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In the dynamic tree problem the goal is the maintenance of an arbitrary n-vertex forest, where the trees are subject to joining and splitting by, respectively, adding and removing edges. Depending on the application, information can be…

Data Structures and Algorithms · Computer Science 2015-09-23 Gabriele Farina , Luigi Laura

While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…

Machine Learning · Computer Science 2022-07-06 Mai Elkady , Jim Lim , David I. Inouye

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…

Machine Learning · Computer Science 2012-10-19 Saeed Amizadeh , Bo Thiesson , Milos Hauskrecht

In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-02 Giovanni Viglietta

Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of…

Methodology · Statistics 2025-01-23 Nikolai Spuck , Matthias Schmid , Moritz Berger

Embedding learning transforms discrete data entities into continuous numerical representations, encoding features/properties of the entities. Despite the outstanding performance reported from different embedding learning algorithms, few…

Machine Learning · Computer Science 2023-08-04 Yan Zheng , Junpeng Wang , Chin-Chia Michael Yeh , Yujie Fan , Huiyuan Chen , Liang Wang , Wei Zhang

Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…

Computational Geometry · Computer Science 2023-09-06 Jonathan Klawitter , Johannes Zink

Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…

Machine Learning · Statistics 2021-10-25 Rafael Blanquero , Emilio Carrizosa , Cristina Molero-Río , Dolores Romero Morales

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…

Statistics Theory · Mathematics 2017-02-14 Jisu Kim , Yen-Chi Chen , Sivaraman Balakrishnan , Alessandro Rinaldo , Larry Wasserman

Phylogenetic trees are the primary framework for conveying evolutionary relationships. While many tools exist for visualizing phylogenetic trees, most are limited to static graphics, require coding expertise, or are developed for a specific…

Populations and Evolution · Quantitative Biology 2026-05-15 Zachary S. L. Foster , Jeff H. Chang , Niklaus J. Grunwald

Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…

Computation · Statistics 2015-10-06 Taylor Arnold

Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local…

Data Structures and Algorithms · Computer Science 2022-01-21 Aritra Chakravorty , William S. Cleveland , Patrick J. Wolfe

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…

Machine Learning · Computer Science 2022-04-13 Maciej Piernik , Dariusz Brzezinski , Pawel Zawadzki

Evolving trees arise in many real-life scenarios from computer file systems and dynamic call graphs, to fake news propagation and disease spread. Most layout algorithms for static trees do not work well in an evolving setting (e.g., they…

Computational Geometry · Computer Science 2022-08-29 Kathryn Gray , Mingwei Li , Reyan Ahmed , Stephen Kobourov

Staged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data…

Applications · Statistics 2024-01-04 Manuele Leonelli , Gherardo Varando

We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…

Machine Learning · Statistics 2023-11-16 Siong Thye Goh , Lesia Semenova , Cynthia Rudin

In exploratory tasks involving high-dimensional datasets, dimensionality reduction (DR) techniques help analysts to discover patterns and other useful information. Although scatter plot representations of DR results allow for cluster…

Large language models achieve strong reasoning performance, yet existing decoding strategies either explore blindly (random sampling) or redundantly (independent multi-sampling). We propose Entropy-Tree, a tree-based decoding method that…

Computation and Language · Computer Science 2026-01-23 Longxuan Wei , Yubo Zhang , Zijiao Zhang , Zhihu Wang , Shiwan Zhao , Tianyu Huang , Huiting Zhao , Chenfei Liu , Shenao Zhang , Junchi Yan

In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…

Methodology · Statistics 2025-07-16 Elodie Maignant , Tim Conrad , Christoph von Tycowicz

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

Machine Learning · Computer Science 2026-03-11 Sabino Francesco Roselli , Eibe Frank
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