A Simple Approximation Method for the Fisher-Rao Distance between Multivariate Normal Distributions

We present a simple method to approximate the Fisher-Rao distance between multivariate normal distributions based on discretizing curves joining normal distributions and approximating the Fisher-Rao distances between successive nearby normal distributions on the curves by the square roots of their Jeffreys divergences. We consider experimentally the linear interpolation curves in the ordinary, natural, and expectation parameterizations of the normal distributions, and compare these curves with a curve derived from the Calvo and Oller's isometric embedding of the Fisher-Rao d-variate normal manifold into the cone of (d+1)×(d+1) symmetric positive-definite matrices. We report on our experiments and assess the quality of our approximation technique by comparing the numerical approximations with both lower and upper bounds. Finally, we present several information-geometric properties of Calvo and Oller's isometric embedding.

Prenatal and early postnatal exposure to perfluoroalkyl substances and bone mineral content and density in the Odense child cohort

INTRODUCTION

Exposure to perfluoroalkyl substances (PFAS) has been associated with lower bone mineral density (BMD) in animal and human studies, but prospective data from children are limited.

OBJECTIVES

To determine associations between prenatal and early postnatal PFAS exposure and BMD at age 7 years.

METHODS

In the Odense Child Cohort, Denmark, pregnant women were recruited in 2010-2012, and their children were invited for subsequent health examinations. At 12 weeks of gestation the pregnant women delivered a serum sample, and at age 18 months serum was obtained from the child to measure perfluorooctane sulfonic acid (PFOS), perfluorooctanoic acid (PFOA), perfluorohexane sulfonic acid (PFHxS), perfluorononanoic acid (PFNA) and perfluorodecanoic acid (PFDA) by LC-MS/MS. At age 7 years DXA scans were performed to measure bone mineral content (BMC) and BMD Z-score. PFAS in pregnancy (n = 924) and/or at age 18 months (n = 511) were regressed against DXA measurements, adjusted for maternal education, child height Z-score, sex (for BMC) and for postnatal exposure, additionally duration of total breastfeeding. We additionally performed structural equation models determining combined effects of pre-and postnatal PFAS exposures.

RESULTS

Higher prenatal and early postnatal serum concentrations of all measured PFAS were associated with lower BMC and BMD Z-scores at age 7 years, all estimates were negative although not all significant. For each doubling of prenatal or 18-month exposure to PFDA, BMD Z-scores were lowered by -0.07 (95 % CI -0.10; -0.03) and -0.14 (-0.25; -0.03), respectively after adjustment. Pre- and postnatal PFAS were correlated, but structural equation models suggested that associations with BMD were stronger for 18-month than prenatal PFAS exposure.

DISCUSSION

Bone density is established in childhood, and a reduction in BMD during early childhood may have long-term implication for peak bone mass and lifelong bone health. Future studies of the impact of PFAS exposure on fracture incidence will help elucidate the clinical relevance.

Internal exposure of Flemish teenagers to environmental pollutants: Results of the Flemish Environment and Health Study 2016-2020 (FLEHS IV)

The Flemish Environment and Health Study (FLEHS) collects information on internal exposure to a broad range of environmental chemicals in the general population in Flanders, the Northern region of Belgium. The aim is to establish biomonitoring exposure distributions for the general population in support of public health and environmental policy, environmental risk assessment and risk management decisions. In 2017-2018, urine and blood samples were collected from 428 teenagers by a stratified clustered two stage randomized design. Samples were analyzed for a broad range of biomarkers related to exposure to chlorinated and newer pesticides, brominated and organophosphate flame retardants (BFR/OPFR), polychlorinated biphenyls (PCBs), bisphenols, phthalates and alternative plasticizers, per-and polyfluoroalkyl substances (PFAS), polycyclic aromatic hydrocarbons (PAHs), benzene, metals and trace elements. The geometric mean levels and percentiles of the distribution were estimated for each biomarker, for the whole study population and following stratification for sex, the household educational attainment and the residence area's urbanicity. Geometric means of biomarkers of lead, dichlorodiphenyltrichloroethane (DDT), PCBs, PAHs, regulated phthalates and bisphenol A (BPA) were lower than in the previous FLEHS cycles. Most biomarker levels were below health-based guidance values (HB-GVs). However, HB-GVs of urinary arsenic, blood lead, blood cadmium, sum of serum perfluorooctane sulfonate (PFOS) and perfluoro-1-hexanesulfonate (PFHxS) and the urinary pyrethroid metabolite (3-PBA) were exceeded in respectively 25%, 12%, 39.5%, 10% and 22% of the teenagers. These results suggest that the levels of exposure in the Flemish population to some environmental chemicals might be of concern. At the same time, we noticed that biomarkers for BPA substitutes, metabolites of OPFRs, an expanded list of PFAS, glyphosate and its metabolite could be measured in substantial proportions of participants. Interpretation of these levels in a health-risk context remains uncertain as HB-GVs are lacking. Household educational attainment and residential urbanicity were significant exposure determinants for many biomarkers and could influence specific biomarker levels up to 70% as shown by multiple regression analysis. The research consortium also took care of the broader external communication of results with participants, policy makers, professional groups and civil society organizations. Our study demonstrated that teenagers are exposed to a wide range of chemicals, it demonstrates the success of public policies to reduce exposure but also points to concern and further priorities and needs for follow up.

