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Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
Medical studies for chronic disease are often interested in the relation between longitudinal risk factor profiles and individuals' later life disease outcomes. These profiles may typically be subject to intermediate structural changes due…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
In this paper, we propose a Gaussian Process (GP) emulator for the calculation of a) tomographic weak lensing band-power spectra, and b) coefficients of summary data massively compressed with the MOPED algorithm. In the former case…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We…
Multi-output Gaussian processes (GPs) are a flexible Bayesian nonparametric framework that has proven useful in jointly modeling the physiological states of patients in medical time series data. However, capturing the short-term effects of…
In critical decision support systems based on medical imaging, the reliability of AI-assisted decision-making is as relevant as predictive accuracy. Although deep learning models have demonstrated significant accuracy, they frequently…
Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes…
Computational models of complex physical systems often rely on simplifying assumptions which inevitably introduce model error, with consequent predictive errors. Given data on model observables, the estimation of parameterized model-error…
Pulmonary Hypertension (PH) is a severe disease characterized by an elevated pulmonary artery pressure. The gold standard for PH diagnosis is measurement of mean Pulmonary Artery Pressure (mPAP) during an invasive Right Heart…
Reliable models of the thermodynamic properties of materials are critical for industrially relevant applications that require a good understanding of equilibrium phase diagrams, thermal and chemical transport, and microstructure evolution.…
Hypertensive disorders of pregnancy occur in about 10% of pregnant women around the world. Though there is evidence that hypertension impacts maternal cardiac functions, the relation between hypertension and cardiac dysfunctions is only…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…
Dynamic prediction of causal effects under different treatment regimes conditional on an individual's characteristics and longitudinal history is an essential problem in precision medicine. This is challenging in practice because outcomes…
High-fidelity modeling of blood flow is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from…
Coarse-grain Lagrangian methods, such as Dissipative Particle Dynamics ( Hoogerbrugge et al., EPL, 1992), are suitable for describing mesoscopic fluid systems that include thermal fluctuations. However, the realistic simulation of liquids…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…