Care Unit (ICU) is a hospital department where machine learning has the potential to provide valuable assistance in clinical decision making. Classical machine learning models usually only provide point-estimates and no…

The vulnerability of machine learning models to adversarial attacks remains a critical security challenge. Traditional defenses, such as adversarial training, typically robustify models by minimizing a worst-case loss. However, these…

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Unconstrained optimization problems are typically solved using iterative methods, which often depend on line search techniques to determine optimal step lengths in each iteration. This paper introduces a novel line search approach.…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Gaussian process regression is widely applied in computational science and engineering for surrogate modeling owning to its kernel-based and probabilistic nature. In this work, we propose a Bayesian approach that integrates the variability…

Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust…

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…