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Uncovering which feature combinations are encoded by visual units is critical to understanding how images are transformed into representations that support recognition. While existing feature visualization approaches typically infer a…

Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean…

In the past three decades, many theoretical measures of complexity have been proposed to help understand complex systems. In this work, for the first time, we place these measures on a level playing field, to explore the qualitative…

The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…

Human label variation (HLV) challenges the standard assumption that a labelled instance has a single ground truth, instead embracing the natural variation in human annotation to train and evaluate models. While various training methods and…

The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii)…

Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…

Heterogeneity is often natural in many contemporary applications involving massive data. While posing new challenges to effective learning, it can play a crucial role in powering meaningful scientific discoveries through the understanding…

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a…

We study nonparametric maximum likelihood estimation of probability densities under a total variation (TV) type penalty, sectional variation norm (also named as Hardy-Krause variation). TV regularization has a long history in regression and…

Vision Transformer (ViT) has emerged as a powerful architecture in the realm of modern computer vision. However, its application in certain imaging fields, such as microscopy and satellite imaging, presents unique challenges. In these…

Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image, but they tend to blur the…

Understanding the learning dynamics and inductive bias of neural networks (NNs) is hindered by the opacity of the relationship between NN parameters and the function represented. We propose reparametrizing ReLU NNs as continuous piecewise…

We introduce a novel unsupervised loss function for learning semantic segmentation with deep convolutional neural nets (ConvNet) when densely labeled training images are not available. More specifically, the proposed loss function penalizes…

In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace…

Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only…

In the realm of signal and image denoising and reconstruction, $\ell_1$ regularization techniques have generated a great deal of attention with a multitude of variants. A key component for their success is that under certain assumptions,…

CoVariance Neural Networks (VNNs) perform graph convolutions on the empirical covariance matrix of signals defined over finite-dimensional Hilbert spaces, motivated by robustness and transferability properties. Yet, little is known about…

The loss and the norm of its gradient separate the healthy and the pathological regimes of neural-network training only weakly, whilst the curvature of the empirical risk differs qualitatively between them but is inaccessible explicitly at…

Invariant risk minimization (IRM) is an arising approach to generalize invariant features to different environments in machine learning. While most related works focus on new IRM settings or new application scenarios, the mathematical…