The TAC SCM Prediction Challenge presents an opportunity for agents designed for the full TAC SCM game to compete solely on their ability to make predictions. Participants are presented with situations from actual TAC SCM games and are evaluated on their prediction accuracy in four categories: current and future computer prices, and current and future component prices. This paper introduces the Prediction Challenge and presents the results from 2007 along with an analysis of how the predictions of the participants compare to each other.

The 2007 TAC SCM Prediction Challenge.

Microbial network analysis help with discovering microbe groups that covariate with environmental factors. However, microbial communities are highly diversified and localized, which poses challenges to existing correlation-based network construction methods in terms of stability and functional significance. In this paper, we propose to explore the high-level relationships in the microbial network structure with the aid of network embedding methods. Microbial function modules are then extracted by spectrum clustering on the embedded networks, rather than the original ones. By investigating the correlation between the obtained modules and the environmental factors on several real-world microbial datasets, we demonstrate that the embedded modules provide feature information of the microbial community that are distinct to traditional correlation-based network modules. Furthermore, we show that the introduction of high-order modules helps with improving the performance of prediction models comparing with using OTU features or traditional correlation-based modules alone. Our study demonstrated that high-order network modules created by network embedding can be served as a potential new biomarker for feature extraction of microbial communities.

Finding High-Order Homologous Microbe Community Modules via Network Embedding

Bayesian networks (BNs) are popular for modeling conditional distributions of variables and causal relationships, especially in biological settings such as protein interactions, gene regulatory networks and microbial interactions. Previous BN structure learning algorithms treat variables with similar tendency separately. In this paper, we propose a grouped sparse Gaussian BN (GSGBN) structure learning algorithm which creates BN based on three assumptions: (i) variables follow a multivariate Gaussian distribution, (ii) the network only contains a few edges (sparse), (iii) similar variables have less-divergent sets of parents, while not-so-similar ones should have divergent sets of parents (variable grouping). We use L1 regularization to make the learned network sparse, and another term to incorporate shared information among variables. For similar variables, GSGBN tends to penalize the differences of similar variables' parent sets more, compared to those not-so-similar variables' parent sets. The similarity of variables is learned from the data by alternating optimization, without prior domain knowledge. Based on this new definition of the optimal BN, a coordinate descent algorithm and a projected gradient descent algorithm are developed to obtain edges of the network and also similarity of variables. Experimental results on both simulated and real datasets show that GSGBN has substantially superior prediction performance for structure learning when compared to several existing algorithms.

/pdf/learning-sparse-gaussian-bayesian-network-structure-by-4lnm0bx5hp.pdf

Learning Sparse Gaussian Bayesian Network Structure by Variable Grouping

Feature selection is important for many biological studies, especially when the number of available samples is limited (in order of hundreds) while the number of input features is large (in order of millions), such as eQTL (expression quantitative trait loci) mapping, GWAS (genome wide association study) and environmental microbial community study. We study the problem of multiple output regression which leverages the underlying common relationship shared by multiple output features and propose an efficient and accurate approach for feature selection. Our approach considers both intra- and inter-group sparsities. The intergroup sparsity assumes that only small set of input features are related to the output features. The intragroup sparsity assumes that each input features may relate to multiple output features which should have different kinds of sparsity. Most existing methods do not model the intragroup sparsity well by either assuming uniform regularization on each group, i.e. each input feature relates to similar number of output features, or requiring prior knowledge of the relationship of input and output features. By modelling the regression coefficients as a mixture distributions of Laplacian and Gaussian, we can shrink group regression coefficients to be small adaptively and learn the intergroup, intragroup sparsity and shrinkage estimation patterns. Empirical studies on the synthetic and real environmental microbial community datasets show that our model has better predictions on test dataset than existing methods such as Lasso, Elastic Net, dirty model and rMTFL (robust multi-task feature learning). Moreover, by using least angle regression or coordinate descent and projected gradient descent techniques for optimization, we can obtain the optimal regression efficiently.

/pdf/intra-and-inter-sparse-multiple-output-regression-with-2ijccqmi77.pdf

Intra- and inter-sparse multiple output regression with application on environmental microbial community study

Building statistical models to explain the association between responses (output) and predictors (input) is critical in many real applications. In reality, responses may not be independent. A promising direction is to predict related responses together (e.g. Multi-task LASSO). However, not all responses have the same degree of relatedness. Sparse Gaussian conditional random field (SGCRF) was developed to learn the degree of relatedness automatically from the samples without any prior knowledge. In real cases, features (both predictors and responses) are not arbitrary, but are dominated by a (smaller) set of related latent factors, e.g. clusters. SGCRF does not capture these latent relations in the model. Being able to model these relations could result in more accurate association between responses and predictors. In this paper, we propose a novel (mixed membership) hierarchical Bayesian model, namely M\(^2\)GCRF, to capture this phenomenon (in terms of clusters). We develop a variational Expectation-Maximization algorithm to infer the latent relations and association matrices. We show that M\(^2\)GCRF clearly outperforms existing methods for both synthetic and real datasets, and the association matrices identified by M\(^2\)GCRF are more accurate.

Jie Yang

Papers

Intra- and inter-sparse multiple output regression with application on environmental microbial community study

Mixed Membership Sparse Gaussian Conditional Random Fields

Learning Sparse Gaussian Bayesian Network Structure by Variable Grouping