Statistical Divergences between Densities of Truncated Exponential Families with Nested Supports: Duo Bregman and Duo Jensen Divergences

By calculating the Kullback–Leibler divergence between two probability measures belonging to different exponential families dominated by the same measure, we obtain a formula that generalizes the ordinary Fenchel–Young divergence. Inspired by this formula, we define the duo Fenchel–Young divergence and report a majorization condition on its pair of strictly convex generators, which guarantees that this divergence is always non-negative. The duo Fenchel–Young divergence is also equivalent to a duo Bregman divergence. We show how to use these duo divergences by calculating the Kullback–Leibler divergence between densities of truncated exponential families with nested supports, and report a formula for the Kullback–Leibler divergence between truncated normal distributions. Finally, we prove that the skewed Bhattacharyya distances between truncated exponential families amount to equivalent skewed duo Jensen divergences.

Fast Approximations of the Jeffreys Divergence between Univariate Gaussian Mixtures via Mixture Conversions to Exponential-Polynomial Distributions

The Jeffreys divergence is a renown arithmetic symmetrization of the oriented Kullback–Leibler divergence broadly used in information sciences. Since the Jeffreys divergence between Gaussian mixture models is not available in closed-form, various techniques with advantages and disadvantages have been proposed in the literature to either estimate, approximate, or lower and upper bound this divergence. In this paper, we propose a simple yet fast heuristic to approximate the Jeffreys divergence between two univariate Gaussian mixtures with arbitrary number of components. Our heuristic relies on converting the mixtures into pairs of dually parameterized probability densities belonging to an exponential-polynomial family. To measure with a closed-form formula the goodness of fit between a Gaussian mixture and an exponential-polynomial density approximating it, we generalize the Hyvärinen divergence to α-Hyvärinen divergences. In particular, the 2-Hyvärinen divergence allows us to perform model selection by choosing the order of the exponential-polynomial densities used to approximate the mixtures. We experimentally demonstrate that our heuristic to approximate the Jeffreys divergence between mixtures improves over the computational time of stochastic Monte Carlo estimations by several orders of magnitude while approximating the Jeffreys divergence reasonably well, especially when the mixtures have a very small number of modes.

q-Neurons: Neuron Activations Based on Stochastic Jackson's Derivative Operators

We propose a new generic type of artificial neurons called q -neurons. A q -neuron is a stochastic neuron with its activation function relying on Jackson's discrete q -derivative for a stochastic parameter q . We show how to generalize neural network architectures with q -neurons and demonstrate the scalability and ease of implementation of q -neurons into legacy deep learning frameworks. We report experimental results that consistently improve performance over state-of-the-art standard activation functions, both on training and test loss functions.

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.

Clustering Patterns Connecting COVID-19 Dynamics and Human Mobility Using Optimal Transport

Social distancing and stay-at-home are among the few measures that are known to be effective in checking the spread of a pandemic such as COVID-19 in a given population. The patterns of dependency between such measures and their effects on disease incidence may vary dynamically and across different populations. We described a new computational framework to measure and compare the temporal relationships between human mobility and new cases of COVID-19 across more than 150 cities of the United States with relatively high incidence of the disease. We used a novel application of Optimal Transport for computing the distance between the normalized patterns induced by bivariate time series for each pair of cities. Thus, we identified 10 clusters of cities with similar temporal dependencies, and computed the Wasserstein barycenter to describe the overall dynamic pattern for each cluster. Finally, we used city-specific socioeconomic covariates to analyze the composition of each cluster.

