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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…

The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…

Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…

Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…

Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…

We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to…

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost…

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…

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…

Alphabetic codes and binary search trees are combinatorial structures that abstract search procedures in ordered sets endowed with probability distributions. In this paper, we design new linear-time algorithms to construct alphabetic codes,…

In recent years, dynamically growing data and incrementally growing number of classes pose new challenges to large-scale data classification research. Most traditional methods struggle to balance the precision and computational burden when…

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

Data augmentation is widely used for training a neural network given little labeled data. A common practice of augmentation training is applying a composition of multiple transformations sequentially to the data. Existing augmentation…

We obtain new non-asymptotic tail bounds for the height of uniformly random trees with a given degree sequence, simply generated trees and conditioned Bienaym\'e trees (the family trees of branching processes), in the process settling three…

As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…

We propose two algorithms for interpretation and boosting of tree-based ensemble methods. Both algorithms make use of mathematical programming models that are constructed with a set of rules extracted from an ensemble of decision trees. The…

We present a new uniform random sampler for binary trees with $n$ internal nodes consuming $2n + \Theta(\log(n)^2)$ random bits on average. This makes it quasi-optimal and out-performs the classical Remy algorithm. We also present a sampler…

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…