PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian GLM inference

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent estimates of uncertainty, incorporation of prior information, and sharing of power across experiments via hierarchical models. In practice, however, the approximate Bayesian methods necessary for inference have either failed to scale to large data sets or failed to provide theoretical guarantees on the quality of inference. We propose a new approach based on constructing polynomial approximate sufficient statistics for GLMs (PASS-GLM). We demonstrate that our method admits a simple algorithm as well as trivial streaming and distributed extensions that do not compound error across computations. We provide theoretical guarantees on the quality of point (MAP) estimates, the approximate posterior, and posterior mean and uncertainty estimates. We validate our approach empirically in the case of logistic regression using a quadratic approximation and show competitive performance with stochastic gradient descent, MCMC, and the Laplace approximation in terms of speed and multiple measures of accuracy -- including on an advertising data set with 40 million data points and 20,000 covariates.Comment: In Proceedings of the 31st Annual Conference on Neural Information Processing Systems (NIPS 2017). v3: corrected typos in Appendix

On the fourth root prescription for dynamical staggered fermions

With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in Lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator D such that (det D_{staggered})^{1/4} = det D. Working in the flavour field representation we show that in the free field case there is a simple and natural candidate D satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with localisation range vanishing ~ (a/m)^{1/2} for lattice spacing a -> 0. Prospects for the interacting case are also discussed, although we do not solve this case here.Comment: 29 pages, 2 figures; some revision and streamlining of the discussions; results unchanged; to appear in PR

General bounds on the Wilson-Dirac operator

Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac operator H(m) have previously been derived for 0<m<2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime dimension. The bounds can alternatively be viewed as localisation bounds on the real spectrum of the usual Wilson-Dirac operator. They are needed for the rigorous evaluation of the classical continuum limit of the axial anomaly and index of the overlap Dirac operator at general values of m, and provide information on the topological phase structure of overlap fermions. They are also useful for understanding the instanton size-dependence of the real spectrum of the Wilson-Dirac operator in an instanton background.Comment: 26 pages, 2 figures. v3: Completely rewritten with new material and new title; to appear in Phys.Rev.

Preliminary results from the heavy ions in space experiment

The Heavy Ions In Space (HIIS) experiment has two primary objectives: (1) to measure the elemental composition of ultraheavy galactic cosmic rays, beginning in the tin-barium region of the periodic table; and (2) to study heavy ions which arrive at LDEF below the geomagnetic cutoff, either because they are not fully stripped of electrons or because their source is within the magnetosphere. Both of these objectives have practical as well as astrophysical consequences. In particular, the high atomic number of the ultraheavy galactic cosmic rays puts them among the most intensely ionizing particles in Nature. They are therefore capable of upsetting electronic components normally considered immune to such effects. The below cutoff heavy ions are intensely ionizing because of their low velocity. They can be a significant source of microelectronic anomalies in low inclination orbits, where Earth's magnetic field protects satellites from most particles from interplanetary space. The HIIS results will lead to significantly improved estimates of the intensely ionizing radiation environment

Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for $\frak{g}=\frak{gl}(r)$ or $\frak{sl}(r)$, with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case $\frak{g=sl}(2)$ is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For $\frak{g=sl}(3)$, the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

A retrospective study of the prevalence of the canine degenerative myelopathy associated superoxide dismutase 1 mutation (SOD1: c. 118G> A) in a referral population of German Shepherd dogs from the UK