Severity of COVID-19 at elevated exposure to perfluorinated alkylates

Background

The course of coronavirus disease 2019 (COVID-19) seems to be aggravated by air pollution, and some industrial chemicals, such as the perfluorinated alkylate substances (PFASs), are immunotoxic and may contribute as well.

Methods

From Danish biobanks, we obtained plasma samples from 323 subjects aged 30-70 years with known SARS-CoV-2 infection. The PFAS concentrations measured at the background exposures included five PFASs known to be immunotoxic. Register data was obtained to classify disease status, other health information, and demographic variables. We used ordinal and ordered logistic regression analyses to determine associations between PFAS concentrations and disease outcome.

Results

Plasma-PFAS concentrations were higher in males, in subjects with Western European background, and tended to increase with age, but were not associated with the presence of chronic disease. Of the study population, 108 (33%) had not been hospitalized, and of those hospitalized, 53 (16%) had been in intensive care or were deceased. Among the five PFASs considered, perfluorobutanoic acid (PFBA) showed an odds ratio (OR) of 2.19 (95% confidence interval, CI, 1.39-3.46) for increasing severities of the disease, although the OR decreased to 1.77 (95% CI, 1.09, 2.87) after adjustment for age, sex, sampling site and interval between blood sampling and diagnosis.

Conclusions

Measures of individual exposures to immunotoxic PFASs included PFBA that accumulates in the lungs. Elevated plasma-PFBA concentrations were associated with an increased risk of more severe course of CIVID-19. Given the low background exposure levels in this study, the role of PFAS exposure in COVID-19 needs to be ascertained in populations with elevated exposures.

An Elementary Introduction to Information Geometry

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity.

The Siegel-Klein Disk: Hilbert Geometry of the Siegel Disk Domain

We study the Hilbert geometry induced by the Siegel disk domain, an open-bounded convex set of complex square matrices of operator norm strictly less than one. This Hilbert geometry yields a generalization of the Klein disk model of hyperbolic geometry, henceforth called the Siegel-Klein disk model to differentiate it from the classical Siegel upper plane and disk domains. In the Siegel-Klein disk, geodesics are by construction always unique and Euclidean straight, allowing one to design efficient geometric algorithms and data structures from computational geometry. For example, we show how to approximate the smallest enclosing ball of a set of complex square matrices in the Siegel disk domains: We compare two generalizations of the iterative core-set algorithm of Badoiu and Clarkson (BC) in the Siegel-Poincaré disk and in the Siegel-Klein disk: We demonstrate that geometric computing in the Siegel-Klein disk allows one (i) to bypass the time-costly recentering operations to the disk origin required at each iteration of the BC algorithm in the Siegel-Poincaré disk model, and (ii) to approximate fast and numerically the Siegel-Klein distance with guaranteed lower and upper bounds derived from nested Hilbert geometries.

Prevalence of borderline personality disorder in immigrants in a psychiatric inpatient setting

Introduction

Information about the relationship between personality disorder and ethnicity or migration is sparse. The few studies regarding the prevalence of borderline personality disorder (BPD) in immigrants compared to an indigenous population are inconsistent.

Aims

The aim of the present study was to compare the frequency of a BPD diagnosis in psychiatric inpatients with and without an immigrant background.

Methods

2494 consecutive patients over a 3-year period at a psychiatric university hospital were reviewed. Data included socio-demographic and clinical variables and also information about an immigrant background. The psychiatric diagnosis was limited to information available from the digital documentation system of the psychiatric clinic and additionally from discharge letters. The diagnosis of borderline personality disorder was based on ICD-10 criteria.

Results

374 individuals (15%) of the study population had an immigrant background. The rates of BPD were 6.5% in the indigenous group (n = 2120) vs. 3.5% in the immigrant group (n = 374). The difference between the indigenous and the immigrant group regarding the rates of BPD-diagnoses was statistically significant (chi2 = 5.02, df = 1, p = 0.025).

Conclusions

The findings suggest that in a clinical sample BPD was diagnosed less frequently in the immigrant group than in the indigenous group. Therefore, our results do not support the concept of immigration as a risk factor for BPD. However, future investigations with a prospective study design and at epidemiological levels need to be conducted in order to get more precise information about the prevalence of BPD in different immigrant groups.

Ssri-related toxic serotonin syndrome: improvement by discontinuation of treatment and propranolol

We report three cases in which toxic serotonin syndrome developed in relation to three different selective serotonin reuptake inhibitors (SSRI) (ie, fluoxetine, sertraline, paroxetine), and which all responded to the discontinuation of the SSRI and also to an additional propranolol treatment.

On the Jensen-Shannon Symmetrization of Distances Relying on Abstract Means

The Jensen-Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However, the Jensen-Shannon divergence between Gaussian distributions is not available in closed form. To bypass this problem, we present a generalization of the Jensen-Shannon (JS) divergence using abstract means which yields closed-form expressions when the mean is chosen according to the parametric family of distributions. More generally, we define the JS-symmetrizations of any distance using parameter mixtures derived from abstract means. In particular, we first show that the geometric mean is well-suited for exponential families, and report two closed-form formula for (i) the geometric Jensen-Shannon divergence between probability densities of the same exponential family; and (ii) the geometric JS-symmetrization of the reverse Kullback-Leibler divergence between probability densities of the same exponential family. As a second illustrating example, we show that the harmonic mean is well-suited for the scale Cauchy distributions, and report a closed-form formula for the harmonic Jensen-Shannon divergence between scale Cauchy distributions. Applications to clustering with respect to these novel Jensen-Shannon divergences are touched upon.

Optofluidic Sensor for Inline Hemolysis Detection on Whole Blood

Hemolysis is the rupture of red blood cells and constitutes the most common reason for unsuitable blood samples in the clinic. To detect hemolysis, one has to separate the hemoglobin in blood plasma from that in red blood cells. However, current methods entail centrifugation for cell-plasma separation, which is complex, time-consuming, and not easy to integrate into point-of-care (PoC) systems. Here, we demonstrate an optofluidic sensor composed of nanofilters on an optical waveguide, which enables evanescent-wave absorption measurement of hemoglobin in plasma with the capability of real-time inline detection on whole blood without extra sample preparation like centrifugation. Long-term testing with inline integration in a modified, commercial blood gas analyzer shows high reliability and repeatability of the measurements even with the presence of interference from bilirubin. We envision that the present work has large potential in improving diagnosis quality by enabling PoC hemolysis detection in blood gas analyzers and can also lend unique sensing capabilities to other applications dealing with complex turbid media.

Computational Information Geometry for Binary Classification of High-Dimensional Random Tensors

Evaluating the performance of Bayesian classification in a high-dimensional random tensor is a fundamental problem, usually difficult and under-studied. In this work, we consider two Signal to Noise Ratio (SNR)-based binary classification problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size N q × R , i.e., for 1 ≤ q ≤ Q , where R , N q → ∞ with R 1 / q / N q converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear ( M 1 , … , M Q ) -rank with large factors of size N q × M q , i.e., for 1 ≤ q ≤ Q , where N q , M q → ∞ with M q / N q converge towards a finite constant. The classification of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the minimal Bayes' error probability is mathematically intractable. To circumvent this difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s ⋆ . In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s ⋆ = 1 / 2 ) cannot solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s ⋆ . However, thanks to powerful random matrix theory tools, a simple analytical expression of s ⋆ is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. This work shows that the BUB is the tightest bound at low SNRs. However, for higher SNRs, the latest property is no longer true.

Looking back and moving forward: 50 years of soil and soil fertility management research in sub-Saharan Africa

Low and declining soil fertility has been recognized for a long time as a major impediment to intensifying agriculture in sub-Saharan Africa (SSA). Consequently, from the inception of international agricultural research, centres operating in SSA have had a research programme focusing on soil and soil fertility management, including the International Institute of Tropical Agriculture (IITA). The scope, content, and approaches of soil and soil fertility management research have changed over the past decades in response to lessons learnt and internal and external drivers and this paper uses IITA as a case study to document and analyse the consequences of strategic decisions taken on technology development, validation, and ultimately uptake by smallholder farmers in SSA. After an initial section describing the external environment within which soil and soil fertility management research is operating, various dimensions of this research area are covered: (i) 'strategic research', 'Research for Development', partnerships, and balancing acts, (ii) changing role of characterization due to the expansion in geographical scope and shift from soils to farms and livelihoods, (iii) technology development: changes in vision, content, and scale of intervention, (iv) technology validation and delivery to farming communities, and (v) impact and feedback to the technology development and validation process. Each of the above sections follows a chronological approach, covering the last five decades (from the late 1960s till today). The paper ends with a number of lessons learnt which could be considered for future initiatives aiming at developing and delivering improved soil and soil fertility management practices to smallholder farming communities in SSA.

Spermatogenic capacity in fertile men with elevated exposure to polychlorinated biphenyls

BACKGROUND

Endocrine disrupting industrial chemicals, such as polychlorinated biphenyls (PCBs), are suspected to adversely affect male reproductive functions.

OBJECTIVES

The Faroe Islands community exhibits an unusually wide range of exposures to dietary contaminants, and in this setting we examined the possible association between PCB exposure and semen quality and reproductive hormones in fertile Faroese men.

METHODS

Participants in this cross-sectional study include 266 proven fertile men residing in the Faroe Islands. PCB levels and hormone profiles were measured in serum samples taken at the clinical examination that included semen quality parameters.

RESULTS

A significant positive association was seen between serum-PCB and the testosterone/estradiol ratio (p=0.04). In the unadjusted analyses, elevated PCB exposure was associated with increased serum concentrations of SHBG (p=0.01) and FSH (p=0.05). We found no association between the serum PCB concentration and the semen quality variables.

CONCLUSION

In this population of highly exposed fertile men, the current serum-PCB concentration was associated with higher androgen/estrogen ratio. Further studies are needed to establish the findings and further document PCB-associated hormonal effects, any time windows of increased susceptibility, and the role of PCB in sub-fecundity.

Gentle Nearest Neighbors Boosting over Proper Scoring Rules

Tailoring nearest neighbors algorithms to boosting is an important problem. Recent papers study an approach, UNN, which provably minimizes particular convex surrogates under weak assumptions. However, numerical issues make it necessary to experimentally tweak parts of the UNN algorithm, at the possible expense of the algorithm's convergence and performance. In this paper, we propose a lightweight Newton-Raphson alternative optimizing proper scoring rules from a very broad set, and establish formal convergence rates under the boosting framework that compete with those known for UNN. To the best of our knowledge, no such boosting-compliant convergence rates were previously known in the popular Gentle Adaboost's lineage. We provide experiments on a dozen domains, including Caltech and SUN computer vision databases, comparing our approach to major families including support vector machines, (Ada)boosting and stochastic gradient descent. They support three major conclusions: (i) GNNB significantly outperforms UNN, in terms of convergence rate and quality of the outputs, (ii) GNNB performs on par with or better than computationally intensive large margin approaches, (iii) on large domains that rule out those latter approaches for computational reasons, GNNB provides a simple and competitive contender to stochastic gradient descent. Experiments include a divide-and-conquer improvement of GNNB exploiting the link with proper scoring rules optimization.

Shape retrieval using hierarchical total Bregman soft clustering

In this paper, we consider the family of total Bregman divergences (tBDs) as an efficient and robust "distance" measure to quantify the dissimilarity between shapes. We use the tBD-based ℓ₁-norm center as the representative of a set of shapes, and call it the t-center. First, we briefly present and analyze the properties of the tBDs and t-centers following our previous work in. Then, we prove that for any tBD, there exists a distribution which belongs to the lifted exponential family (lEF) of statistical distributions. Further, we show that finding the maximum a posteriori (MAP) estimate of the parameters of the lifted exponential family distribution is equivalent to minimizing the tBD to find the t-centers. This leads to a new clustering technique, namely, the total Bregman soft clustering algorithm. We evaluate the tBD, t-center, and the soft clustering algorithm on shape retrieval applications. Our shape retrieval framework is composed of three steps: 1) extraction of the shape boundary points, 2) affine alignment of the shapes and use of a Gaussian mixture model (GMM) to represent the aligned boundaries, and 3) comparison of the GMMs using tBD to find the best matches given a query shape. To further speed up the shape retrieval algorithm, we perform hierarchical clustering of the shapes using our total Bregman soft clustering algorithm. This enables us to compare the query with a small subset of shapes which are chosen to be the cluster t-centers. We evaluate our method on various public domain 2D and 3D databases, and demonstrate comparable or better results than state-of-the-art retrieval techniques.