We describe a framework to build distances by measuring the tightness of inequalities and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities and present two novel classes of Hölder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy–Schwarz divergence. We report closed-form formulas for those statistical dissimilarities when considering distributions belonging to the same exponential family provided that the natural parameter space is a cone (e.g., multivariate Gaussians) or affine (e.g., categorical distributions). Those new classes of Hölder distances are invariant to rescaling and thus do not require distributions to be normalized. Finally, we show how to compute statistical Hölder centroids with respect to those divergences and carry out center-based clustering toy experiments on a set of Gaussian distributions which demonstrate empirically that symmetrized Hölder divergences outperform the symmetric Cauchy–Schwarz divergence.

Introduction: High yield HIV testing strategies are critical to reach epidemic control in high prevalence and low-resource settings such as East and Southern Africa. In this study, we aimed to predict the HIV status of individuals living in Angola, Burundi, Ethiopia, Lesotho, Malawi, Mozambique, Namibia, Rwanda, Zambia and Zimbabwe with the highest precision and sensitivity for different policy targets and constraints based on a minimal set of socio-behavioural characteristics. Methods: We analysed the most recent Demographic and Health Survey from these 10 countries to predict individual’s HIV status using four different algorithms (a penalized logistic regression, a generalized additive model, a support vector machine, and a gradient boosting trees). The algorithms were trained and validated on 80% of the data, and tested on the remaining 20%. We compared the predictions based on the F1 score, the harmonic mean of sensitivity and positive predictive value (PPV), and we assessed the generalization of our models by testing them against an independent left-out country. The best performing algorithm was trained on a minimal subset of variables which were identified as the most predictive, and used to 1) identify 95% of people living with HIV (PLHIV) while maximising precision and 2) identify groups of individuals by adjusting the probability threshold of being HIV positive (90% in our scenario) for achieving specific testing strategies. Results: Overall 55,151 males and 69,626 females were included in the analysis. The gradient boosting trees algorithm performed best in predicting HIV status with a mean F1 score of 76.8% [95% confidence interval (CI) 76.0%-77.6%] for males (vs [CI 67.8%-70.6%] for SVM) and 78.8% [CI 78.2%-79.4%] for females (vs [CI 73.4%-75.8%] for SVM). Among the ten most predictive variables for each sex, nine were identical: longitude, latitude and, altitude of place of residence, current age, age of most recent partner, total lifetime number of sexual partners, years lived in current place of residence, condom use during last intercourse and, wealth index. Only age at first sex for male (ranked 10th) and Rohrer’s index for female (ranked 6th) were not similar for both sexes. Our large-scale scenario, which consisted in identifying 95% of all PLHIV, would have required testing 49.4% of males and 48.1% of females while achieving a precision of 15.4% for males and 22.7% for females. For the second scenario, only 4.6% of males and 6.0% of females would have had to be tested to find 55.7% of all males and 50.5% of all females living with HIV. Conclusions: We trained a gradient boosting trees algorithm to find 95% of PLHIV with a precision twice higher than with general population testing by using only a limited number of socio-behavioural characteristics. We also successfully identified people at high risk of infection who may be offered pre-exposure prophylaxis or voluntary medical male circumcision. These findings can inform the implementation of new high-yield HIV tests and help develop very precise strategies based on low-resource settings constraints.

Twitter has significant potential as a source of Volunteered Geographic Information (VGI), as its content is updated at high frequency, with high availability thanks to dedicated interfaces. However, the diversity of content types and the low average accuracy of geographic information attached to individual tweets remain obstacles in this context. The contributions in this paper relate to the general goal of extracting actionable information regarding the impact of natural hazards on a specific region from social platforms, such as Twitter. Specifically, our contributions describe the construction of a model classifying whether given spatio-temporal coordinates, materialized by raster cells in a remote sensing context, lie in a flooded area. For training, remotely sensed data are used as the target variable, and the input covariates are built on the sole basis of textual and spatial data extracted from a Twitter corpus. Our contributions enable the use of trained models for arbitrary new Twitter corpora collected for the same region, but at different times, allowing for the construction of a flooded area measurement proxy available at a higher temporal frequency. Experimental validation uses true data that were collected during Hurricane Harvey, which caused significant flooding in the Houston urban area between mid-August and mid-September 2017. Our experimental section compares several spatial information extraction methods, as well as various textual representation and aggregation techniques, which were applied to the collected Twitter data. The best configuration yields a F1 score of 0.425, boosted to 0.834 if restricted to the 10% most confident predictions.

Background: There is a need for high yield HIV testing strategies to reach epidemic control. We aimed to predict the HIV status of individuals based on socio-behavioural characteristics. Methods: We analysed over 3,200 variables from the most recent Demographic Health Survey from 10 countries in East and Southern Africa. We trained four machine-learning algorithms and selected the best based on the f1 score. Training and validation were done on 80% of the data. The model was tested on the remaining 20% and on a left-out country which was rotated around. The best algorithm was retrained on the variables which were most predictive. We studied two scenarios: one aiming to identify 95% of people living with HIV (PLHIV) and one aiming to identify individuals with 95% or higher probability of being HIV positive. Findings: Overall 55,151 males and 69,626 females were included. XGBoost performed best in predicting HIV with a mean f1 of 76·8% [95% confidence interval 76·0%-77·6%] for males and 78·8% [78·2%-79·4%] for females. Among the ten most predictive variables, nine were identical for both sexes: longitude, latitude and, altitude of place of residence, current age, age of most recent partner, total lifetime number of sexual partners, years lived in current place of residence, condom use during last intercourse and, wealth index. Model performance based on these variables decreased minimally. For the first scenario, 7 males and 5 females would need to be tested to identify one HIV positive person. For the second scenario, 4·2% of males and 6·2% of females would have been identified as high-risk population. Interpretation: We were able to identify PLHIV and those at high risk of infection who may be offered pre-exposure prophylaxis and/or voluntary medical male circumcision. These findings can inform the implementation of HIV prevention and testing strategies. Funding: Swiss National Science Foundation.