Validation Diagnostics for SBI algorithms based on Normalizing Flows

Building on the recent trend of new deep generative models known as Normalizing Flows (NF), simulation-based inference (SBI) algorithms can now efficiently accommodate arbitrary complex and high-dimensional data distributions. The development of appropriate validation methods however has fallen behind. Indeed, most of the existing metrics either require access to the true posterior distribution, or fail to provide theoretical guarantees on the consistency of the inferred approximation beyond the one-dimensional setting. This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. The proposed workflow can be used to check, analyse and guarantee consistent behavior of the estimator. The method is illustrated with a challenging example that involves tightly coupled parameters in the context of computational neuroscience. This work should help the design of better specified models or drive the development of novel SBI-algorithms, hence allowing to build up trust on their ability to address important questions in experimental science.Comment: 7 pages, 2 figures, 1 appendix, published at "Machine Learning and the Physical Sciences" workshop (NeurIPS 2022): https://ml4physicalsciences.github.io/2022

L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce L-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret - e.g. graphical - diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, L-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, L-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of L-C2ST on a challenging application from computational neuroscience.Comment: 20 pages, 4 figures, 7 appendices, in proceeding

Slow equivariant lump dynamics on the two sphere

The low-energy, rotationally equivariant dynamics of n CP^1 lumps on S^2 is studied within the approximation of geodesic motion in the moduli space of static solutions. The volume and curvature properties of this moduli space are computed. By lifting the geodesic flow to the completion of an n-fold cover of the moduli space, a good understanding of nearly singular lump dynamics within this approximation is obtained.Comment: 12 pages, 3 figure

Aluminium in Brain Tissue in Multiple Sclerosis.

Multiple sclerosis (MS) is a devastating and debilitating neurodegenerative disease of unknown cause. A consensus suggests the involvement of both genetic and environmental factors of which the latter may involve human exposure to aluminium. There are no data on the content and distribution of aluminium in human brain tissue in MS. The aluminium content of brain tissue from 14 donors with a diagnosis of MS was determined by transversely heated graphite furnace atomic absorption spectrometry. The location of aluminium in the brain tissue of two donors was investigated by aluminium-specific fluorescence microscopy. The aluminium content of brain tissue in MS was universally high with many tissues bearing concentrations in excess of 10 μg/g dry wt. (10 ppm) and some exceeding 50 ppm. There were no statistically significant relationships between brain lobes, donor age or donor gender. Aluminium-specific fluorescence successfully identified aluminium in brain tissue in both intracellular and extracellular locations. The association of aluminium with corpora amylacea suggests a role for aluminium in neurodegeneration in MS

Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere

In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide strong evidence for the conjecture that large energy initial data develop singularities in finite time and that singularity formation has the universal form of adiabatic shrinking of the degree-one harmonic map from $\mathbb{R}^2$ into $S^2$.Comment: 14 pages, 5 figures, final version to be published in Nonlinearit

High prevalence of missed information related on bone health in orthogeriatric patients with fragility fractures of the pelvis-an institutional register-based analysis

This is the first study that highlighted the amount of missed information related on bone health in orthogeriatric patients suffering fragility fractures of the pelvis and also evaluated its prevalence and differing etiology in the assessed patients, regarding osteoporosis and/or osteomalacia, based on laboratory and instrumental measurements. This evaluation should become a standardized procedure in the treatment of orthogeriatric patients presenting with a FFP. INTRODUCTION Fragility fractures of the pelvis (FFP) are common in orthogeriatric patients. Secondary fracture prevention regarding evaluation and treatment of an underlying osteoporosis or osteomalacia is still often neglected. The purpose of this study was to evaluate the amount of missed information related on bone health in older adult FFP patients, the prevalence of vitamin D deficiency in assessed patients, and if fracture type-dependent distribution patterns could be observed. METHODS A retrospective analysis of prospectively collected data of an institutional register was performed. Patients aged 80~years and older (n = 456) admitted with a FFP from 01/2003 until 12/2019 to a level I trauma center were included. RESULTS In 456 patients, FFP type II were leading (66.7%). Diagnostics were conducted in 37.1% of the patients regarding measurement of vitamin D levels and 21.7% regarding DXA measurements; vitamin D deficiency was observed in 62.7%, indicators for an underlying osteomalacia in 45.8%, and an osteoporosis in 46.5% of the assessed patients. CONCLUSION Although FFP are common and will increase, there is still a lack of secondary fracture prevention, starting with information related on bone health. In the assessed patients, a high prevalence of vitamin D deficiency was present, but no significant correlation between vitamin D level and type of fracture was observed. Ongoing education for varying etiology and specific treatment of these fractures is necessary, as surgical treatment was unified, but drug therapy remains different

Host-pathogen evolutionary signatures reveal dynamics and future invasions of vampire bat rabies

Anticipating how epidemics will spread across landscapes requires understanding host dispersal events that are notoriously difficult to measure. Here, we contrast host and virus genetic signatures to resolve the spatiotemporal dynamics underlying geographic expansions of vampire bat rabies virus (VBRV) in Peru. Phylogenetic analysis revealed recent viral spread between populations that, according to extreme geographic structure in maternally inherited host mitochondrial DNA, appeared completely isolated. In contrast, greater population connectivity in biparentally inherited nuclear microsatellites explained the historical limits of invasions, suggesting that dispersing male bats spread VBRV between genetically isolated female populations. Host nuclear DNA further indicated unanticipated gene flow through the Andes mountains connecting the VBRV-free Pacific coast to the VBRV-endemic Amazon rainforest. By combining Bayesian phylogeography with landscape resistance models, we projected invasion routes through northern Peru that were validated by real-time livestock rabies mortality data. The first outbreaks of VBRV on the Pacific coast of South America could occur by June 2020, which would have serious implications for agriculture, wildlife conservation, and human health. Our results show that combining host and pathogen genetic data can identify sex biases in pathogen spatial spread, which may be a widespread but underappreciated phenomenon, and demonstrate that genetic forecasting can aid preparedness for impending viral invasions

Phenotypic characteristics of the p.Asn215Ser (p.N215S) GLA mutation in male and female patients with Fabry disease: A multicenter Fabry Registry study.

BackgroundThe p.Asn215Ser or p.N215S GLA variant has been associated with late-onset cardiac variant of Fabry disease.MethodsTo expand on the scarce phenotype data, we analyzed natural history data from 125 p.N215S patients (66 females, 59 males) enrolled in the Fabry Registry (NCT00196742) and compared it with data from 401 patients (237 females, 164 males) harboring mutations associated with classic Fabry disease. We evaluated interventricular septum thickness (IVST), left ventricular posterior wall thickness (LVPWT), estimated glomerular filtration rate and severe clinical events.ResultsIn p.N215S males, mildly abnormal mean IVST and LVPWT values were observed in patients aged 25-34 years, and values gradually increased with advancing age. Mean values were similar to those of classic males. In p.N215S females, these abnormalities occurred primarily in patients aged 55-64 years. Severe clinical events in p.N215S patients were mainly cardiac (males 31%, females 8%) while renal and cerebrovascular events were rare. Renal impairment occurred in 17% of p.N215S males (mostly in patients aged 65-74 years), and rarely in females (3%).Conclusionp.N215S is a disease-causing mutation with severe clinical manifestations found primarily in the heart. Cardiac involvement may become as severe as in classic Fabry patients, especially in males