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Nowadays stochastic approximation methods are one of the major research direction to deal with the largescale machine learning problems. From stochastic first order methods, now the focus is shifting to stochastic second order methods due to their faster convergence and availability of computing resources. In this paper, we have proposed a novel stochastic trust region inexact Newton method, called as STRON, which uses conjugate gradient (CG) to solve trust region subproblem. The method uses progressive subsampling in the calculation of gradient and Hessian values to take the advantage of both stochastic and full batch regimes. We have extended STRON using existing variance reduction techniques to deal with the noisy gradients and using preconditioned conjugate gradient (PCG) as subproblem solver, and empirically proved that they do not work, as expected, for the large-scale learning problems. We further extend STRON to solve SVM. Finally, our empirical results prove efficacy of the proposed method against existing methods with bench marked datasets.

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Supply networks (SNs) play a vital role in fuelling trade and economic growth. Due to their interconnectedness, firm-level disruptions can cause perturbations to ripple through SNs, magnifying initial impact. Contemporary research on ripple effects focussed on understanding various structural features of SNs to predict and control disruption propagation. Our work adds to this body of knowledge by analysing an intriguing topological property that emerges in SNs: 'nestedness', which is defined as a pattern of organisation where products that are supplied by specialist suppliers are a subset of products that are supplied by generalist suppliers. In other words, generalists are also specialists. While previous research examined the emergence of nestedness and its possible reasons, its relationship to SN resilience remained unknown. Here, we develop a cascade model by bringing together the product-supplier-buyer structure; which provides us with fine-grained information on SN dependencies. We simulate disruptions in nested and non-nested organisations of the global automotive SN, and find that nested organisations are significantly more robust to random disruptions but vulnerable to hub disruptions under cascade conditions. However, nested structures are not as resilient; as they do not benefit from a response strategy where buyers seek alternative suppliers; because alternative suppliers do not exist. On the other hand, randomly connected SNs are vulnerable to cascades but can allow network reconfiguration.

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