The Short Version: Put a hat on it. Ideally with error bars.
The Long Version: My research focuses on developing new analytical tools to facilitate understanding of dynamical processes that occur on networks. By realizing information theoretic analyses via nonparametric statistics, researchers can gain new insights into the organization of complex systems. A selection of my research interests are summarized below.
Understanding Complex Social Systems
For the first time in human history, we have massive data sets about how humans interact with each other and with their environment. This data arises from diverse settings, from cell phone call records to geotagged images to interactions on social media. The prevalence of such data has caused a renaissance in the social sciences, allowing for the quantitative study of how large populations of humans behave outside of the laboratory. However, the abundance of such data does not in itself offer understanding. Instead, we must turn to models that describe and explain this data. This has been the core mission behind the nascent field of computational social science. During my time in graduate school, I worked to advance this mission by developing statistical methods for understanding time series data drawn from complex social systems. You can find my PhD thesis related to this work here.
Specific Information Dynamics
Information theory provides a mathematical framework for describing how a system stores, processes, and transmits information. Developed by Claude Shannon in the 1940s to model communication channels, information theory has undergone a renaissance, finding applications in the physical, biological, and social sciences. My research focuses on developing new information theoretic measures that can be estimated from data, with an emphasis on methods applicable to dynamical systems. Two new state-dependent measures of predictive uncertainty along these lines are Specific Entropy Rate and the Specific Transfer Entropy, which fall under the umbrella of Specific Information Dynamics.
Specific Information Dynamics for Connectivity Analysis in Neuroscience
Typical connectivity analysis in neuroscience requires either strong / weak stationarity for epoched analysis or temporal binning for time-varying analysis. Because Specific Information Dynamics applies under the much weaker assumption of conditional stationarity, it allows for the direct investigation of predictive information storage, generation, and transfer as measured by electrophysiological activity. This analysis works especially well for paradigms that induce evoked activity, and allows for by-trial or across-trial analysis.
Operationalizing Computational Mechanics
Computational mechanics is a subdiscipline of the theory of stochastic processes motivated by finding the minimal representation of a stochastic process based on its predictive distribution. It is not this, and really warrants its own Wikipedia entry. For a good overview, see here, and here, while the course material still exists. An excellent review article is here.
The central object of study for computational mechanics is the causal or predictive states of the process, resulting from partitioning pasts of the process based on their predictive distributions, and the transitions between those states.
My main contribution to the practice of computational mechanics is the first implementation of a reconstruction algorithm for the predictive states of an input-output process, called Transducer Causal State Splitting Reconstruction, or transCSSR for short. You can find a Python module that implements transCSSR here.