An Information Geometric Approach to Increase Representational Power in Unsupervised Learning

Machine learning models increase their representational power by increasing the number of parameters in the model. The number of parameters in the model can be increased by introducing hidden nodes, higher-order interaction effects or by introducing new features into the model. In this thesis we study different approaches to increase the representational power in unsupervised machine learning models. We investigate the use of incidence algebra and information geometry to develop novel machine learning models to include higher-order interactions effects into the model. Incidence algebra provides a natural formulation for combinatorics by expressing it as a generative function and information geometry provides many theoretical guarantees in the model by projecting the problem onto a dually flat Riemannian structure for optimization. Combining the two techniques together formulates the information geometric formulation of the binary log-linear model. We first use the information geometric formulation of the binary log-linear model to formulate the higher-order Boltzmann machine (HBM) to compare the different behaviours when using hidden nodes and higher-order feature interactions to increase the representational power of the model. We then apply the concepts learnt from this study to include higher-order interaction terms in Blind Source Separation (BSS) and to create an efficient approach to estimate higher order functions in Poisson process. Lastly, we explore the possibility to use Bayesian non-parametrics to automatically reduce the number of higher-order interactions effects included in the model

Multivariate Approaches to Classification in Extragalactic Astronomy

Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still largely in use, together with numerous mono-or bivariate classifications most often made by eye. However, a classification must be driven by the data, and sophisticated multivariate statistical tools are used more and more often. In this paper we review these different approaches in order to situate them in the general context of unsupervised and supervised learning. We insist on the astrophysical outcomes of these studies to show that multivariate analyses provide an obvious path toward a renewal of our classification of galaxies and are invaluable tools to investigate the physics and evolution of galaxies.Comment: Open Access paper. http://www.frontiersin.org/milky\_way\_and\_galaxies/10.3389/fspas.2015.00003/abstract\>. \<10.3389/fspas.2015.00003 \&g

Big data clustering: Data preprocessing, variable selection, and dimension reduction

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Photodisintegration of the Deuteron at 18 MeV using Linearly Polarized Photons

This thesis reports the: cross section, parameterized differential cross section, and analyzing power (a.k.a. the photon asymmetry), for neutron production via the photodisintegration of the unpolarized deuteron at 18 MeV using linearly polarized photons. The data were collected in October 2010 using the High Intensity Gamma Source at the Duke Free-Electron Laser Laboratory located at Duke University in Durham, North Carolina. The ejectile neutrons from the photodisintegration reaction were measured using the Blowfish detector array: a spherical array of 88 BC-505 liquid organic scintillator cells which cover approximately pi steradians. The initial goal of our experiment was to perform tests on the detector characteristics and check a few potential sources of systematic error, and so uncontaminated experimental runs were only taken with the remaining beam-time. Our data are therefore not optimized for precision, and so presented a number of data analysis challenges. This thesis delineates the challenges and respective solutions. Contrary to earlier results near deuteron binding energy threshold, we see reasonable agreement with a theoretical calculation based on retarded one meson exchange with empirical cutoffs in the propagators, including: off-shell corrections, relativistic corrections and the Delta isobar degree-of-freedom. Our results show similar agreement to theory as previous experiments at 14 and 16 MeV, although we see no target length dependence: such has been observed at 20 MeV