Related papers: A Systematic Computational Framework for Practical…

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…

We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…

Insufficient performance of optimization approaches for fitting of mathematical models is still a major bottleneck in systems biology. In this manuscript, the reasons and methodological challenges are summarized as well as their impact in…

The use of machine learning (ML) techniques in the biomedical field has become increasingly important, particularly with the large amounts of data generated by the aftermath of the COVID-19 pandemic. However, due to the complex nature of…

Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…

Structural identifiability concerns the question of which unknown parameters of a model can be recovered from (perfect) input-output data. If all of the parameters of a model can be recovered from data, the model is said to be identifiable.…

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…

There is an ongoing and dedicated effort to estimate bounds on the generalization error of deep learning models, coupled with an increasing interest with practical metrics that can be used to experimentally evaluate a model's ability to…

Parametric model checking (PMC) computes algebraic formulae that express key non-functional properties of a system (reliability, performance, etc.) as rational functions of the system and environment parameters. In software engineering, PMC…

The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…

Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the process to quantify the uncertainties of random input parameters based on experimental data. The introduction of model discrepancy term is significant because…

Systems biology relies on mathematical models that often involve complex and intractable likelihood functions, posing challenges for efficient inference and model selection. Generative models, such as normalizing flows, have shown…

Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…

Systems biology models are useful models of complex biological systems that may require a large amount of experimental data to fit each model's parameters or to approximate a likelihood function. These models range from a few to thousands…

Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…

Regression models with functional responses and covariates constitute a powerful and increasingly important model class. However, regression with functional data poses well known and challenging problems of non-identifiability. This…

Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…