There are emerging opportunities to assess health indicators at truly small areas with increasing availability of data geocoded to micro geographic units and advanced modeling techniques. The utility of such fine-grained data can be fully leveraged if linked to local governance units that are accountable for implementation of programs and interventions. We used data from the 2011 Indian Census for village-level demographic and amenities features and the 2016 Indian Demographic and Health Survey in a bias-corrected semisupervised regression framework to predict child anthropometric failures for all villages in India. Of the total geographic variation in predicted child anthropometric failure estimates, 54.2 to 72.3% were attributed to the village level followed by 20.6 to 39.5% to the state level. The mean predicted stunting was 37.9% (SD: 10.1%; IQR: 31.2 to 44.7%), and substantial variation was found across villages ranging from less than 5% for 691 villages to over 70% in 453 villages. Estimates at the village level can potentially shift the paradigm of policy discussion in India by enabling more informed prioritization and precise targeting. The proposed methodology can be adapted and applied to diverse population health indicators, and in other contexts, to reveal spatial heterogeneity at a finer geographic scale and identify local areas with the greatest needs and with direct implications for actions to take place.

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While digital trace data from sources like search engines hold enormous potential for tracking and understanding human behavior, these streams of data lack information about the actual experiences of those individuals generating the data. Moreover, most current methods ignore or under-utilize human processing capabilities that allow humans to solve problems not yet solvable by computers (human computation). We demonstrate how behavioral research, linking digital and real-world behavior, along with human computation, can be utilized to improve the performance of studies using digital data streams. This study looks at the use of search data to track prevalence of Influenza-Like Illness (ILI). We build a behavioral model of flu search based on survey data linked to users’ online browsing data. We then utilize human computation for classifying search strings. Leveraging these resources, we construct a tracking model of ILI prevalence that outperforms strong historical benchmarks using only a limited stream of search data and lends itself to tracking ILI in smaller geographic units. While this paper only addresses searches related to ILI, the method we describe has potential for tracking a broad set of phenomena in near real-time.

We present online prediction methods for time series that let us explicitly handle nonstationary artifacts (e.g. trend and seasonality) present in most real time series. Specifically, we show that applying appropriate transformations to such time series before prediction can lead to improved theoretical and empirical prediction performance. Moreover, since these transformations are usually unknown, we employ the learning with experts setting to develop a fully online method (NonSTOP-NonSTationary Online Prediction) for predicting nonstationary time series. This framework allows for seasonality and/or other trends in univariate time series and cointegration in multivariate time series. Our algorithms and regret analysis subsume recent related work while significantly expanding the applicability of such methods. For all the methods, we provide sub-linear regret bounds using relaxed assumptions. The theoretical guarantees do not fully capture the benefits of the transformations, thus we provide a data-dependent analysis of the follow-the-leader algorithm that provides insight into the success of using such transformations. We support all of our results with experiments on simulated and real data.

We study a distributed consensus-based stochastic gradient descent (SGD) algorithm and show that the rate of convergence involves the spectral properties of two matrices: the standard spectral gap of a weight matrix from the network topology and a new term depending on the spectral norm of the sample covariance matrix of the data. This data-dependent convergence rate shows that distributed SGD algorithms perform better on datasets with small spectral norm. Our analysis method also allows us to find data-dependent convergence rates as we limit the amount of communication. Spreading a fixed amount of data across more nodes slows convergence; for asymptotically growing data sets we show that adding more machines can help when minimizing twice-differentiable losses. arXiv:1603.04379v2 [math.OC] 1 Sep 2016In such a computational model, nodes can perform local computations and send messages to each other to jointly minimize (1). The strategy we analyze is what is referred to as distributed primal averaging [3]: each node in the network processes points sequentially, performing a SGD update locally and averaging the current iterate values of their neighbors after each gradient step. This can also be thought of as a distributed consensus-based version of Pegasos [4] when the loss function is the hinge loss. We consider a general topology with m nodes attempting to minimize a global objective function J(w) that decomposes into a sum of m local objectives:. This is a model for optimization in systems such as data centers, distributed control systems, and sensor networks.Main Results. Our goal in this paper is to characterize how the spectral norm ρ 2 = σ 1 (EP [xx ]) of the sample covariance affects the rate of convergence of stochastic consensus schemes under different communication requirements. Elucidating this dependence can help guide empirical practice by providing insight into when these methods will work well. We prove an upper bound on the suboptimality gap for distributed primal averaging that depends on ρ 2 as well as the mixing time of the weight matrix associated to the algorithm. Our result shows that networks of size m < 1 ρ 2 gain from parallelization. To understand the communication-limited regime, we extend our analysis to intermittent communication. In a setting with finite data and sparse connectivity, convergence will deteriorate with increasing m because we split the data to more machines that are farther apart. We also show that by using a mini-batching strategy we can offset the penalty of infrequent communication by communicating after a mini-batch (sub)gradient step. Finally, in an asymptotic regime with infinite data at every node we show using results of Bianchi et al. [5] that for twice-differentiable loss functions this network effect disappears and that we gain from additional parallelization.Related Work. Several authors have proposed distributed algorithms involving nodes computing local gradient steps and averaging iterates, gradients, or other functions of their neighbors [3,6,7]. By alte...