Related papers: Bayesian Inference and Learning in Nonlinear Dynam…
Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…
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…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…
We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…
Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work,…
Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…
This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…
Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
Representation learning is a fundamental building block for analyzing entities in a database. While the existing embedding learning methods are effective in various data mining problems, their applicability is often limited because these…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…
A central characteristic of Bayesian statistics is the ability to consistently incorporate prior knowledge into various modeling processes. In this paper, we focus on translating domain expert knowledge into corresponding prior…
Deep generative frameworks including GANs and normalizing flow models have proven successful at filling in missing values in partially observed data samples by effectively learning -- either explicitly or implicitly -- complex,…
Deep learning has shown its human-level performance in various applications. However, current deep learning models are characterised by catastrophic forgetting of old knowledge when learning new classes. This poses a challenge particularly…
This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined…
Meta-learning aims to extract useful inductive biases from a set of related datasets. In Bayesian meta-learning, this is typically achieved by constructing a prior distribution over neural network parameters. However, specifying families of…