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This paper proposes a task-agnostic discovery layer for multivariate time series that constructs a relational hypothesis graph over entities without assuming linearity, stationarity, or a downstream objective. The method learns window-level…

Processing sentence constituency trees in binarised form is a common and popular approach in literature. However, constituency trees are non-binary by nature. The binarisation procedure changes deeply the structure, furthering constituents…

We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable…

Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site…

Nonnegative matrix factorization (NMF) has been widely used in machine learning and signal processing because of its non-subtractive, part-based property which enhances interpretability. It is often assumed that the latent dimensionality…

Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to…

We discuss structured Schatten norms for tensor decomposition that includes two recently proposed norms ("overlapped" and "latent") for convex-optimization-based tensor decomposition, and connect tensor decomposition with wider literature…

A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A…

Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…

Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…

In many application domains, it is important to characterize how complex learned models make their decisions across the distribution of instances. One way to do this is to identify the features and interactions among them that contribute to…

There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…

We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…

We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are…

This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model…