Invariances for Gaussian models

At the heart of a statistical analysis, we are interested in drawing conclusions about random variables and the laws they follow. For this we require a sample, therefore our approach is best described as learning from data. In many instances, we already have an intuition about the generating process, meaning the space of all possible models reduces to a specific class that is defined up to a set of unknown parameters. Consequently, learning becomes the task of inferring these parameters given observations. Within this scope, the thesis answers the following two questions: Why are invariances needed? Among all parameters of the model, we often distinguish between those of interest and the so-called nuisance. The latter does not carry any meaning for our purposes, but may still play a crucial role in how the model supports the parameters of interest. This is a fundamental problem in statistics which is solved by finding suitable transformations such that the model becomes invariant against unidentifiable properties. Often, the application at hand already decides upon the necessary requirements: a Euclidean distance matrix, for example, does not carry translational information of the underlying coordinate system. Why Gaussian models? The normal distribution constitutes an important class in statistics due to frequent occurrences in nature, hence it is highly relevant for many research disciplines including physics, astronomy, engineering, but also psychology and social sciences. Besides fundamental results like the central limit theorem, a significant part of its appeal is rooted in convenient mathematical properties which permit closed-form solutions to numerous problems. In this work, we develop and discuss generalizations of three established models: a Gaussian mixture model, a Gaussian graphical model and the Gaussian information bottleneck. On the one hand, all of these are analytically convenient, but on the other hand they suffer from strict normality requirements which seriously limit their range of application. To this end, our focus is to explore solutions and relax these restrictions. We successfully show that with the addition of invariances, the aforementioned models gain a substantial leap forward while retaining their core concepts of the Gaussian foundation

Eine urnenfelderzeitliche Siedlung von Unterradlberg, VB St. Pölten

Die Diplomarbeit behandelt eine zweiphasige urnenfelderzeitliche Siedlung

Measurement of tau decays into a charged hadron accompanied by neutral pi-mesons and determination of the CKM matrix element |V_us|

This thesis presents the branching fraction measurement of the tau^-->K^- npi^0 nu_tau (n = 0,1,2,3) and tau^-->pi^- npi^0 nu_tau (n = 3,4) decays. The measurement is based on a data sample of 435 million tau pairs produced in e^+e^- collisions and collected with the Babar detector in 1999-2008. The analysis is validated using precisely known tau decays as control modes. The measured branching fractions are BR( tau^-->K^-nu_tau) = (7.100 +- 0.033 +- 0.156) x 10^{-3}, BR( tau^-->K^- pi^0 nu_tau) =(5.000 +- 0.020 +- 0.139) x 10^{-3}, BR( tau^-->K^- 2pi^0 nu_tau) = (5.654 +- 0.144 +- 0.323) x 10^{-4}, BR( tau^-->K^- 3pi^0 nu_tau) = (1.642 +- 0.279 +- 0.375) x 10^{-4}, BR(tau^-->pi^- 3pi^0 nu_tau) = (1.216 +- 0.010 +- 0.047) x 10^{-2}, BR(tau^-->pi^- 4pi^0 nu_tau) = (1.041 +- 0.067 +- 0.090) x 10^{-3}, where the first uncertainty is statistical and the second systematic. The branching fraction BR(tau^-->pi^- 4pi^0 nu_tau) is measured for the first time. The precision of the results is comparable or significantly improved with respect to previous measurements. The branching fraction BR(tau^-->K^- nu_tau) is combined with a lattice QCD calculation of the kaon decay constant to obtain the Cabibbo-Kobayashi-Maskawa matrix element |V_us| = 0.2224 +- 0.0025(exp) +- 0.0029(theo). The branching fractions of the tau decays into a kaon are combined with the current world averages. The resulting averages are used in the determination of the total tau branching fraction, BR_{strange}, into strangeness |S| = 1 final states. BR_{strange} is used in conjunction with |V_ud| and a small SU(3)-symmetry breaking correction to compute |V_us| = 0.2176 +- 0.0025(exp) +- 0.0010(theo)

On the Breeds of Cattle—Historic and Current Classifications

Classification of cattle breeds contributes to our understanding of the history of cattle and is essential for an effective conservation of genetic diversity. Here we review the various classifications over the last two centuries and compare the most recent classifications with genetic data. The classifications devised during the 19th to the late 20th century were in line with the Linnaean taxonomy and emphasized cranial or horn morphology. Subsequent classifications were based on coat color, geographic origin or molecular markers. Several theories were developed that linked breed characteristics either to a supposed ancestral aurochs subspecies or to a presumed ethnic origin. Most of the older classifications have now been discarded, but have introduced several Latin terms that are still in use. The most consistent classification was proposed in 1995 by Felius and emphasizes the geographic origin of breeds. This is largely in agreement with the breed clusters indicated by a biochemical and molecular genetic analysis, which reflect either groups of breeds with a common geographic origin or single breeds that have expanded by export and/or crossbreeding. We propose that this information is also relevant for managing the genetic diversity of cattl

Recovering networks from distance data

A fully probabilistic approach to reconstructing Gaussian graphical models from distance data is presented. The main idea is to extend the usual central Wishart model in traditional methods to using a likelihood depending only on pairwise distances, thus being independent of geometric assumptions about the underlying Euclidean space. This extension has two advantages: the model becomes invariant against potential bias terms in the measurements, and can be used in situations which on input use a kernel- or distance matrix, without requiring direct access to the underlying vectors. The latter aspect opens up a huge new application field for Gaussian graphical models, as network reconstruction is now possible from any Mercer kernel, be it on graphs, strings, probabilities or more complex objects. We combine this likelihood with a suitable prior to enable Bayesian network inference. We present an efficient MCMC sampler for this model and discuss the estimation of module networks. Experiments depict the high quality and usefulness of the inferred network

The effect of temporal pattern of injury on disability in learning networks

How networks endure damage is a central issue in neural network research. This includes temporal as well as spatial pattern of damage. Here, based on some very simple models we study the difference between a slow-growing and acute damage and the relation between the size and rate of injury. Our result shows that in both a three-layer and a homeostasis model a slow-growing damage has a decreasing effect on network disability as compared with a fast growing one. This finding is in accord with clinical reports where the state of patients before and after the operation for slow-growing injuries is much better that those patients with acute injuries.Comment: Latex, 17 pages, 7 figures, 2 table

A search for the decay modes B+/- to h+/- tau l

We present a search for the lepton flavor violating decay modes B+/- to h+/- tau l (h= K,pi; l= e,mu) using the BaBar data sample, which corresponds to 472 million BBbar pairs. The search uses events where one B meson is fully reconstructed in one of several hadronic final states. Using the momenta of the reconstructed B, h, and l candidates, we are able to fully determine the tau four-momentum. The resulting tau candidate mass is our main discriminant against combinatorial background. We see no evidence for B+/- to h+/- tau l decays and set a 90% confidence level upper limit on each branching fraction at the level of a few times 10^-5.Comment: 15 pages, 7 figures, submitted to Phys. Rev.