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Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…
Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…
Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
Graph anomaly detection (GAD) is a critical task in graph machine learning, with the primary objective of identifying anomalous nodes that deviate significantly from the majority. This task is widely applied in various real-world scenarios,…
Recent advances on Out-of-Distribution (OoD) generalization reveal the robustness of deep learning models against distribution shifts. However, existing works focus on OoD algorithms, such as invariant risk minimization, domain…
Network motif algorithms have been a topic of research mainly after the 2002-seminal paper from Milo \emph{et al}, that provided motifs as a way to uncover the basic building blocks of most networks. In Bioinformatics, motifs have been…
Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time…
Graph neural architecture search (GraphNAS) has demonstrated advantages in mitigating performance degradation of graph neural networks (GNNs) due to distribution shifts. Recent approaches introduce weight sharing across tailored…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
Automated essay scoring (AES) predicts multiple rubric-defined trait scores for each essay, where each trait follows an ordered discrete rating scale. Most LLM-based AES methods cast scoring as autoregressive token generation and obtain the…
Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
We investigate anomaly detection in an unsupervised framework and introduce Long Short Term Memory (LSTM) neural network based algorithms. In particular, given variable length data sequences, we first pass these sequences through our LSTM…
Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there…
Autism spectrum disorder (ASD) is a complex neurodevelopmental condition characterized by atypical functional brain connectivity and subtle structural alterations. rs-fMRI has been widely used to identify disruptions in large-scale brain…
We introduce the tree-decomposition-based parameter totally $\Delta$-modular treewidth (TDM-treewidth) for matrices with two nonzero entries per row. We show how to solve integer programs whose matrices have bounded TDM-treewidth in…
Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…