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Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…
This paper introduces a novel paradigm to impute missing data that combines a decision tree with an auto-associative neural network (AANN) based model and a principal component analysis-neural network (PCA-NN) based model. For each model,…
High-dimensional compositional covariates, often derived from count data, are subject to measurement error and are frequently analyzed after aggregation along a prespecified tree to improve interpretability in applications such as…
DNA microarrays are a relatively new technology that can simultaneously measure the expression level of thousands of genes. They have become an important tool for a wide variety of biological experiments. One of the most common goals of DNA…
Anatomical trees play a central role in clinical diagnosis and treatment planning. However, accurately representing anatomical trees is challenging due to their varying and complex topology and geometry. Traditional methods for representing…
Single-cell RNA sequencing (scRNA-seq) provides unprecedented insights into cellular heterogeneity, enabling detailed analysis of complex biological systems at single-cell resolution. However, the high dimensionality and technical noise…
Microarray technology is a process that allows thousands of genes simultaneously monitor to various experimental conditions. It is used to identify the co-expressed genes in specific cells or tissues that are actively used to make proteins,…
Given a gene tree and a species tree, ancestral configurations represent the combinatorially distinct sets of gene lineages that can reach a given node of the species tree. They have been introduced as a data structure for use in the…
In this paper we face the problem of representation of functional data with the tools of algebraic topology. We represent functions by means of merge trees, which, like the more commonly used persistence diagrams, are invariant under…
The widely used genetic pleiotropic analysis of multiple phenotypes are often designed for examining the relationship between common variants and a few phenotypes. They are not suited for both high dimensional phenotypes and high…
Huffman coding is a widely used method for lossless data compression because it optimally stores data based on how often the characters occur in Huffman trees. An $n$-ary Huffman tree is a connected, cycle-lacking graph where each vertex…
It has been classically conjectured that the brain compresses data by assigning probabilistic models to sequences of stimuli. An important issue associated to this conjecture is what class of models is used by the brain to perform its…
Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…
We propose a quantitative method to estimate the statistical properties of sets of genes for which expression data are available and co-registered to a reference atlas of the brain. It is based on graph-theoretic properties of co-expression…
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…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
Cataloging the neuronal cell types that comprise circuitry of individual brain regions is a major goal of modern neuroscience and the BRAIN initiative. Single-cell RNA sequencing can now be used to measure the gene expression profiles of…
Natural language text corpora are often available as sets of syntactically parsed trees. A wide range of expressive tree queries are possible over such parsed trees that open a new avenue in searching over natural language text. They not…
With the astonishing rate that the genomic and metagenomic sequence data sets are accumulating, there are many reasons to constrain the data analyses. One approach to such constrained analyses is to focus on select subsets of gene families…
Ren et al. recently introduced a method for aggregating multiple decision trees into a strong predictor by interpreting a path taken by a sample down each tree as a binary vector and performing linear regression on top of these vectors…