I am interested in a variety of problems in the mathematical foundations of Data Science, motivated by the need to exploit data to advance scientific discovery and build generalizable, interpretable predictive models. These problems require ideas and techniques from a variety of areas, including Harmonic Analysis, Approximation Theory, Probability and Statistics. Scalable algorithms are a requirement in applications, and I often use multiscale techniques to develop near-linear time algorithms.
I apply these techniques to the study of physical systems, e.g. to the analysis of molecular dynamics data in order to automatically learn reduced models or speed up simulations, or to infer models of complex agent-based systems (e.g. to model cell dynamics), to the study of hyperspectral images (e.g. for unsupervised segmentation or anomaly detection), to reinforcement learning (to learn optimal policies for automated agents).
See my Research page for more info about:
- Learning Interaction Kernels in interacting particle- or agent-based systems.
- Diffusion Wavelets: a construction of families of wavelets and Multi-resolution Analyses on graphs, manifolds and point clouds. Pictures, papers and presentations available.
- Diffusion Geometries: here are some links to the use of diffusion geometries in data analysis.
- Multiscale Geometric Methods for Data: various techniques for studying geometry of high-dimensional data in a multiscale fashion.
- Analysis of Molecular Dynamics Data: in collaboration with Cecilia Clementi and her lab, we use the geometric structure of data generated from molecular dynamics data to construct observables that provide reaction coordinates and reduced, low-dimensional dynamics that well-approximates the long-time dynamics of the original system.
- Multiscale Analysis of Markov Decision Processes.
- Visualization of large data sets.
- Harmonic Analysis and Wavelets: here I talk a bit about Harmonic Analysis and provide links to related web pages.
- HyperSpectral Imaging and Pathology: hyper-spectral imaging applied to pathology.
Academic year 2020-2021: I am on sabbatical, partially funded by a generous Simons Fellowship and will be slower than usual in replying to e-mails, especially those on administrative matters.
Contact info: my e-mail is mauro@maggioni-jhu-@-icloud.com, with all the – characters and the first @ removed. I do not monitor consistently @jh.edu and @jhu.edu addresses; e-mails sent to those addresses from non-Hopkins e-mail addresses are filtered, may be modified with warning banners against non-Hopkins sources, or directly marked as spam by Hopkins, regardless of the relevance of their content, in a way that prevents e-mails, especially from non-Hopkins addresses, to reliably reach me. Furthermore, links in those e-mails are transformed into trackable links so that all clicks on them become traceable (likely at least by Hopkins and Microsoft),and become incompatible with certain browsers, VPNs, and private browsing settings (e.g. Apple’s private relay in its current incarnation), at Microsoft’s discretion (which appears to change frequently).
Covid data: if you think data in terms of absolute numbers reported across groups, states, countries by websites at Hopkins is not helpful for making comparisons, see the summaries and list of resources at Data bits on Covid, which also contains a visualization of JHU data from the JHU testing dashboard that I find more useful than those at the source.
Postdocs and students
My research group may have open positions for graduate students and postdocs. Areas of interest include stochastic dynamical systems, statistical signal processing, statistical/machine learning, high-dimensional probability and geometry, spectral graph theory and signal processing on graphs, reinforcement learning. Please use mathjobs to apply, and also consider the J.J. Sylvester Asst. Prof. positions in Math.
In a field which is so complicated [as education] that true science is not yet able to get anywhere, we have to rely on a kind of old-fashioned wisdom, a kind of definite straightforwardness. I am trying to inspire the teacher at the bottom to have some hope and some self-confidence in common sense and natural intelligence. The experts who are leading you may be wrong.