Adversarial Interpretation of Bayesian Inference

We build on the optimization-centric view on Bayesian inference advocated by Knoblauch et al. (2019). Thinking about Bayesian and generalized Bayesian posteriors as the solutions to a regularized minimization problem allows us to answer an intriguing question: If minimization is the primal problem, then what is its dual? By deriving the Fenchel dual of the problem, we demonstrate that this dual corresponds to an adversarial game: In the dual space, the prior becomes the cost function for an adversary that seeks to perturb the likelihood [loss] function targeted by standard [generalized] Bayesian inference. This implies that Bayes-like procedures are adversarially robust—providing another firm theoretical foundation for their empirical performance. Our contributions are foundational, and apply to a wide-ranging set of Machine Learning methods. This includes standard Bayesian inference, generalized Bayesian and Gibbs posteriors (Bissiri et al., 2016), as well as a diverse set of other methods including Generalized Variational Inference (Knoblauch et al., 2019) and the Wasserstein Autoencoder (Tolstikhin et al., 2017)

Zero delay synchronization of chaos in coupled map lattices

We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.Comment: 9 pages, 9 figures ; To appear in Phys. Rev.

Spatial mobility and large-scale resource extraction: an analysis of community well-being and health in a copper mining area of Zambia

We examine population mobility around a newly-developed large-scale copper mine in Zambia and analyse how socioeconomic and health indicators differed amongst migrants, resettled households, and non-mobile local (e.g. non-migrant/-resettled) populations. Two cross-sectional household surveys in 2015 and 2019 collected quan-titative data on health, socioeconomic indicators, and resettlement and migration status. A wealth index for the pooled sample (N =990 households) was computed using a simplified list of household assets adapted from the Zambia Demographic and Health Survey. Logistic regression models were conducted to assess associations with health outcomes. In-migrants were younger than non-mobile locals (mean age of household head 33.9 vs. 37.7 years), more highly educated (34.3% of household heads completed secondary school vs. 7.3%), had higher employment (43.8% vs. 15.8%), and higher mean wealth (3.6 vs. 3.0). The odds of having a child <5 years diagnosed with malaria (OR: 0.53, 95% CI: 0.40, 0.71) or classified as stunted (OR: 0.66, 95% CI: 0.50, 0.87) were significantly lower for migrants during the construction phase, even after adjusting for family wealth score. Migrant and resettled households had greater wealth and assets even after adjusting for age, education, and employment, suggesting spatial mobility is associated with improved socioeconomic status and disease prevention

Estrogen receptor negative/progesterone receptor positive breast cancer is not a reproducible subtype

Introduction: Estrogen receptor (ER) and progesterone receptor (PR) testing are performed in the evaluation of breast cancer. While the clinical utility of ER as a predictive biomarker to identify patients likely to benefit from hormonal therapy is well-established, the added value of PR is less well-defined. The primary goals of our study were to assess the distribution, inter-assay reproducibility, and prognostic significance of breast cancer subtypes defined by patterns of ER and PR expression. Methods: We integrated gene expression microarray (GEM) and clinico-pathologic data from 20 published studies to determine the frequency (n = 4,111) and inter-assay reproducibility (n = 1,752) of ER/PR subtypes (ER+/PR+, ER+/PR-, ER-/PR-, ER-/PR+). To extend our findings, we utilized a cohort of patients from the Nurses’ Health Study (NHS) with ER/PR data recorded in the medical record and assessed on tissue microarrays (n = 2,011). In both datasets, we assessed the association of ER and PR expression with survival. Results: In a genome-wide analysis, progesterone receptor was among the least variable genes in ER- breast cancer. The ER-/PR+ subtype was rare (approximately 1 to 4%) and showed no significant reproducibility (Kappa = 0.02 and 0.06, in the GEM and NHS datasets, respectively). The vast majority of patients classified as ER-/PR+ in the medical record (97% and 94%, in the GEM and NHS datasets) were re-classified by a second method. In the GEM dataset (n = 2,731), progesterone receptor mRNA expression was associated with prognosis in ER+ breast cancer (adjusted P <0.001), but not in ER- breast cancer (adjusted P = 0.21). PR protein expression did not contribute significant prognostic information to multivariate models considering ER and other standard clinico-pathologic features in the GEM or NHS datasets. Conclusion: ER-/PR+ breast cancer is not a reproducible subtype. PR expression is not associated with prognosis in ER- breast cancer, and PR does not contribute significant independent prognostic information to multivariate models considering ER and other standard clinico-pathologic factors. Given that PR provides no clinically actionable information in ER+ breast cancer, these findings question the utility of routine PR testing in breast cancer

Changes in household wealth in communities living in proximity to a large-scale copper mine in Zambia

Large-scale mining can alter the living conditions of surrounding communities in positive and negative ways. A health impact assessment conducted in the context of a newly developed large-scale copper mine in rural Zambia gave us the opportunity to measure changes in health determinants over time. We conducted periodic household surveys at baseline in 2011, during the construction phase in 2015 and during the operational phase in 2019. Data collected included economic indicators that were based on the standardized list of household assets used in the Zambia Demographic and Health Survey, which we subsequently converted into a wealth score using principal component analysis. We compared mean wealth scores in six communities directly impacted by the mine with comparison communities, as well as the rest of the North-Western province of Zambia. A difference-indifferences linear regression model was used to compare changes over time. Mean wealth of the communities near the mine was significantly lower at baseline than that of the North-Western province (? 0.54 points; pvalue< 0.001) in 2011, but surpassed the regional average in 2019 (+1.07 points; p-value <0.001). Mean wealth increased more rapidly in communities directly impacted by mine than in the comparison communities (+0.30 points, p-value <0.001). These results suggest a positive impact on living conditions in communities living near this copper mine. Our findings underscore the potential of the mining sector to contribute to economic development in Zambia