Related papers: Kernel Regression of Multi-Way Data via Tensor Tra…

We study nonparametric methods for the setting where multiple distinct networks are observed on the same set of nodes. Such samples may arise in the form of replicated networks drawn from a common distribution, or in the form of…

Tensor Train (TT) decompositions provide a powerful framework to compress grid-structured data, such as sampled function values, on regular Cartesian grids. Such high compression, in turn, enables efficient high-dimensional computations.…

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

We consider learning in decentralized heterogeneous networks: agents seek to minimize a convex functional that aggregates data across the network, while only having access to their local data streams. We focus on the case where agents seek…

Heterogeneous graph neural networks (HeteGNNs) have demonstrated strong abilities to learn node representations by effectively extracting complex structural and semantic information in heterogeneous graphs. Most of the prevailing HeteGNNs…

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…

Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Accurate trajectory prediction is a cornerstone for the safe operation of autonomous driving systems, where understanding the dynamic behavior of surrounding agents is crucial. Transformer-based architectures have demonstrated significant…

The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key…

We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…

Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general…

With the rise of the Internet of Things, strategies for effectively processing big data are essential for discovering meaningul insights. The time series datasets produced by groups of interconnected devices contain valuable underlying…

Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably…

Hypergraphs are a generalized data structure of graphs to model higher-order correlations among entities, which have been successfully adopted into various research domains. Meanwhile, HyperGraph Neural Network (HGNN) is currently the…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

Spatio-temporal graphs (ST-graphs) have been used to model time series tasks such as traffic forecasting, human motion modeling, and action recognition. The high-level structure and corresponding features from ST-graphs have led to improved…