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Decision Trees are some of the most popular machine learning models today due to their out-of-the-box performance and interpretability. Often, Decision Trees models are constructed greedily in a top-down fashion via heuristic search…
Given a permutation $\sigma$, its corresponding binary search tree is obtained by recursively inserting the values $\sigma(1),\ldots,\sigma(n)$ into a binary tree so that the label of each node is larger than the labels of its left subtree…
Motivated by online recommendation systems, we study a family of random forests. The vertices of the forest are labeled by integers. Each non-positive integer $i\le 0$ is the root of a tree. Vertices labeled by positive integers $n \ge 1$…
We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question…
Rooted trees with probabilities are convenient to represent a class of random processes with memory. They allow to describe and analyze variable length codes for data compression and distribution matching. In this work, the Leaf-Average…
We study some essential arithmetic properties of a new tree-based number representation, {\em hereditarily binary numbers}, defined by applying recursively run-length encoding of bijective base-2 digits. Our representation expresses giant…
We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split…
Rebalancing schemes for dynamic binary search trees are numerous in the literature, where the goal is to maintain trees of low height, either in the worst-case or expected sense. In this paper we study randomized rebalancing schemes for…
The constant rate birth--death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces `reconstructed trees' which describe the relationship between extant…
Random binary search trees are obtained by recursively inserting the elements $\sigma(1),\sigma(2),\ldots,\sigma(n)$ of a uniformly random permutation $\sigma$ of $[n]=\{1,\dots,n\}$ into a binary search tree data structure. Devroye (1986)…
Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum…
Tree ensembles are machine learning models with strong predictive performance and interpretability, and remain widely used for tabular data. Standard pruning methods for tree ensembles typically optimize an accuracy-compression trade-off…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and…
In this work we consider random two-colourings of random linear preferential attachment trees, which includes random recursive trees, random plane-oriented recursive trees, random binary search trees, and a class of random $d$-ary trees.…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
Decision trees and randomized forests are widely used in computer vision and machine learning. Standard algorithms for decision tree induction optimize the split functions one node at a time according to some splitting criteria. This greedy…
In this paper we introduce a new model of random spanning trees that we call choice spanning trees, constructed from so-called choice random walks. These are random walks for which each step is chosen from a subset of random options,…