My research has focused primarily on applications related to neuroscience, information theory and computer vision. These topics provide ample opportunities to participate in collaborative, interdisciplinary research, something that I value and enjoy, and they relate to a subject that I find fascinating: the mathematical and computational foundations of learning and intelligence. They also provide an endless supply of interesting mathematical and statistical problems.

Over the next several years I plan to continue existing collaborations and develop new collaborations with scientists studying biological and machine intelligence. Anticipating the specific research questions that will arise is dicult, but probability, statistics and computing will surely play important
roles. I expect neuroscience, information theory and computer vision to remain central to my work.

Neuroscience

Perception, cognition and behavior arise in part from the electrical signals among billions of neurons. The details of this process are still a mystery. Modern neurophysiological techniques permit the
simultaneous recording of the electrical activity of hundreds of individual neurons (and this number is quickly growing) or, more coarsely, the global activity of brain regions comprised of hundreds
of thousands of neurons. The high dimensionality of the resulting data sets, combined with the peculiarities of neural activity patterns, create challenging statistical issues. Methods for exploratory statistical analysis are crucial right now in neuroscience, and will probably remain crucial for years to come. This is not to say that statistical modeling is premature but rather, that models are typically used in an exploratory fashion. The conflux of rapidly changing technology, high-dimensional datasets, demand
for exploratory methods, and sustained scientific excitement (and funding) all combine to create a fertile environment for statistical creativity and novel methodology.

Information theory

Information theory provides a rigorous probabilistic setting for understanding the fundamental limits of digital coding and communication. Because of its tight connection to probability theory,
many results in probability and statistics can be interpreted from an information theoretic point of view. This new perspective has led to a variety of insights, such as the minimum description length
(MDL) approach to model selection and learning [1]. Information theoretic ideas and interpretations are becoming commonplace in several applied areas, such as the biological sciences. Typically these applications borrow ideas, like entropy, that are related to theoretical lossless compression. Theoretical lossy compression, on the other hand, is a much less developed field with few existing
connections to scientific applications. The rate-distortion function plays the role of the entropy and describes the optimal amount of achievable compression. Furthermore, practical lossy compression
lags far behind practical lossless compression in terms of approaching optimal compression performance. Closing this gap will likely require new mathematical and computational insights,
as will drawing tighter connections between lossy compression and scientific applications. (I am convinced such connections exist. For example, lossy compression (which attempts to preserve semantic content at the expense of precise detail) seems more analogous to biological learning and perception than does lossless compression (which must preserve every detail).

Computer vision

The gap between biological and machine vision is substantial. The technological impact of closing this gap and the potential benefits for society are quite profound. One place where this gap is
especially apparent is visual learning. A child can accurately learn a novel visual category (like "helicopter") with only a few examples (maybe only a single example). But a visual category is an
incredibly complicated, high-dimensional statistical object (think of the collection of retinal images that contain a helicopter). How is rapid learning possible? Knowledge sharing (or transfer) among visual categories is often suggested as a possible solution. Inheriting ideas from my PhD advisor, Stuart Geman, I believe that highly structured statistical models (in particular, compositional models) are required for efficient sharing and transfer of knowledge. In any event, visual category learning represents an incredibly difficult statistical problem for which we know a solution exists. Even partial progress will push the boundaries of statistical methodology, generate new technology and provide scientic insights into biological
vision.

Please see Curriculum Vita

• Phi Beta Kappa, University of Virginia (1997)
• Jefferson Scholarship, University of Virginia (1994-1998)
• Howard Hughes Medical Institute Predoctoral Fellowship in Biological Sciences Awardee (1998)
• National Defense Science and Engineering Graduate Fellowship (1998-2001)
• The manuscript associated with abstract 5.f.xv above won an IBM Thomas J. Watson Research Center Student Research Award for my student Jeffrey Miller.
• The manuscript 5.c.xv above was one of 40 papers out of 1420 submissions selected for a full oral presentation at NIPS 2013.
• Philip J. Bray Award for Excellence in Teaching in the Physical Sciences (2014)

1. current and previous professional memberships: SIAM, SFN, IMS, IEEE, ASA, AMS
2. ad hoc reviewer for: The American Statistician, Annals of Applied Statistics, Annals of Statistics, Biometrics, Computation and Systems Neuroscience (COSYNE), Encylcopedia of Computational Neuroscience, Electronic Journal of Statistics, Entropy, European Conference on Computer Vision (ECCV), Frontiers in Computational Neuroscience, IEEE Information Theory Workshop (ITW), IEEE International Symposium on Information Theory (ISIT), IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing, International Conference on Computer Vision and Pattern Recognition (CVPR), Journal of Computational Neuroscience, Journal of Computational Physics, Journal of Computational Statistics and Data Analysis, Journal of Neurophysiology, Journal of Neuroscience Methods, Journal of Neural Engineering, Journal of the Royal Statistical Society, Neural Computation, Neural Information Processing Systems (NIPS), Neural Systems & Circuits, Neuron, PLoS Computational Biology, Proceedings of the National Academy of Science, Science, SIAM Journal on Imaging Sciences, Statistica Sinica, Statistical Analysis and Data Mining, Statistics and Probability Letters
3. invited session organizer, Statistical Methods in Neuroscience, 8^th World Congress on Probability and Statistics, Istanbul, Turkey (2012)
4. co-chair, organizing committee, Bayesian Nonparametrics Workshop, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, RI (2012) 
5. US National Science Foundation (NSF) research proposal panelist (2014, 2015, 2016), ad hoc reviewer (2016)
6. senior program committee member, AISTATS (2017)
7. organizer for the CRCNS 2017 PI-meeting 

Probability and Mathematical Statistics
Intermediate Statistics
Probability Theory and Random Processes
Engineering Statistics and Quality Control
Mathematical Methods in the Brain Sciences