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Wolfram Summer School

June 24–July 14, 2018
Bentley University, Waltham, MA

Alumni

Sebastian Bodenstein

Class of 2013

Bio

Sebastian is currently completing his PhD in Physics at the University of Cape Town. His recent work has included precision quark mass determinations, as well as investigating the current disagreement between the experimental and theoretical prediction of the anomalous magnetic moment of the muon.

Other interests include playing the blues guitar, watching and playing soccer, multi-day hikes, and geeky discussions on Middle Earth lore.

Project

Suppose we are interested in a probabilistic system characterized by some set of random variables {X1,X2,...,Xn}. The joint distribution P(X1,X2,...,Xn) is the most complete available representation of the probabilistic system, as all other probabalistic quantities of interest can be obtained from it.

The project will consist of two parts. First, Mathematica lacks certain built-in functionality with respect to manipulating probability distributions. For example, it lacks a CategoricalDistribution or ConditionalDistribution function. The former is the most general distribution over a random variable with K non-ordered outcomes. The latter takes in a distribution and condition and returns the conditioned distribution. These functions will be written.

The second part of the project deals with the major computational problem of using joint distributions: the exponential growth in memory usage with increase in joint distribution dimension. For high-dimensional distributions, some approximation scheme for the joint distribution is needed. Two general classes of non-parametric approximations exist in the literature: spectral methods and causal decompositions (or Bayesian networks). In the project, we will implement the causal decomposition approach, where the causal structure of the random variables can be inferred, leading to a more efficient representation of the probabilistic system.

Favorite Four-Color, Four State Turing Machine

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