Related papers: Dirichlet Fragmentation Processes
We study a branching-process random iterated function system (RIFS) defined by a recursive replacement of leaves by finite subtrees at strictly smaller contraction scales. This construction yields a tree-valued, infinite-depth random…
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…
In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of…
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location…
Tree ensemble algorithms as RandomForest and GradientBoosting are currently the dominant methods for modeling discrete or tabular data, however, they are unable to perform a hierarchical representation learning from raw data as…
We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the…
Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…
The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is…
Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of…
Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…
Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, or partitioning, where each data point is modeled as being associated with one and only one of some collection of groups called…
The cooperative hierarchical structure is a common and significant data structure observed in, or adopted by, many research areas, such as: text mining (author-paper-word) and multi-label classification (label-instance-feature). Renowned…
We describe a nonparametric topic model for labeled data. The model uses a mixture of random measures (MRM) as a base distribution of the Dirichlet process (DP) of the HDP framework, so we call it the DP-MRM. To model labeled data, we…
We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…