Related papers: Bias- and Variance-Aware Probabilistic Rounding Er…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…
While the {estimation} of risk is an important question in the daily business of banking and insurance, many existing plug-in estimation procedures suffer from an unnecessary bias. This often leads to the underestimation of risk and…
Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having…
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…
When exposed to human-generated data, language models are known to learn and amplify societal biases. While previous works introduced benchmarks that can be used to assess the bias in these models, they rely on assumptions that may not be…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…
Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…
In application areas where data generation is expensive, Gaussian processes are a preferred supervised learning model due to their high data-efficiency. Particularly in model-based control, Gaussian processes allow the derivation of…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
Decisions about health interventions are often made using limited evidence. Mathematical models used to inform such decisions often include uncertainty analysis to account for the effect of uncertainty in the current evidence base on…
The polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous input) is a model that represents the dynamics of physical systems. This polynomial contains information from the past of the inputs and outputs of the…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…
Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…
Policymakers in resource-constrained settings require experimental designs that satisfy strict budget limits while ensuring precise estimation of treatment effects. We propose a framework that applies a dependent randomized rounding…
Large-scale numerical computations make increasing use of low-precision (LP) floating point formats and mixed precision arithmetic, which can be enhanced by the technique of stochastic rounding (SR), that is, rounding an intermediate…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…