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Network-based assessments are important for disentangling complex microbial and microbial–host interactions and can provide the basis for microbial engineering. There is a growing recognition that chemical-mediated interactions are important for the coexistence of microbial species. However, so far, the methods used to infer microbial interactions have been validated with models assuming direct species-species interactions, such as generalized Lotka–Volterra models. Therefore, it is unclear how effective existing approaches are in detecting chemical-mediated interactions. In this paper, we used time series of simulated microbial dynamics to benchmark five major/state-of-the-art methods. We found that only two methods (CCM and LIMITS) were capable of detecting interactions. While LIMITS performed better than CCM, it was less robust to the presence of chemical-mediated interactions, and the presence of trophic competition was essential for the interactions to be detectable. We show that the existence of chemical-mediated interactions among microbial species poses a new challenge to overcome for the development of a network-based understanding of microbiomes and their interactions with hosts and the environment.

Interpretability requirements, complex uncertain data processing, and limited training data are characteristics of classification in some real industry applications. The interval belief rule base (IBRB) can deal with various types of uncertainty and provides high interpretability. However, there is a large number of parameters in IBRB, which makes it difficult for experts to accurately set them manually, limiting its application scope. To address this issue, this paper proposes an interval rule inference network (IRIN) with interpretability for classification models to automatically generate IBRB through integrating the ideas of the IBRB and the neural network. Firstly, hybrid data with different types are transformed into an interval belief distribution for automatic generation processing. Secondly, the interval evidence reasoning method is utilized as the inference engine to transfer information ensuring the process’s interpretability. Finally, a reasonable IBRB is generated automatically by updating the parameters by employing the learning engine in the neural network. Moreover, the differentiability of the interval evidence reasoning method in the IRIN is proved as a theoretical foundation of the IRIN, and an interpretability analysis of the IRIN’s structures is discussed. Experimental results demonstrate that the proposed method possesses high interpretability, enhancing the reliability of classification and maintaining the accuracy. Its application in an actual engineering case illustrates that it is particularly suitable for engineering problems where the explanation of results is a critical requirement.

Background Relatively small changes to gene expression data dramatically affect co-expression networks inferred from that data which, in turn, can significantly alter the subsequent biological interpretation. This error propagation is an underappreciated problem that, while hinted at in the literature, has not yet been thoroughly explored. Resampling methods (e.g. bootstrap aggregation, random subspace method) are hypothesized to alleviate variability in network inference methods by minimizing outlier effects and distilling persistent associations in the data. But the efficacy of the approach assumes the generalization from statistical theory holds true in biological network inference applications. Results We evaluated the effect of bootstrap aggregation on inferred networks using commonly applied network inference methods in terms of stability, or resilience to perturbations in the underlying expression data, a metric for accuracy, and functional enrichment of edge interactions. Conclusion Bootstrap aggregation results in improved stability and, depending on the size of the input dataset, a marginal improvement to accuracy assessed by each method’s ability to link genes in the same functional pathway.

Quantitatively identifying direct dependencies between variables is an important task in data analysis, in particular for reconstructing various types of networks and causal relations in science and engineering. One of the most widely used criteria is partial correlation, but it can only measure linearly direct association and miss nonlinear associations. However, based on conditional independence, conditional mutual information (CMI) is able to quantify nonlinearly direct relationships among variables from the observed data, superior to linear measures, but suffers from a serious problem of underestimation, in particular for those variables with tight associations in a network, which severely limits its applications. In this work, we propose a new concept, “partial independence,” with a new measure, “part mutual information” (PMI), which not only can overcome the problem of CMI but also retains the quantification properties of both mutual information (MI) and CMI. Specifically, we first defined PMI to measure nonlinearly direct dependencies between variables and then derived its relations with MI and CMI. Finally, we used a number of simulated data as benchmark examples to numerically demonstrate PMI features and further real gene expression data from Escherichia coli and yeast to reconstruct gene regulatory networks, which all validated the advantages of PMI for accurately quantifying nonlinearly direct associations in networks.

Network method of moments (Ann. Statist. 39 (2011) 2280–2301) is an important tool for nonparametric network inference. However, there has been little investigation on accurate descriptions of the sampling distributions of network moment statistics. In this paper, we present the first higher-order accurate approximation to the sampling CDF of a studentized network moment by Edgeworth expansion. In sharp contrast to classical literature on noiseless U-statistics, we show that the Edgeworth expansion of a network moment statistic as a noisy U-statistic can achieve higher-order accuracy without nonlattice or smoothness assumptions but just requiring weak regularity conditions. Behind this result is our surprising discovery that the two typically-hated factors in network analysis, namely, sparsity and edgewise observational errors, jointly play a blessing role, contributing a crucial self-smoothing effect in the network moment statistic and making it analytically tractable. Our assumptions match the minimum requirements in related literature. For sparse networks, our theory shows that our empirical Edgeworth expansion and a simple normal approximation both achieve the same gradually depreciating Berry–Esseen-type bound as the network becomes sparser. This result also significantly refines the best previous theoretical result. For practitioners, our empirical Edgeworth expansion is highly accurate and computationally efficient. It is also easy to implement and convenient for parallel computing. We demonstrate the clear advantage of our method by several comprehensive simulation studies. As a byproduct, we also provide a finite-sample analysis of the network jackknife. We showcase three applications of our results in network inference. We prove, to our knowledge, the first theoretical guarantee of higher-order accuracy for some network bootstrap schemes, and moreover, the first theoretical guidance for selecting the subsample size for network subsampling. We also derive a one-sample test and the Cornish–Fisher confidence interval for a given moment with higher-order accurate controls of confidence level and type I error, respectively.

