Related papers: Approximation of trees by self-nested trees
Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such…
A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa…
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…
In a supercritical branching particle system, the trimmed tree consists of those particles which have descendants at all times. We develop this concept in the superprocess setting. For a class of continuous superprocesses with Feller…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family $\mathcal{D}(n)$, for $n \ge 3$ an integer, and a continuous family $\mathcal{C}(t)$, for $t \ne 1$ a complex number. The construction…
The tree code for the approximate evaluation of gravitational forces is extended and substantially accelerated by including mutual cell-cell interactions. These are computed by a Taylor series in Cartesian coordinates and in a completely…
Research into the classification of time series has made enormous progress in the last decade. The UCR time series archive has played a significant role in challenging and guiding the development of new learners for time series…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…
Deep neural networks and decision trees operate on largely separate paradigms; typically, the former performs representation learning with pre-specified architectures, while the latter is characterised by learning hierarchies over…
We introduce a semiparametric approach to neighbor-based classification. We build off the recently proposed Boundary Trees algorithm by Mathy et al.(2015) which enables fast neighbor-based classification, regression and retrieval in large…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…
This paper presents the Cascaded Metric Tree (CMT) for efficient satisfaction of metric search queries over a dataset of N objects. It provides extra information that permits query algorithms to exploit all distance calculations performed…
We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…