Private Graphon Estimation for Sparse Graphs

We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a node-differentially-private nonparametric block model approximation. By node-differentially-private, we mean that our output hides the insertion or removal of a vertex and all its adjacent edges. If $G$ is an instance of the network obtained from a generative nonparametric model defined in terms of a graphon $W$, our model guarantees consistency, in the sense that as the number of vertices tends to infinity, the output of our algorithm converges to $W$ in an appropriate version of the $L_2$ norm. In particular, this means we can estimate the sizes of all multi-way cuts in $G$. Our results hold as long as $W$ is bounded, the average degree of $G$ grows at least like the log of the number of vertices, and the number of blocks goes to infinity at an appropriate rate. We give explicit error bounds in terms of the parameters of the model; in several settings, our bounds improve on or match known nonprivate results.Comment: 36 page

A Community-Focused Health & Work Service (HWS)

We recommend establishment of a community-focused Health & Work Service (HWS) dedicated to responding rapidly to new health-related work absence among working people due to potentially disabling conditions. The first few days and weeks after onset are an especially critical period during which the likelihood of a good long-term outcome is being influenced, either favorably or unfavorably, by some simple things that either do or do not happen during that interval. It is the optimal window of opportunity to improve outcomes by simultaneously attending to the worker’s basic needs and concerns as well as coordinating the medical, functional restoration, and occupational aspects of the situation in a coordinated fashion

Economic integration in a multicone world?

This paper examines whether economic integration favors countries' convergence into a common cone of diversification. We analyze the manufacturing specialization patterns for a sample of 19 current and potential European Union countries over the period 1963-1998, and assess the impact of integration on their evolution. We perform year-by-year threshold estimations of Rybczynski relationships to identify the diversification cones and then estimate discrete choice models to investigate whether membership in the European Union is associated with a higher probability of being in a same cone. Economic integration in Europe is found to have promoted convergence from lower to higher diversification cones. --Multiple Diversification Cones,Convergence,European Integration,Threshold Estimation,Dynamic Probit Models