Related papers: Tree Structured Synthesis of Gaussian Trees

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

Latent Gaussian models and boosting are widely used techniques in statistics and machine learning. Tree-boosting shows excellent prediction accuracy on many data sets, but potential drawbacks are that it assumes conditional independence of…

Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…

Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…

Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good…

We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…

In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian…

Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…

In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in…

We study the problem of determining the distribution of vertices of a particular given type in the set of all Feynman tree graphs in quantum field theories. We show that in almost all cases a Gaussian distribution arises asymptotically, and…

We consider general Gaussian latent tree models in which the observed variables are not restricted to be leaves of the tree. Extending related recent work, we give a full semi-algebraic description of the set of covariance matrices of any…

The ability to automatically generate music that appropriately matches an arbitrary input track is a challenging task. We present a novel controllable system for generating single stems to accompany musical mixes of arbitrary length. At the…

A learning algorithm is presented which given the structure of a causal tree, will estimate its link probabilities by sequential measurements on the leaves only. Internal nodes of the tree represent conceptual (hidden) variables…

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…