Related papers: Uncertainty principles and optimally sparse wavele…
Aligning structured data is a fundamental problem in computer vision and machine learning, underlying tasks such as time series analysis, human action recognition, and visual representation learning. Existing alignment methods, including…
Many applications in signal processing benefit from the sparsity of signals in a certain transform domain or dictionary. Synthesis sparsifying dictionaries that are directly adapted to data have been popular in applications such as image…
Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…
Precisely tracking uncertainties is crucial for robots to successfully and safely operate in unstructured and dynamic environments. We present a probabilistic framework to precisely keep track of uncertainties throughout the entire…
Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood…
Weak gravitational lensing, resulting from the bending of light due to the presence of matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It stands as a…
Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…
Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…
Goals for planning problems are typically conceived of as subsets of the state space. However, for many practical planning problems in robotics, we expect the robot to predict goals, e.g. from noisy sensors or by generalizing learned models…
Learning from limited data is challenging because data scarcity leads to a poor generalization of the trained model. A classical global pooled representation will probably lose useful local information. Many few-shot learning methods have…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
Being a task of establishing spatial correspondences, medical image registration is often formalized as finding the optimal transformation that best aligns two images. Since the transformation is such an essential component of registration,…
In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…
Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically…
We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer…
We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the…