Mauro Maggioni

  • Research Professor of Mathematics
External address: 117 Physics Bldg, Office #293, Durham, NC 27708
Internal office address: 319 Gross Hall, Information Initiative at Duke, Durham, NC 27708
Phone: (919) 660-2825

Research Areas and Keywords

Analysis
harmonic analysis, statistical learning, signal processing, stochastic dynamical systems
Computational Mathematics
statistical learning, machine learning, signal processing, algorithms
PDE & Dynamical Systems
harmonic analysis, stochastic dynamical systems
Probability
harmonic analysis, statistical learning, machine learning, signal processing, high-dimensional probability, stochastic dynamical systems, algorithms

I am interested in novel constructions inspired by classical harmonic analysis that allow to analyse the geometry of manifolds and graphs and functions on such structures. These constructions are motivated by several important applications across many fields. In many situations we are confronted with large amounts of apparently unstructured high-dimensional data. I find fascinating to study the intrinsic geometry of such data, and exploiting in order to study, explore, visualize, characterize statistical properties of the data. Oftentimes such data is modeled as a manifold (or something "close to a manifold") or a graph, and functions on these spaces need to approximated or "learned" from the data and experiments on the data. For example each data point could be a document, a graph associated with the documents could be given by for example hyperlinks, or by similarity of word frequencies, and a function on the set of documents would be how interesting I personally score a document. One may wish to learn how to predict how much I would score documents I have not seen yet. This can be cast as an approximation problem on the graph of documents, and it turns out that one can generalize Euclidean-type approximation techniques (in particular multiscale regression techniques) to tackle this problem. An application of the above techniques that I find particularly interesting is Markov Decision Processes and Reinforcement Learning, where the problem of learning a behaviour from experience is cast in a rather general optimization and learning framework that involves approximations of functions and operators on graphs and manifolds. I am also interested in imaging, in particular I am working on novel classes of nonlinear denoising algorithms, based on diffusion processes on graphs of features built from images. Another interest is in the geometry of multiscale dynamical systems, and the construction of algorithms for the empirical construction of approximate equations for such systems. I also work on hyperspectral imaging, in particular in building automatic classifiers for discriminating normal from cancerous biopsies, for automated diagnostics and pathology.

Education & Training
  • Ph.D., Washington University 2002

  • M.S., Washington University 2000

Dimension Reduction for Open Quantum Systems awarded by Stanford University (Principal Investigator). 2016 to 2020

BIGDATA:Collaborative Research:F:From Data Geometries to Information Networks awarded by National Science Foundation (Principal Investigator). 2016 to 2019

Statistical learning for high-dimensional stochastic dynamical systems awarded by National Science Foundation (Principal Investigator). 2015 to 2018

Collaborative Research: SI2-CHE-ExTASY Extensible Tools for Advanced Sampling and AnalYsis awarded by National Science Foundation (Principal Investigator). 2013 to 2017

Structured Dictionary Models and Learning for High Resolution Images awarded by National Science Foundation (Principal Investigator). 2013 to 2017

EMSW21-RTG: Geometric, Topological awarded by National Science Foundation (Co-Principal Investigator). 2011 to 2017

Geometric Approximation and Estimation of Probability Measures in High Dimensions awarded by Air Force Office of Scientific Research (Principal Investigator). 2013 to 2016

Multiscale Analysis of Dynamic Graphs awarded by Office of Naval Research (Principal Investigator). 2012 to 2016

X-Ray Scatter and Phase Imaging for Explosive Detection awarded by US Department of Homeland Security (Co-Principal Investigator). 2011 to 2015

Pages

Bongini, M, Fornasier, M, Hansen, M, and Maggioni, M. "Inferring interaction rules from observations of evolutive systems I: The variational approach." Mathematical Models and Methods in Applied Sciences 27.05 (May 2017): 909-951. Full Text

Crosskey, M, and Maggioni, M. "ATLAS: A Geometric Approach to Learning High-Dimensional Stochastic Systems Near Manifolds." Multiscale Modeling & Simulation 15.1 (January 2017): 110-156. Full Text

Wang, Y, Chen, G, and Maggioni, M. "High-Dimensional Data Modeling Techniques for Detection of Chemical Plumes and Anomalies in Hyperspectral Images and Movies." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 9.9 (September 2016): 4316-4324. Full Text

Goetzmann, WN, Jones, PW, Maggioni, M, and Walden, J. "Beauty is in the bid of the beholder: An empirical basis for style." Research in Economics 70.3 (September 2016): 388-402. Full Text

Little, AV, Maggioni, M, and Rosasco, L. "Multiscale geometric methods for data sets I: Multiscale SVD, noise and curvature." Applied and Computational Harmonic Analysis (March 2016). Full Text

Maggioni, M, Minsker, S, and Strawn, N. "Multiscale dictionary learning: Non-asymptotic bounds and robustness." Journal of Machine Learning Research 17 (January 1, 2016).

Maggioni, M. "Geometry of Data and Biology." Notices of the American Mathematical Society 62.10 (November 1, 2015): 1185-1188. Full Text

Altemose, N, Miga, KH, Maggioni, M, and Willard, HF. "Genomic characterization of large heterochromatic gaps in the human genome assembly." PLoS computational biology 10.5 (May 15, 2014): e1003628-. Full Text

Coppola, A, Wenner, BR, Ilkayeva, O, Stevens, RD, Maggioni, M, Slotkin, TA, Levin, ED, and Newgard, CB. "Branched-chain amino acids alter neurobehavioral function in rats." Am J Physiol Endocrinol Metab 304.4 (February 15, 2013): E405-E413. Full Text

Krishnamurthy, K, Mrozack, A, Maggioni, M, and Brady, D. "Multiscale, dictionary-based speckle denoising." Optics InfoBase Conference Papers (January 1, 2013).

Pages