Inference of a combinatorial function from multiple independent variables (parents) to a dependent variable (child) in a discrete space can be useful in detecting nonlinear relationships in biological systems. Popular conditional independency measures, heavily used in combinatorial inference, are often insensitive to the direction of functional dependency. To address this issue, we define multivariate and conditional functional chi-squared statistics. We also present an algorithm called CFDF for bivariate discrete function inference via an exclusive-effect strategy, in order to identify a best parent set for a given child. It requires each parent to make sufficient contribution beyond any marginal effect. Simulation studies suggest a marked advantage of our framework over alternatives. Applying the method to transcriptome data in genetically perturbed biological systems, we reproduced combinatorial gene interactions known in the literature. Most importantly, we identified combinatorial patterns from joint RNA and protein data to rebut a dispute on the founding principle of molecular biology.
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Joint Grid Discretization for Biological Pattern Discovery
The complexity, dynamics, and scale of data acquired by modern biotechnology increasingly favor model-free computational methods that make minimal assumptions about underlying biological mechanisms. For example, single-cell transcriptome and proteome data have a throughput several orders more than bulk methods. Many model-free statistical methods for pattern discovery such as mutual information and chi-squared tests, however, require discrete data. Most discretization methods minimize squared errors for each variable independently, not necessarily retaining joint patterns. To address this issue, we present a joint grid discretization algorithm that preserves clusters in the original data. We evaluated this algorithm on simulated data to show its advantage over other methods in maintaining clusters as measured by the adjusted Rand index. We also show it promotes global functional patterns over independent patterns. On single-cell proteome and transcriptome of leukemia and healthy blood, joint grid discretization captured known protein-to-RNA regulatory relationships, while revealing previously unknown interactions. As such, the joint grid discretization is applicable as a data transformation step in associative, functional, and causal inference of molecular interactions fundamental to systems biology. The developed software is publicly available at https://cran.r-project.org/package=GridOnClusters
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- Award ID(s):
- 1661331
- NSF-PAR ID:
- 10236467
- Date Published:
- Journal Name:
- Proceedings. The 11th ACM Int'l Conf on Bioinform, Comput Biol and Health Inform
- Page Range / eLocation ID:
- Article No.: 57
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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SUMMARY A fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. The algorithm uses a non-linear Gramian constraint to impose correlation between the density and susceptibility of the reconstructed models. The global objective function is formulated in the space of the weighted parameters, but the Gramian constraint is implemented in the original space, and the non-linear constraint is imposed using two separate Lagrange parameters, one for each model domain. It is significant that this combined approach, using the two spaces provides more similarity between the reconstructed models. Moreover, it is shown theoretically that the gradient for the use of the unweighted space is not a scalar multiple of that used for the weighted space, and hence cannot be accounted for by adjusting the Lagrange parameters. It is assumed that the measured data are obtained on a uniform grid and that a consistent regular discretization of the volume domain is imposed. Then, the sensitivity matrices exhibit a block-Toeplitz-Toeplitz-block structure for each depth layer of the model domain, and both forward and transpose operations with the matrices can be implemented efficiently using two dimensional fast Fourier transforms. This makes it feasible to solve for large scale problems with respect to both computational costs and memory demands, and to solve the non-linear problem by applying iterative methods that rely only on matrix–vector multiplications. As such, the use of the regularized reweighted conjugate gradient algorithm, in conjunction with the structure of the sensitivity matrices, leads to a fast methodology for large-scale joint inversion of geophysical data sets. Numerical simulations demonstrate that it is possible to apply a non-linear joint inversion algorithm, with Lp-norm stabilisers, for the reconstruction of large model domains on a standard laptop computer. It is demonstrated, that while the p = 1 choice provides sparse reconstructed solutions with sharp boundaries, it is also possible to use p = 2 in order to provide smooth and blurred models. The methodology is used for inverting gravity and magnetic data obtained over an area in northwest of Mesoproterozoic St Francois Terrane, southeast of Missouri, USA.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3388440.3412415
