Hierarchicality of Trade Flow Networks Reveals Complexity of Products

With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be regarded as a value chain. The problem is weather we can discriminate between these products based on their unique flow network structure. This paper applies the flow analysis method developed in ecology to 638 trading flow networks of different products. We claim that the allometric scaling exponent $\eta$ can be used to characterize the degree of hierarchicality of a flow network, i.e., whether the trading products flow on long hierarchical chains. Then, the flow networks of products with higher added values and complexity, such as machinery&transport equipment with larger exponents, are highlighted. These higher values indicate that their trade flow networks are more hierarchical. As a result, without extra data such as global input-output table, we can identify the product categories with higher complexity and the relative importance of a country in the global value chain solely by the trading network.Comment: 14 pages,7 figure

High-dimensional covariance regression with application to co-expression QTL detection

While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level covariates. In this paper, we present a new sparse multivariate regression framework that models the covariance matrix as a function of subject-level covariates. In the context of co-expression quantitative trait locus (QTL) studies, our method can be used to determine if and how gene co-expressions vary with genetic variations. To accommodate high-dimensional responses and covariates, we stipulate a combined sparsity structure that encourages covariates with non-zero effects and edges that are modulated by these covariates to be simultaneously sparse. We approach parameter estimation with a blockwise coordinate descent algorithm, and investigate the $\ell_2$ convergence rate of the estimated parameters. In addition, we propose a computationally efficient debiased inference procedure for uncertainty quantification. The efficacy of the proposed method is demonstrated through numerical experiments and an application to a gene co-expression network study with brain cancer patients

Learning to Diversify Web Search Results with a Document Repulsion Model

Search diversification (also called diversity search), is an important approach to tackling the query ambiguity problem in information retrieval. It aims to diversify the search results that are originally ranked according to their probabilities of relevance to a given query, by re-ranking them to cover as many as possible different aspects (or subtopics) of the query. Most existing diversity search models heuristically balance the relevance ranking and the diversity ranking, yet lacking an efficient learning mechanism to reach an optimized parameter setting. To address this problem, we propose a learning-to-diversify approach which can directly optimize the search diversification performance (in term of any effectiveness metric). We first extend the ranking function of a widely used learning-to-rank framework, i.e., LambdaMART, so that the extended ranking function can correlate relevance and diversity indicators. Furthermore, we develop an effective learning algorithm, namely Document Repulsion Model (DRM), to train the ranking function based on a Document Repulsion Theory (DRT). DRT assumes that two result documents covering similar query aspects (i.e., subtopics) should be mutually repulsive, for the purpose of search diversification. Accordingly, the proposed DRM exerts a repulsion force between each pair of similar documents in the learning process, and includes the diversity effectiveness metric to be optimized as part of the loss function. Although there have been existing learning based diversity search methods, they often involve an iterative sequential selection process in the ranking process, which is computationally complex and time consuming for training, while our proposed learning strategy can largely reduce the time cost. Extensive experiments are conducted on the TREC diversity track data (2009, 2010 and 2011). The results demonstrate that our model significantly outperforms a number of baselines in terms of effectiveness and robustness. Further, an efficiency analysis shows that the proposed DRM has a lower computational complexity than the state of the art learning-to-diversify methods