Daniel Andrés Díaz-Pachón

Daniel Andrés Díaz-Pachón is a Research Assistant Professor in the Division of Biostatistics since September 2014. His research, current and former, can be divided into four big areas:

In probability, he is working on population genetics. Particularly, his current interest is on the Spatial Lambda-Fleming-Viot process (SLFV) to model evolution in the spatial continuum, developed by Alison Etheridge and collaborators. Surprisingly enough, his current work relies heavily on the research for his doctoral dissertation, which was entirely focused on continuum percolation and large deviations of stable allocations.

In information theory, he is working on active information, based on Bernoulli's Principle of Insufficient Reason. In this endeavor, he is collaborating with engineer Robert Marks II, who developed the concept with his collaborators for uniform distributions. Dr. Díaz-Pachón's project is on the generalization of the concept to more general distributions.

In machine learning, he has currently begun to work with Sunil Rao and Hemant Ishwaran on the problem of learnability, which depends on a concept called stability. Part of the interest is to analyze, and hopefully improve, some existent inequalities. In the past, as part of his postdoctoral research and together with Rao and Jean-Eudes Dazard, he was able to transform a supervised bump-hunting algorithm into a more efficient unsupervised one, when the sample is large.

In theoretical statistics, together with Rao and Dazard, he is working to understand when in learning settings, mainly regression, the rotation (not the projection of the space) to principal components of the explanatory variables makes sense to explain the response. In order to achieve this goal, Dr. Díaz-Pachón has relied entirely on stochastic geometry, partially solving this open problem of around 70 years. He and his collaborators continue working on a full solution for this problem.