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There are many functions which are continuous everywhere but not differentiable at some points, like in physical systems of ECG, EEG plots, and cracks pattern and for several other phenomena. Using classical calculus those functions cannot…

Understanding the causal effects of organ-specific features from medical imaging on clinical outcomes is essential for biomedical research and patient care. We propose a novel Functional Linear Structural Equation Model (FLSEM) to capture…

Graphs are versatile tools for representing structured data. As a result, a variety of machine learning methods have been studied for graph data analysis. Although many such learning methods depend on the measurement of differences between…

We consider the problem of extracting features from passive, multi-channel electroencephalogram (EEG) devices for downstream inference tasks related to high-level mental states such as stress and cognitive load. Our proposed method…

Estimation of differences in conditional independence graphs (CIGs) of two time series Gaussian graphical models (TSGGMs) is investigated where the two TSGGMs are known to have similar structure. The TSGGM structure is encoded in the…

The human brain can be considered as complex networks, composed of various regions that continuously exchange their information with each other, forming the brain network graph, from which nodes and edges are extracted using resting-state…

Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting…

An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among…

Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Different MRI acquisitions provide different brain networks at the…

Federated Knowledge Graph Embedding (FKGE) has recently garnered considerable interest due to its capacity to extract expressive representations from distributed knowledge graphs, while concurrently safeguarding the privacy of individual…

This paper focuses on analysis and design of time-varying complex networks having fractional order dynamics. These systems are key in modeling the complex dynamical processes arising in several natural and man made systems. Notably,…

Graph neural networks (GNNs) have emerged as the state of the art for a variety of graph-related tasks and have been widely used in Heterogeneous Graphs (HetGs), where meta-paths help encode specific semantics between various node types.…

While federated learning has shown strong results in optimizing a machine learning model without direct access to the original data, its performance may be hindered by intermittent client availability which slows down the convergence and…

Brain network analysis is a useful approach to studying human brain disorders because it can distinguish patients from healthy people by detecting abnormal connections. Due to the complementary information from multiple modal neuroimages,…

Patterns of brain activity are associated with different brain processes and can be used to identify different brain states and make behavioral predictions. However, the relevant features are not readily apparent and accessible. To mine…

Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…

Functional data consist of trajectories observed over a continuous domain, such as time, space, or wavelength. Here we consider curves observed on different groups of subjects and propose a Bayesian multi-group functional factor analysis…

Multi-modal neuroimaging technology has greatlly facilitated the efficiency and diagnosis accuracy, which provides complementary information in discovering objective disease biomarkers. Conventional deep learning methods, e.g. convolutional…

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems…

We present a method for learning "spectrally descriptive" edge weights for graphs. We generalize a previously known distance measure on graphs (Graph Diffusion Distance), thereby allowing it to be tuned to minimize an arbitrary loss…