Related papers: Discussion of: Treelets--An adaptive multi-scale b…

Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…

We provide a logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees. This results is useful for analyzing phylogenetic mixture models. The proof depends on interpreting multisets of trees as high…

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…

Phylogenetic networks are a generalisation of phylogenetic trees that allow for more complex evolutionary histories that include hybridisation-like processes. It is of considerable interest whether a network can be considered `tree-like' or…

This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown…

We focus on the increasingly important area of sparse regression problems where there are many variables and the effects of a large subset of these are negligible. This paper describes the construction of hierarchical prior distributions…

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if…

Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to…

We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…

Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…

Scaling regression to large datasets is a common problem in many application areas. We propose a two step approach to scaling regression to large datasets. Using a regression tree (CART) to segment the large dataset constitutes the first…

Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for…

The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…

A brief description of tree structured sparse coding on the binary cube.

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

Relational Databases are universally conceived as an advance over their predecessors Network and Hierarchical models. Superior in every querying respect, they turned out to be surprisingly incomplete when modeling transitive dependencies.…

Density Estimation Trees can play an important role in exploratory data analysis for multidimensional, multi-modal data models of large samples. I briefly discuss the algorithm, a self-optimization technique based on kernel density…

We develop Clustered Random Forests, a random forests algorithm for clustered data, arising from independent groups that exhibit within-cluster dependence. The leaf-wise predictions for each decision tree making up clustered random forests…

The paper proposes a new variant of a decision tree, called an Extreme Learning Tree. It consists of an extremely random tree with non-linear data transformation, and a linear observer that provides predictions based on the leaf index where…