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Multi-channel imaging data is a prevalent data format in scientific fields such as astronomy and biology. The structured information and the high dimensionality of these 3-D tensor data makes the analysis an intriguing but challenging topic…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
The aim of this paper is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. Our STMs…
We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…
The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…
Deep generative models are rapidly gaining traction in medical imaging. Nonetheless, most generative architectures struggle to capture the underlying probability distributions of volumetric data, exhibit convergence problems, and offer no…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
In neuroscience, researchers seek to uncover the connectivity of neurons from large-scale neural recordings or imaging; often people employ graphical model selection and estimation techniques for this purpose. But, existing technologies can…
In the domain of 3D scene representation, 3D Gaussian Splatting (3DGS) has emerged as a pivotal technology. However, its application to large-scale, high-resolution scenes (exceeding 4k$\times$4k pixels) is hindered by the excessive…
Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI, as it allows for more meaningful spatial smoothing and is more compatible with the common assumptions of isotropy and stationarity in…
Reliable multimodal sensor fusion algorithms require accurate spatiotemporal calibration. Recently, targetless calibration techniques based on implicit neural representations have proven to provide precise and robust results. Nevertheless,…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…
Recovering high-fidelity 3D images from sparse or degraded 2D images is a fundamental challenge in medical imaging, with broad applications ranging from 3D ultrasound reconstruction to MRI super-resolution. In the context of fetal MRI,…
3D Gaussian Splatting (3DGS) has revolutionized novel view synthesis with high-quality rendering through continuous aggregations of millions of 3D Gaussian primitives. However, it suffers from a substantial memory footprint, particularly…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
Working memory (WM) was one of the first cognitive processes studied with functional magnetic resonance imaging. With now over 20 years of studies on WM, each study with tiny sample sizes, there is a need for meta-analysis to identify the…
Neural image representations have emerged as a promising approach for encoding and rendering visual data. Combined with learning-based workflows, they demonstrate impressive trade-offs between visual fidelity and memory footprint. Existing…