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no code implementations • 1 Dec 2022 • Christian Kümmerle, Mauro Maggioni, Sui Tang

This Spatio-Temporal Transition Operator Recovery problem is motivated by the recent interest in learning time-varying graph signals that are driven by graph operators depending on the underlying graph topology.

no code implementations • 4 Aug 2022 • Jinchao Feng, Mauro Maggioni, Patrick Martin, Ming Zhong

Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e. g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents.

no code implementations • 12 Jul 2022 • Qingci An, Yannis Kevrekidis, Fei Lu, Mauro Maggioni

Assuming abundant data of the observation process along with the distribution of the state process, we introduce a nonparametric generalized moment method to estimate the observation function via constrained regression.

no code implementations • 26 Aug 2021 • Ming Zhong, Jason Miller, Mauro Maggioni

Building accurate and predictive models of the underlying mechanisms of celestial motion has inspired fundamental developments in theoretical physics.

no code implementations • 5 Apr 2021 • Felix X. -F. Ye, Sichen Yang, Mauro Maggioni

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes.

no code implementations • 30 Jan 2021 • Mauro Maggioni, Jason Miller, Hongda Qiu, Ming Zhong

Interacting agent and particle systems are extensively used to model complex phenomena in science and engineering.

no code implementations • 13 Jan 2021 • Wenjing Liao, Mauro Maggioni, Stefano Vigogna

We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $.

no code implementations • 21 Oct 2020 • Haley G. Abramson, Dan M. Popescu, Rebecca Yu, Changxin Lai, Julie K. Shade, Katherine C. Wu, Mauro Maggioni, Natalia A. Trayanova

Visualizing disease-induced scarring and fibrosis in the heart on cardiac magnetic resonance (CMR) imaging with contrast enhancement (LGE) is paramount in characterizing disease progression and quantifying pathophysiological substrates of arrhythmias.

no code implementations • 8 Oct 2020 • Jason Miller, Sui Tang, Ming Zhong, Mauro Maggioni

Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning.

no code implementations • 30 Jul 2020 • Fei Lu, Mauro Maggioni, Sui Tang

Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.

1 code implementation • 23 Dec 2019 • Mauro Maggioni, Jason Miller, Ming Zhong

We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of trajectories, in particular for collective dynamical systems exhibiting emergent behaviors with complicated interaction kernels, in a nonparametric fashion, and for kernels which are parametrized by a single unknown parameter.

no code implementations • 10 Oct 2019 • Fei Lu, Mauro Maggioni, Sui Tang

These simulations also suggest that our estimators are robust to noise in the observations, and produce accurate predictions of dynamics in relative large time intervals, even when they are learned from data collected in short time intervals.

no code implementations • 30 May 2019 • Mauro Maggioni, James M. Murphy

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs.

no code implementations • 8 Feb 2019 • James M. Murphy, Mauro Maggioni

The explicit incorporation of spatial regularity into the diffusion construction leads to smoother random processes that are more adapted for unsupervised machine learning than those based on spectra alone.

1 code implementation • 14 Dec 2018 • Fei Lu, Mauro Maggioni, Sui Tang, Ming Zhong

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines.

no code implementations • 15 Oct 2018 • Mauro Maggioni, James M. Murphy

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation.

1 code implementation • 17 Dec 2017 • Anna Little, Mauro Maggioni, James M. Murphy

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters.

1 code implementation • 5 Sep 2017 • Joshua T. Vogelstein, Eric Bridgeford, Minh Tang, Da Zheng, Christopher Douville, Randal Burns, Mauro Maggioni

To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences.

2 code implementations • 8 Aug 2017 • Samuel Gerber, Mauro Maggioni

The approach is based on an adaptive multiscale decomposition of the point sets.

no code implementations • 26 Apr 2017 • James M. Murphy, Mauro Maggioni

The problem of unsupervised learning and segmentation of hyperspectral images is a significant challenge in remote sensing.

no code implementations • 3 Nov 2016 • Wenjing Liao, Mauro Maggioni

We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example supported on a $d$-dimensional Riemannian manifold.

4 code implementations • 16 Sep 2016 • Joshua T. Vogelstein, Eric Bridgeford, Qing Wang, Carey E. Priebe, Mauro Maggioni, Cencheng Shen

Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets.

no code implementations • 24 Sep 2015 • Yi, Wang, Guangliang Chen, Mauro Maggioni

We briefly review recent progress in techniques for modeling and analyzing hyperspectral images and movies, in particular for detecting plumes of both known and unknown chemicals.

2 code implementations • 10 Jun 2015 • Tyler M. Tomita, James Browne, Cencheng Shen, Jaewon Chung, Jesse L. Patsolic, Benjamin Falk, Jason Yim, Carey E. Priebe, Randal Burns, Mauro Maggioni, Joshua T. Vogelstein

Unfortunately, these extensions forfeit one or more of the favorable properties of decision forests based on axis-aligned splits, such as robustness to many noise dimensions, interpretability, or computational efficiency.

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