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We introduce a low dimensional function of the site frequency spectrum that is tailor-made for distinguishing coalescent models with multiple mergers from Kingman coalescent models with population growth, and use this function to construct…
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…
Task-specific functional MRI (fMRI) images provide excellent modalities for studying the neuronal basis of cognitive processes. We use fMRI data to formulate and solve the problem of deconvolving task-specific aggregate neuronal networks…
The bilevel functional data under consideration has two sources of repeated measurements. One is to densely and repeatedly measure a variable from each subject at a series of regular time/spatial points, which is named as functional data.…
Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…
Sentiment analysis is attracting more and more attentions and has become a very hot research topic due to its potential applications in personalized recommendation, opinion mining, etc. Most of the existing methods are based on either…
We present a scheme for investigating arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. Extending the grand canonical ensemble yields any given observable as an explicit hyper-density functional.…
When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…
The integration of quantum machine learning with classical deep learning offers promising avenues for medical image analysis by mapping data into high-dimensional Hilbert spaces. However, effectively unifying these distinct paradigms…
We consider analysis of dependent functional data that are correlated because of a longitudinal-based design: each subject is observed at repeated time visits and for each visit we record a functional variable. We propose a novel…
Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…
Conventional approaches to statistical inference preclude structures that facilitate incorporation of supplemental information acquired from similar circumstances. For example, the analysis of data obtained using perfusion computed…
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
Tumor segmentation in multimodal medical images has seen a growing trend towards deep learning based methods. Typically, studies dealing with this topic fuse multimodal image data to improve the tumor segmentation contour for a single…
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…
Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important…
Recent studies invoke the superiority of the multivariate Total Correlation concept over the conventional pairwise measures of functional connectivity in biological networks. Those seminal works certainly show that empirical measures of…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
Expanding upon previous work, using the path-integral formalism we derive expressions for the one-particle reduced density matrix and the two-point correlation function for a quadratic system of bosons that interact through a general class…