HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference

A large proportion of recent invertible neural architectures is based on a coupling block design. It operates by dividing incoming variables into two sub-spaces, one of which parameterizes an easily invertible (usually affine) transformation that is applied to the other. While the Jacobian of such a transformation is triangular, it is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that (affine) coupling can be repeated recursively within the resulting sub-spaces, leading to an efficiently invertible block with dense triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We demonstrate the power of our method for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities

Identification of gene pathways implicated in Alzheimer's disease using longitudinal imaging phenotypes with sparse regression

We present a new method for the detection of gene pathways associated with a multivariate quantitative trait, and use it to identify causal pathways associated with an imaging endophenotype characteristic of longitudinal structural change in the brains of patients with Alzheimer's disease (AD). Our method, known as pathways sparse reduced-rank regression (PsRRR), uses group lasso penalised regression to jointly model the effects of genome-wide single nucleotide polymorphisms (SNPs), grouped into functional pathways using prior knowledge of gene-gene interactions. Pathways are ranked in order of importance using a resampling strategy that exploits finite sample variability. Our application study uses whole genome scans and MR images from 464 subjects in the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. 66,182 SNPs are mapped to 185 gene pathways from the KEGG pathways database. Voxel-wise imaging signatures characteristic of AD are obtained by analysing 3D patterns of structural change at 6, 12 and 24 months relative to baseline. High-ranking, AD endophenotype-associated pathways in our study include those describing chemokine, Jak-stat and insulin signalling pathways, and tight junction interactions. All of these have been previously implicated in AD biology. In a secondary analysis, we investigate SNPs and genes that may be driving pathway selection, and identify a number of previously validated AD genes including CR1, APOE and TOMM40

On Accelerated Inertial Frames in Gravity and Electromagnetism

When a charged insulating spherical shell is uniformly accelerated, an oppositely directed electric field is produced inside. Outside the field is the Born field of a uniformly accelerated charge, modified by a dipole. Radiation is produced. When the acceleration is annulled by the nearly uniform gravity field of an external shell with a 1 + beta cos theta surface distribution of mass, the differently viewed Born field is static and joins a static field outside the external shell; no radiation is produced. We discuss gravitational analogues of these phenomena. When a massive spherical shell is accelerated, an untouched test mass inside experiences a uniform gravity field and accelerates parallelly to the surrounding shell. In the strong gravity regime we illustrate these effects using exact conformastatic solutions of the Einstein-Maxwell equations with charged dust. We consider a massive charged shell on which the forces due to nearly uniform electrical and gravitational fields balance. Both fields are reduced inside by the ratio of the g_00 inside the shell to that away from it. The acceleration of a free test particle, relative to a static observer, is reduced correspondingly. We give physical explanations of these effects.Comment: 25 pages, LaTeX with 6 encapsulated postscript figures included. To appear in Annals of Physic