Detecting change points in the large-scale structure of evolving networks

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks

The Influence of the Business Cycle on Mortality

We analyze the impact of short-run economic fluctuations on age-specific mortality using Bayesian time series econometrics and contribute to the debate on the procyclicality of mortality. For the first time, we examine the differing consequences of economic changes for all individual age classes. We employ a recently developed model to set up structural VARs of a latent mortality variable and of unemployment and GDP growth as main business cycle indicators. We find that young adults noticeably differ from the rest of the population. They exhibit increased mortality in a recession, whereas most of the other age classes between childhood and old age react with lower mortality to increased unemployment or decreased GDP growth. In order to avoid that opposed effects may cancel each other, our findings suggest to differentiate closely between particular age classes, especially in the age range of young adults. The results for the U.S. in the period 1956–2004 are confirmed by an international comparison with France and Japan. Long- term changes in the relationship between macroeconomic conditions and mortality are investigated with data since 1933.Age-specific Mortality, Business Cycle, Unemployment, Bayesian Econometrics, Health, Epidemiology

Quantum kernels for unattributed graphs using discrete-time quantum walks

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency