Related papers: A Variational Approach to Parameter Estimation in …

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance…

In biomedical studies, we are often interested in the association between different types of covariates and the times to disease events. Because the relationship between the covariates and event times is often complex, standard survival…

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…

Many real-world systems can be usefully represented as sets of interacting components. Examples include computational systems, such as query processors and compilers, natural systems, such as cells and ecosystems, and social systems, such…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…

We developed a novel statistical method to identify structural differences between networks characterized by structural equation models. We propose to reparameterize the model to separate the differential structures from common structures,…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…

The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…

A molecular understanding of how protein function is related to protein structure will require an ability to understand large conformational changes between multiple states. Unfortunately these states are often separated by high free energy…

Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…

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…

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process…

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…

Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on…