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Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over…
Variational models with coupling terms are becoming increasingly popular in image analysis. They involve auxiliary variables, such that their energy minimisation splits into multiple fractional steps that can be solved easier and more…
With the increasing demand for interpretability in machine learning, functional ANOVA decomposition has gained renewed attention as a principled tool for breaking down high-dimensional function into low-dimensional components that reveal…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
This paper deals with the state estimation of stochastic systems and examines the possible employment of tensor decompositions in grid-based filtering routines, in particular, the tensor-train decomposition. The aim is to show that these…
Decomposition, statically dividing a program into multiple units, is a common programming technique for realizing parallelism and refining programs. The decomposition of a sequential program into components is tedious, due to the…
Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…
Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
Simulating multi-scale phenomena such as turbulent fluid flows is typically computationally very expensive. Filtering the smaller scales allows for using coarse discretizations, however, this requires closure models to account for the…
Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied…
The paper introduces two new aggregation functions to encode structural knowledge from tree-structured data. They leverage the Canonical and Tensor-Train decompositions to yield expressive context aggregation while limiting the number of…
The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according…