Related papers: A Bayesian Reflection on Surfaces

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…

The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic…

In image-based camera localization systems, information about the environment is usually stored in some representation, which can be referred to as a map. Conventionally, most maps are built upon hand-crafted features. Recently, neural…

Recently, continuous representation methods emerge as novel paradigms that characterize the intrinsic structures of real-world data through function representations that map positional coordinates to their corresponding values in the…

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…

Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…

Integrating heterogeneous data sources and expert knowledge is essential for overcoming data scarcity and enhancing estimation accuracy. Two main frameworks naturally arise to perform the integration of these multiple sources: sequential…

We propose a Bayesian neural network-based continual learning algorithm using Variational Inference, aiming to overcome several drawbacks of existing methods. Specifically, in continual learning scenarios, storing network parameters at each…

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…

Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Classical solutions such that Kalman filter and Particle filter are introduced in this report. Gaussian processes have been introduced as…

In this paper, we propose a Bayesian approach for multiscale problems with the availability of dynamic observational data. Our method selects important degrees of freedom probabilistically in a Generalized multiscale finite element method…

The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper…

A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…

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…

We propose a generalised framework for the updating of a prior ensemble to a posterior ensemble, an essential yet challenging part in ensemble-based filtering methods. The proposed framework is based on a generalised and fully Bayesian view…

During the ongoing debate over the representation of uncertainty in Artificial Intelligence, Cheeseman, Lemmer, Pearl, and others have argued that probability theory, and in particular the Bayesian theory, should be used as the basis for…

This is a preliminary version of visual interpretation integrating multiple sensors in SUCCESSOR, an intelligent, model-based vision system. We pursue a thorough integration of hierarchical Bayesian inference with comprehensive physical…

Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…

Continual learning is an online paradigm where a learner continually accumulates knowledge from different tasks encountered over sequential time steps. Importantly, the learner is required to extend and update its knowledge without…

We introduce Consistent Instance Field, a continuous and probabilistic spatio-temporal representation for dynamic scene understanding. Unlike prior methods that rely on discrete tracking or view-dependent features, our approach disentangles…