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Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
We would like to congratulate Lee, Nadler and Wasserman on their contribution to clustering and data reduction methods for high $p$ and low $n$ situations. A composite of clustering and traditional principal components analysis, treelets is…
The motivation of this work is two-fold - a) to compare between two different modes of visualizing data that exists in a bag of vectors format b) to propose a theoretical model that supports a new mode of visualizing data. Visualizing high…
New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from…
We propose a novel methodology, forest floor, to visualize and interpret random forest (RF) models. RF is a popular and useful tool for non-linear multi-variate classification and regression, which yields a good trade-off between robustness…
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute…
Plant species identification in the wild is a difficult problem in part due to the high variability of the input data, but also because of complications induced by the long-tail effects of the datasets distribution. Inspired by the most…
When studying ecosystems, hierarchical trees are often used to organize entities based on proximity criteria, such as the taxonomy in microbiology, social classes in geography, or product types in retail businesses, offering valuable…
We consider the problem of drawing multiple gene trees inside a single species tree in order to visualize multispecies coalescent trees. Specifically, the drawing of the species tree fills a rectangle in which each of its edges is…
Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…
Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
Beyond the immediate biophysical benefits, urban trees play a foundational role in environmental sustainability and disaster mitigation. Precise mapping of urban trees is essential for environmental monitoring, post-disaster assessment, and…
This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
Visualization is a powerful paradigm for exploratory data analysis. Visualizing large graphs, however, often results in a meaningless hairball. In this paper, we propose a different approach that helps the user adaptively explore large…
Modality alignment is critical for vision-language models (VLMs) to effectively integrate information across modalities. However, existing methods extract hierarchical features from text while representing each image with a single feature,…
Accurate and consistent methods for counting trees based on remote sensing data are needed to support sustainable forest management, assess climate change mitigation strategies, and build trust in tree carbon credits. Two-dimensional remote…