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Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…

The magnitude of Pearson correlation between two scalar random variables can be visually judged from the two-dimensional scatter plot of an independent and identically distributed sample drawn from the joint distribution of the two…

A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel). Not all directed graphs contain kernels, and computing a kernel or deciding…

In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-like shapes and study metrics on the shape space. This shape space has singularities, corresponding to topological…

In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide…

Accurate anatomical labeling and analysis of the pulmonary structure and its surrounding anatomy from thoracic CT is getting increasingly important for understanding the etilogy of abnormalities or supporting targetted therapy and early…

Tree kernels are fundamental tools that have been leveraged in many applications, particularly those based on machine learning for Natural Language Processing tasks. In this paper, we devise a parallel implementation of the sequential…

We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and…

The Weisfeiler-Lehman graph kernels are among the most prevalent graph kernels due to their remarkable time complexity and predictive performance. Their key concept is based on an implicit comparison of neighborhood representing trees with…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

The analysis of human microbiome data is often based on dimension-reduced graphical displays and clustering derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated…

Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…

The identification of pulmonary lobes is of great importance in disease diagnosis and treatment. A few lung diseases have regional disorders at lobar level. Thus, an accurate segmentation of pulmonary lobes is necessary. In this work, we…

We present the discrete version of heat kernel smoothing on graph data structure. The method is used to smooth data in an irregularly shaped domains in 3D images. New statistical properties are derived. As an application, we show how to…

Accurate, automatic and complete extraction of pulmonary airway in medical images plays an important role in analyzing thoracic CT volumes such as lung cancer detection, chronic obstructive pulmonary disease (COPD), and…

Neurodegeneration affects cortical gray matter leading to loss of cortical mantle volume. As a result of such volume loss, the geometrical arrangement of the regions on the cortical surface is expected to be altered in comparison to healthy…

Chronic obstructive pulmonary disease (COPD) is one of the most common chronic illnesses in the world and the third leading cause of mortality worldwide. It is often underdiagnosed or not diagnosed until later in the disease course.…

Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…

We investigate a recently proposed family of positive-definite kernels that mimic the computation in large neural networks. We examine the properties of these kernels using tools from differential geometry; specifically, we analyze the…