Discovering significant pathways rather than single genes or small gene sets involved in metastasis is becoming more and more important in the study of breast cancer. Many researches have shed light on this problem. However, most of the existing works are relying on some priori biological information, which may bring bias to the models. The authors propose a new method that detects metastasis-related pathways by identifying and comparing modules in metastasis and non-metastasis gene co-expression networks. The gene co-expression networks are built by Pearson correlation coefficients, and then the modules inferred in these two networks are compared. In metastasis and non-metastasis networks, 36 and 41 significant modules are identified. Also, 27.8% (metastasis) and 29.3% (non-metastasis) of the modules are enriched significantly for one or several pathways with p-value <0.05. Many breast cancer genes including RB1, CCND1 and TP53 are included in these identified pathways. Five significant pathways are discovered only in metastasis network: glycolysis pathway, cell adhesion molecules, focal adhesion, stathmin and breast cancer resistance to antimicrotubule agents, and cytosolic DNA-sensing pathway. The first three pathways have been proved to be closely associated with metastasis. The rest two can be taken as a guide for future research in breast cancer metastasis.
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and other related performance measures of interest. We propose an optimization-based framework to compute statistically valid bounds on input quantities. The framework utilizes constraints that connect the statistical information of the real-world outputs with the input-output relation via a simulable map. We analyze the statistical guarantees of this approach from the view of data-driven robust optimization, and show how the guarantees relate to the function complexity of the constraints arising in our framework.We investigate an iterative procedure based on a stochastic quadratic penalty method to approximately solve the resulting optimization. We conduct numerical experiments to demonstrate our performance in bounding the input models and related quantities. Daley D, Servi L (1998) Moment estimation of customer loss rates from transactional data. International Journal of Stochastic Analysis 11(3):301-310. Dang CD, Lan G (2015) Stochastic block mirror descent methods for nonsmooth and stochastic optimization. SIAM Journal on Optimization 25(2):856-881. Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research 58(3):595-612. Donoho DL, Johnstone IM, Hoch JC, Stern AS (1992) Maximum entropy and the nearly black object. Journal of the Royal Statistical Society. Series B (Methodological) 41-81. Duchi J, Glynn P, Namkoong H (2016) Statistics of robust optimization: A generalized empirical likelihood approach. arXiv preprint arXiv:1610.03425 . Durrett R (2010) Probability: Theory and Examples (Cambridge university press). Esfahani PM, Kuhn D (2015) Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations. arXiv preprint arXiv:1505.05116 . Fan W, Hong LJ, Zhang X (2013) Robust selection of the best. Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with wasserstein distance. arXiv preprint arXiv:1604.02199 . Ghadimi S, Lan G (2013) Stochastic first-and zeroth-order methods for nonconvex stochastic programming. SIAM Journal on Optimization 23(4):2341-2368. Ghadimi S, Lan G (2015) Accelerated gradient methods for nonconvex nonlinear and stochastic programming. Mathematical Programming 1-41. Ghadimi S, Lan G, Zhang H (2016) Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization. Mathematical Programming 155(1-2):267-305. Ghosh S, Lam H (2015a) Computing worst-case input models in stochastic simulation. Available at http://arxiv.org/pdf/1507.05609v1.pdf . Ghosh S, Lam H (2015b) Mirror descent stochastic approximation for computing worst-case stochastic input models. Proceedings of the 2015 Winter Simulation Conference, 425-436 (IEEE Press). 35 Ghosh S, Lam H (2015c) Robust...
In data-driven optimization, solution feasibility is often ensured through a "safe" reformulation of the uncertain constraints, such that an obtained data-driven solution is guaranteed to be feasible for the oracle formulation with high statistical confidence. Such approaches generally involve an implicit estimation of the whole feasible set that can scale rapidly with the problem dimension, in turn leading to over-conservative solutions. In this paper, we investigate a validation-based strategy to avoid set estimation by exploiting the intrinsic low dimensionality among all possible solutions output from a given reformulation. We demonstrate how our obtained solutions satisfy statistical feasibility guarantees with light dimension dependence, and how they are asymptotically optimal and thus regarded as the least conservative with respect to the considered reformulation classes. We apply this strategy to several data-driven optimization paradigms including (distributionally) robust optimization, sample average approximation and scenario optimization. Numerical experiments show encouraging performances of our strategy compared to established benchmarks.
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