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)

Robust and Scalable Bayesian Online Changepoint Detection

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian perspective, and also addresses the scalability issues of previous attempts. Specifically, the proposed generalised Bayesian formalism leads to conjugate posteriors whose parameters are available in closed form by leveraging diffusion score matching. The resulting algorithm is exact, can be updated through simple algebra, and is more than 10 times faster than its closest competitor

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.

Greenhouse gas production in degrading ice-rich permafrost deposits in northeastern Siberia

Permafrost deposits have been a sink for atmospheric carbon for millennia. Thaw-erosional processes, however, can lead to rapid degradation of ice-rich permafrost and the release of substantial amounts of organic carbon (OC). The amount of the OC stored in these deposits and their potential to be microbially decomposed to the greenhouse gases carbon dioxide (CO2) and methane (CH4) depends on climatic and environmental conditions during deposition and the decomposition history before incorporation into the permafrost. Here, we examine potential greenhouse gas production in degrading ice-rich permafrost deposits from three locations in the northeast Siberian Laptev Sea region. The deposits span a period of about 55 kyr from the last glacial period and Holocene interglacial. Samples from all three locations were incubated under aerobic and anaerobic conditions for 134 days at 4 °C. Greenhouse gas production was generally higher in deposits from glacial periods, where 0.2–6.1% of the initially available OC was decomposed to CO2. In contrast, only 0.1–4.0% of initial OC were decomposed in permafrost deposits from the Holocene and the late glacial transition. Within the deposits from the Kargin interstadial period (Marine Isotope Stage 3), local depositional environments, especially soil moisture, also affected the preservation of OC. Sediments deposited under wet conditions contained more labile OC and thus produced more greenhouse gases than sediments deposited under drier conditions. To assess the greenhouse gas production potentials over longer periods, deposits from two locations were incubated for a total of 785 days. However, more than 50% of total CO2 production over 785 days occurred within the first 134 days under aerobic conditions while even 80% were produced over the same period under anaerobic conditions, which emphasizes the non-linearity of the OC decomposition processes. Methanogenesis was generally observed in active layer samples but only sporadically in permafrost samples and was several orders of magnitude smaller than CO2 production

Constraining Phosphorus in Surface Waters of the New York City Watershed: Dairy Farm Resource Use and Profitability

The New York City Watershed Agricultural Program seeks to reduce the potential for phosphorus movement from farms to surface waters. A "phosphorus index for site evaluation" (P-index) provides planners in the New York City Watershed Agricultural Program with a tool for identifying individual farm business, phosphorus related problems, and evaluating solutions. A linear programming model is employed to examine dairy farm resource use and profitability, with the P-index used to impose phosphorus movement constraints. Results indicate dramatic differences in farm resource use and farm business profitability depending on the level of the P-index. Small changes in the target index level result in large shifts in optimal resource use and business profitability. These differences illustrate that restrictions on phosphorus movement from land to surface waters potentially have major impacts on resource use and farm profitability in the New York City Watershed

Robust generalised Bayesian inference for intractable likelihoods

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the normalisation constant and produces generalised posteriors that are either closed form or accessible using the standard Markov chain Monte Carlo. On a theoretical level, we show consistency, asymptotic normality, and bias-robustness of the generalised posterior, highlighting how these properties are impacted by the choice of Stein discrepancy. Then, we provide numerical experiments on a range of intractable distributions, including applications to kernel-based exponential family models and non-Gaussian graphical models

Evaluation of a Technology-Based Survivor Care Plan for Breast Cancer Survivors: Pre-Post Pilot Study.

BACKGROUND: As of 2016, almost 16 million individuals were cancer survivors, including over 3.5 million survivors of breast cancer. Because cancer survivors are living longer and have unique health care needs, the Institute of Medicine proposed a survivor care plan as a way to alleviate the many medical, emotional, and care coordination problems of survivors. OBJECTIVE: This pilot study for breast cancer survivors was undertaken to: (1) examine self-reported changes in knowledge, confidence, and activation from before receipt to after receipt of a survivor care plan; and (2) describe survivor preferences for, and satisfaction with, a technology-based survivor care plan. METHODS: A single group pretest-posttest design was used to study breast cancer survivors in an academic cancer center and a community cancer center during their medical visit after they completed chemotherapy. The intervention was a technology-based survivor care plan. Measures were taken before, immediately after, and 1 month after receipt of the survivor care plan. RESULTS: A total of 38 breast cancer survivors agreed to participate in the study. Compared to baseline levels before receipt of the survivor care plan, participants reported increased knowledge both immediately after its receipt at the academic center (P\u3c.001) and the community center (P\u3c.001) as well as one month later at the academic center (P=.002) and the community center (P\u3c.001). Participants also reported increased confidence immediately following receipt of the survivor care plan at the academic center (P=.63) and the community center (P=.003) and one month later at both the academic center (P=.63) and the community center (P\u3c.001). Activation was increased from baseline to post-survivor care plan at both the academic center (P=.05) and community center (P\u3c.001) as well as from baseline to 1-month follow-up at the academic center (P=.56) and the community center (P\u3c.001). Overall, community center participants had lower knowledge, confidence, and activation at baseline compared with academic center participants. Overall, 22/38 (58%) participants chose the fully functional electronic survivor care plan. However, 12/23 (52%) in the community center group chose the paper version compared to 4/15 (27%) in the academic center group. Satisfaction with the format (38/38 participants) and the content (37/38 participants) of the survivor care plan was high for both groups. CONCLUSIONS: This study provides evidence that knowledge, confidence, and activation of survivors were associated with implementation of the survivor care plan. This research agrees with previous research showing that cancer survivors found the technology-based survivor care plan to be acceptable. More research is needed to determine the optimal approach to survivor care planning to ensure that all cancer survivors can benefit from it