BACKGROUND: Canine degenerative myelopathy (CDM) is an adult onset, progressive neurodegenerative disease of the spinal cord. The disease was originally described in the German Shepherd dog (GSD), but it is now known to occur in many other dog breeds. A previous study has identified a mutation in the superoxide dismutase 1 gene (SOD1:c.118G > A) that is associated with susceptibility to CDM. In the present study, restriction fragment length polymorphism (RFLP) analysis was used to genotype GSD for SOD1:c.118G > A in order to estimate the prevalence of the mutation in a referral population of GSD in the UK. RESULTS: This study demonstrated that the RFLP assay, based on use of PCR and subsequent digestion with the Eco571 enzyme, provided a simple genotyping test for the SOD1:c.118G > A mutation. In a young GSD population (i.e. dogs less than 6 years of age, before clinical signs of the disease usually become apparent), 8 of 50 dogs were found to be homozygous and a further 19 were heterozygous for the mutation. In dogs over 8 years of age, 21 of 50 dogs admitted to a tertiary referral hospital with pelvic limb ataxia as a major clinical sign were homozygous for the mutation, compared to none of 50 dogs of similar age, but where no neurological disease was reported on referral. CONCLUSIONS: This data suggests that genotyping for the SOD1:c.118G > A mutation is clinically applicable and that the mutation has a high degree of penetrance. Genotyping might also be useful for screening the GSD population to avoid mating of two carriers, but since the allele frequency is relatively high in the UK population of GSD, care should be taken to avoid reduction in genetic diversity within the breed

Physical disruption of intervertebral disc promotes cell clustering and a degenerative phenotype

© 2019, The Author(s). To test the hypothesis that physical disruption of an intervertebral disc disturbs cell-matrix binding, leading to cell clustering and increased expression of matrix degrading enzymes that contribute towards degenerative disc cell phenotype. Lumbar disc tissue was removed at surgery from 21 patients with disc herniation, 11 with disc degeneration, and 8 with adolescent scoliosis. 5 μm sections were examined with histology, and 30-µm sections by confocal microscopy. Antibodies were used against integrin α5beta1, matrix metalloproteinases (MMP) 1, MMP-3, caspase 3, and denatured collagen types I and II. Spatial associations were sought between cell clustering and various degenerative features. An additional, 11 non-herniated human discs were used to examine causality: half of each specimen was cultured in a manner that allowed free ‘unconstrained’ swelling (similar to a herniated disc in vivo), while the other half was cultured within a perspex ring that allowed ‘constrained’ swelling. Changes were monitored over 36 h using live-cell imaging. 1,9-Di-methyl methylene blue (DMMB) assay for glycosaminoglycan loss was carried out from tissue medium. Partially constrained specimens showed little swelling or cell movement in vitro. In contrast, unconstrained swelling significantly increased matrix distortion, glycosaminoglycan loss, exposure of integrin binding sites, expression of MMPs 1 and 3, and collagen denaturation. In the association studies, herniated disc specimens showed changes that resembled unconstrained swelling in vitro. In addition, they exhibited increased cell clustering, apoptosis, MMP expression, and collagen denaturation compared to ‘control’ discs. Results support our hypothesis. Further confirmation will require longitudinal animal experiments

The impact of an electricity generation tax on the South African economy

In the 2008 budget of the Minister of Finance, the South African Government proposed to impose a 2 cents/kilowatt-hour (c/kWh) tax on the sale of electricity generated from non-renewable sources; this tax is to be collected at source by the producers/generators of electricity. The intention of this measure is to serve a dual purpose of protecting the environment and helping to manage the current electricity supply shortages by reducing demand. The objective here is to evaluate the impact of such an electricity generation tax on the South African, SACU and SADC economies. The paper firstly considers the theoretical foundations of an electricity generation tax supported by international experiences in this regard. This section also contrasts the suitability of a permit with a tax system to achieve CO2 emission reduction. We subsequently apply the Global Trade Analysis Project (GTAP) model to evaluate the impact of an electricity generation tax on the South African, SACU and SADC economies. We simulate the proposed tax as a 10 percent increase in the output price of electricity. We assume a closure rule that allows unskilled labour to migrate and a limited skilled workforce. As expected, the electricity generation tax will reduce demand. Due to the decrease in domestic demand, export volume increases and import volume decreases, this is despite a weaker terms of trade. We also found that unemployment for unskilled labour increases and wages of skilled workers are expected to decrease. A unilateral electricity generation tax will benefit other SACU and SADC countries through an improvement in relative competitiveness, as shown by the improvement of the terms of trade for these regions. If, however, the benefits of pollution abatement are internalised, then electricity generation tax is expected to yield a positive effect on the South African economy.