Related papers: Binary search trees of permuton samples
Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary…
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
Prediction suffix trees (PST) provide an effective tool for sequence modelling and prediction. Current prediction techniques for PSTs rely on exact matching between the suffix of the current sequence and the previously observed sequence. We…
Tree-based models are increasingly popular due to their ability to identify complex relationships that are beyond the scope of parametric models. Survival tree methods adapt these models to allow for the analysis of censored outcomes, which…
This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size $n$ is proved to have a limiting theta distribution, both in a…
Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…
The ordered set is one of the most important data type in both theoretical algorithm design and analysis and practical programming. In this paper we study the set operations on two ordered sets, including Union, Intersect and Difference,…
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…
Binary rooted trees, both in the ordered and in the un-ordered case, are well studied structures in the field of combinatorics. The aim of this work is to study particular patterns in these classes of trees. We consider completely…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
In this work, we develop the Batch Belief Trees (BBT) algorithm for motion planning under motion and sensing uncertainties. The algorithm interleaves between batch sampling, building a graph of nominal trajectories in the state space, and…
This paper considers direct sampling methods from discrete target distributions. The inverse transform sampling (ITS) method is one of the most popular direct sampling methods. The main purpose of this paper is to propose a direct sampling…
We study maximal clades in random phylogenetic trees with the Yule-Harding model or, equivalently, in binary search trees. We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In…
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to…
Rapidly-exploring Random Tree star (RRT*) has recently gained immense popularity in the motion planning community as it provides a probabilistically complete and asymptotically optimal solution without requiring the complete information of…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
We survey permutation-based methods for approximate k-nearest neighbor search. In these methods, every data point is represented by a ranked list of pivots sorted by the distance to this point. Such ranked lists are called permutations. The…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
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…