Related papers: Unfolding Latent Tree Structures using 4th Order T…

Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

Despite the popularity of deep learning, structure learning for deep models remains a relatively under-explored area. In contrast, structure learning has been studied extensively for probabilistic graphical models (PGMs). In particular, an…

Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…

Classifying states as entangled or separable is a fundamental, but expensive task. This paper presents a method, the forest algorithm, to improve the amount of resources needed to detect entanglement. Starting from 'optimized' methods for…

Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…

In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional operators with separable coefficients. In this work, we focus on…

The pursuit of discovering new phenomena at the Large Hadron Collider (LHC) demands constant innovation in algorithms and technologies. Tensor networks are mathematical models on the intersection of classical and quantum machine learning,…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…

We propose a novel tree-like curvilinear structure reconstruction algorithm based on supervised learning and graph theory. In this work we analyze image patches to obtain the local major orientations and the rankings that correspond to the…

Hierarchical taxonomies are common in many contexts, and they are a very natural structure humans use to organise information. In machine learning, the family of methods that use the 'extra' information is called hierarchical…

Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the…

Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…

Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable…