Related papers: G-Lets: Signal Processing Using Transformation Gro…

Insufficient training data is a major bottleneck for most deep learning practices, not least in medical imaging where data is difficult to collect and publicly available datasets are scarce due to ethics and privacy. This work investigates…

In many state-of-the-art compression systems, signal transformation is an integral part of the encoding and decoding process, where transforms provide compact representations for the signals of interest. This paper introduces a class of…

Group Anomaly Detection (GAD) identifies unusual pattern in groups where individual members might not be anomalous. This task is of major importance across multiple disciplines, in which also sequences like trajectories can be considered as…

The main goal of representation learning is to acquire meaningful representations from real-world sensory inputs without supervision. Representation learning explains some aspects of human development. Various neural network (NN) models…

The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional…

Subgroup identification (clustering) is an important problem in biomedical research. Gene expression profiles are commonly utilized to define subgroups. Longitudinal gene expression profiles might provide additional information on disease…

Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…

In this paper we give a multiresolution construction in Bergman space. The successful application of rational orthogonal bases needs a priori knowledge of the poles of the transfer function that may cause a drawback of the method. We give a…

In medical imaging, a general problem is that it is costly and time consuming to collect high quality data from healthy and diseased subjects. Generative adversarial networks (GANs) is a deep learning method that has been developed for…

In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…

The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple…

Stratifying cancer patients based on their gene expression levels allows improving diagnosis, survival analysis and treatment planning. However, such data is extremely highly dimensional as it contains expression values for over 20000 genes…

This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…

Thanks to the recent development of deep generative models, it is becoming possible to generate high-quality images with both fidelity and diversity. However, the training of such generative models requires a large dataset. To reduce the…

We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…

In this paper, we give polynomial-time algorithms that can take a graph G with a given combinatorial embedding on an orientable surface S of genus g and produce a planar drawing of G in R^2, with a bounding face defined by a polygonal…

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics,…

Despite the success of deep learning in domains such as image, voice, and graphs, there has been little progress in deep representation learning for domains without a known structure between features. For instance, a tabular dataset of…

This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…