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Here are some recent projects:

  1. QMCPy: Development of Python software and methodologies for quasi Monte Carlo
  2. Materials design for optimally performing glass fabrication
  3. Prefopt: Sample efficient search for most preferred designs
  4. GaussQR: A Matlab library in support of our textbook on kernel methods
Scatter plots of quasi random points
QMCPy: Development of Python software and methodologies for quasi Monte Carlo qmcpy.org
A collaboration between academia and industry

Dr. Fred Hickernell, Dr. Sou-Cheng Choi and I came together to organize this project, which works to bring quasi Monte Carlo methods to a broader audience by encapsulating cutting edge technologies into a Python library. Quasi Monte Carlo methods improve on standard Monte Carlo methods by replacing the i.i.d. sampling of points with a specially structured sampling of points. Aleksei Sorokin and Dr. Jagadees Rathanival have worked hard to implement methodologies and work with experts in other communities to identify opportunities for quasi Monte Carlo methods to shine. Check out our blog, and reach out if you are interested in learning more about quasi Monte Carlo.

Results of a fabrication experiment
Materials design for optimally performing glass fabrication
Bringing AI/ML to the materials science community

An increasingly important theme in the AI/ML community is to reach outside of the standard ML conference participants and find opportunities for AI/ML to be applied more broadly. To this end, Dr. Harvey Cheng and I worked with materials scientists Dr. Paul Leu and Dr. Sajad Haghanifar to use active learning and Bayesian optimization to find high performing glass fabrication strategies with minimal experimentation.

Check out our articles on building glass which is easily cleaned, and glass with low reflectivity.

Graph of the distance between two pairs of 3D vectors
Alignment as an individual-derived attribute to study team-level outcomes
Applying math to help analyze teamwork

Dr. Kyle Emich and Dr. Li Lu invited me to join a project involving studying team dynamics. In particular, we wanted to devise a strategy to incorporate individual-level attributes across team members to identify how the alignment between two or more attribtues can be used to predict team-level outcomes. We created multiple mechanisms for computing alignment based on mathematical/physical concepts which are not generally present in the business/psychology literature in which we are studying this situation.

Check out our article on how this alignment can be defined for two attributes. We are currently working on new research to push this to higher numbers of attributes.

Tolerance dropping and converging
Prefopt: Sample efficient search for most preferred designs
Optimization without an explicit objective

Dr. Greg Fasshauer and I worked together for a year and a half to write up a research textbook to help bring together the research on kernel methods in the numerical analysis and spatial statistics communities. Part of the purpose was to help unify notation, as possible. Part is to provide a computational implementation (in this case, in Matlab, to speak to graduate students). Part is to discuss recent exciting advances, such as the Hilbert-Schmidt SVD and Generalized Sobolev spaces. Future work will include applications of Gaussian processes (such as active learning and Bayesian optimization) and will probably include a Python implementation as well as the Matlab implementation.

Check out our workshop papers at the 2017 Bayesian deep learning workshop, and the 2019 human in the loop learning workshop.

GaussQR images
GaussQR: A Matlab library in support of our textbook on kernel methods
Providing access to new strategies for stable computation

In many circumstances, customers may be able to state preferences for certain outcomes without being able to quantify those preferences. For example, I may prefer Pepsi over Coke, but I cannot provide a numerical representation for that. This prevents standard optimization tool from being used to identify the most preferred outcome, even though that is surely the outcome which should be sought. Ian Dewancker and I worked to develop some software to apply Gaussian processes in latent space to effect such a search.

If you are feeling very generous, or very bored, feel free to check our book.