Significance: Convolutional neural networks (CNNs) show the potential for automated classification of different cancer lesions. However, their lack of interpretability and explainability makes CNNs less than understandable. Furthermore, CNNs may incorrectly concentrate on other areas surrounding the salient object, rather than the network’s attention focusing directly on the object to be recognized, as the network has no incentive to focus solely on the correct subjects to be detected. This inhibits the reliability of CNNs, especially for biomedical applications. Aim: Develop a deep learning training approach that could provide understandability to its predictions and directly guide the network to concentrate its attention and accurately delineate cancerous regions of the image. Approach: We utilized Selvaraju et al.’s gradient-weighted class activation mapping to inject interpretability and explainability into CNNs. We adopted a two-stage training process with data augmentation techniques and Li et al.’s guided attention inference network (GAIN) to train images captured using our customized mobile oral screening devices. The GAIN architecture consists of three streams of network training: classification stream, attention mining stream, and bounding box stream. By adopting the GAIN training architecture, we jointly optimized the classification and segmentation accuracy of our CNN by treating these attention maps as reliable priors to develop attention maps with more complete and accurate segmentation. Results: The network’s attention map will help us to actively understand what the network is focusing on and looking at during its decision-making process. The results also show that the proposed method could guide the trained neural network to highlight and focus its attention on the correct lesion areas in the images when making a decision, rather than focusing its attention on relevant yet incorrect regions. Conclusions: We demonstrate the effectiveness of our approach for more interpretable and reliable oral potentially malignant lesion and malignant lesion classification.

Network link inference from measured time series data of the behavior of dynamically interacting network nodes is an important problem with wide-ranging applications, e.g., estimating synaptic connectivity among neurons from measurements of their calcium fluorescence. Network inference methods typically begin by using the measured time series to assign to any given ordered pair of nodes a numerical score reflecting the likelihood of a directed link between those two nodes. In typical cases, the measured time series data may be subject to limitations, including limited duration, low sampling rate, observational noise, and partial nodal state measurement. However, it is unknown how the performance of link inference techniques on such datasets depends on these experimental limitations of data acquisition. Here, we utilize both synthetic data generated from coupled chaotic systems as well as experimental data obtained from Caenorhabditis elegans neural activity to systematically assess the influence of data limitations on the character of scores reflecting the likelihood of a directed link between a given node pair. Wedo this for three network inference techniques: Granger causality, transfer entropy, and, a machine learning-based method. Furthermore, we assess the ability of appropriate surrogate data to determine statistical confidence levels associated with the results of link-inference techniques.

Regulatory networks as large and complex as those implicated in cell-fate choice are expected to exhibit intricate, very high-dimensional dynamics. Cell-fate choice, however, is a macroscopically simple process. Additionally, regulatory network models are almost always incomplete and/or inexact, and do not incorporate all the regulators and interactions that may be involved in cell-fate regulation. In spite of these issues, regulatory network models have proven to be incredibly effective tools for understanding cell-fate choice across contexts and for making useful predictions. Here, we show that minimal frustration—a feature of biological networks across contexts but not of random networks—can compel simple, low-dimensional steady-state behavior even in large and complex networks. Moreover, the steady-state behavior of minimally frustrated networks can be recapitulated by simpler networks such as those lacking many of the nodes and edges and those that treat multiple regulators as one. The present study provides a theoretical explanation for the success of network models in biology and for the challenges in network inference.

Abstract Reconstructing dynamics of complex systems from sparse, incomplete time series data is a challenging problem with applications in various domains. Here, we develop an iterative heuristic method to infer the underlying network structure and parameters governed by Ising dynamics from incomplete spin configurations based on sparse and small-sized samples. Our method iterates between imputing missing spin states given current coupling strengths and re-estimating couplings from completed spin state data. Central to our approach is the novel application of adaptive $$l_1$$ l 1 regularization on updating coupling strengths, which features an automatic adjustment of the regularization strength throughout the iterative inference process. By doing so, we aim at preventing over-fitting and enforcing the sparsity of couplings without access to ground truth parameters. We demonstrate that this approach accurately recovers parameters and imputes missing spins even with substantial missing data and short time series, providing improvements in the inference of Ising model parameters even for relatively small sample sizes.