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PubMed2005

Finding local community structure in networks.

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(k2d) for general graphs when d is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time consuming, the running time is linear, O(k). We show that on computer-generated graphs the average behavior of this technique approximates that of algorithms that require global knowledge. As an application, we use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer.

Journal Article↗

PubMed1994

Simulations of a ventrolateral medullary neural network for respiratory rhythmogenesis inferred from spike train cross-correlation.

Connections among ventrolateral medullary respiratory neurons inferred from spike train analysis were incorporated into a model and simulated with the program SYSTM11 (MacGregor 1987). Inspiratory (I) and expiratory (E) neurons with augmenting (AUG) and decrementing (DEC) discharge patterns and rostral I-E/I neurons exhibited varying degrees of adaptation, but no endogenous bursting properties. Simulation parameters were adjusted so that respiratory phase durations, neuronal discharge patterns, and short-time scale correlations were similar to corresponding measurements from anesthetized, vagotomized, adult cats. Rhythmogenesis persisted when the strength of each set of connections was increased 100% over a smaller effective value. Changes in phase durations and discharge patterns caused by manipulation of connection strengths or population activity led to several predictions. (a) Excitation of the I-E/I population prolongs the inspiratory phase. (b) Rhythmic activity can be reestablished in the absence of I-E/I activity by unpatterned excitation of I-DEC and I-AUG neurons. (c) An increase in I-DEC neuron activity can cause an apneustic respiratory pattern. (d) A decrease in I-DEC neuron activity increases the slope of the inspiratory ramp and shortens inspiration. (e) Excitation of the E-DEC population prolongs the expiratory phase or produces apnea; inhibition of E-DEC neurons reduces expiratory time. (f) Excitation of E-AUG cells causes I-AUG neurons to exhibit a step rather than a ramp increase in firing rate at the onset of their active phase. The results suggest mechanisms by which the duration of each phase of breathing and neuronal discharge patterns may be regulated.

Animals↗

PubMed1978

An inference upon the neural network finding binocular correspondence.

Previously, the authors proposed a model of neural network extracting binocular parallax (Hirai and Fukushima, 1975). It is a multilayered network whose final layers consist of neural elements corresponding to "binocular depth neurons" found in monkey's visual cortex. The binocular depth neuron is selectively sensitive to a binocular stimulus with a specific amount of binocular parallax and does not respond to a monocular one. As described in the last chapter of the previous article (Hirai and Fukushima, 1975), when a binocular pair of input patterns consist of, for example, many vertical bars placed very closely to each other, the binocular depth neurons might respond not only to correct binocular pairs, but also to incorrect ones. Our present study is concentrated upon how the visual system finds correct binocular pairs or binocular correspondence. It is assumed that some neural network is cascaded after the binocular depth neurons and finds out correct binocular correspondence by eliminating the incorrect binocular pairs. In this article a model of such neural network is proposed. The performance of the model has been simulated on a digital computer. The results of the computer simulation show that this model finds binocular correspondence satisfactorily. It has been demonstrated by the computer simulation that this model also explains the mechanism of the hysteresis in the binocular depth perception reported by Fender and Julesz (1967).

Computers↗

PubMed2005

Inference of transcriptional regulatory network by two-stage constrained space factor analysis.

MOTIVATION: Microarray gene expression and cross-linking chromatin immunoprecipitation data contain voluminous information that can help the identification of transcriptional regulatory networks at the full genome scale. Such high-throughput data are noisy however. In contrast, from the biomedical literature, we can find many evidenced transcription factor (TF)-target gene binding relationships that have been elucidated at the molecular level. But such sporadically generated knowledge only offers glimpses on limited patches of the network. How to incorporate this valuable knowledge resource to build more reliable network models remains a question. RESULTS: We present a modified factor analysis approach. Our algorithm starts with the evidenced TF-gene linkages. It iterates between the network configuration estimation step and the connection strength estimation step, using the high-throughput data, till convergence. We report two comprehensive regulatory networks obtained for Saccharomyces cerevisiae, one under the normal growth condition and the other under the environmental stress condition. SUPPLEMENTARY INFORMATION: http://kiefer.stat.ucla.edu/lap2/download/bti656_supplement.pdf.

Algorithms↗

PubMed2006

Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks.

BACKGROUND: The learning of global genetic regulatory networks from expression data is a severely under-constrained problem that is aided by reducing the dimensionality of the search space by means of clustering genes into putatively co-regulated groups, as opposed to those that are simply co-expressed. Be cause genes may be co-regulated only across a subset of all observed experimental conditions, biclustering (clustering of genes and conditions) is more appropriate than standard clustering. Co-regulated genes are also often functionally (physically, spatially, genetically, and/or evolutionarily) associated, and such a priori known or pre-computed associations can provide support for appropriately grouping genes. One important association is the presence of one or more common cis-regulatory motifs. In organisms where these motifs are not known, their de novo detection, integrated into the clustering algorithm, can help to guide the process towards more biologically parsimonious solutions. RESULTS: We have developed an algorithm, cMonkey, that detects putative co-regulated gene groupings by integrating the biclustering of gene expression data and various functional associations with the de novo detection of sequence motifs. CONCLUSION: We have applied this procedure to the archaeon Halobacterium NRC-1, as part of our efforts to decipher its regulatory network. In addition, we used cMonkey on public data for three organisms in the other two domains of life: Helicobacter pylori, Saccharomyces cerevisiae, and Escherichia coli. The biclusters detected by cMonkey both recapitulated known biology and enabled novel predictions (some for Halobacterium were subsequently confirmed in the laboratory). For example, it identified the bacteriorhodopsin regulon, assigned additional genes to this regulon with apparently unrelated function, and detected its known promoter motif. We have performed a thorough comparison of cMonkey results against other clustering methods, and find that cMonkey biclusters are more parsimonious with all available evidence for co-regulation.

Algorithms↗

PubMed2004

Inference of gene regulatory networks by means of dynamic differential Bayesian networks and nonparametric regression.

We propose a dynamic differential Bayesian networks (DDBNs) and nonparametric regression model. This model is an extended model of traditional dynamic Bayesian networks (DBNs), which can incorporate temporal information in a natural way and directly handle real-valued data obtained from microarrays without any transformation. In addition, it can cope with differential information between gene expression levels, without any loss to the traditional advantage, i.e., the capability of estimating non-linear relationships between genes. We apply DDBNs to analyze simulated data and real data, i.e., Saccharomyces cerevisiae cell cycle gene expression data. We have confirmed the effectiveness of our approach in the sense that some edges have been successfully detected only by DDBNs, not by DBNs.

Algorithms↗

PubMed2006

Perspectives of probabilistic inferences: Reinforcement learning and an adaptive network compared.

The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. The strategy selection learning theory specifies how people select strategies from this repertoire. The theory assumes that individuals select strategies proportional to their subjective expectations of how well the strategies solve particular problems; such expectations are assumed to be updated by reinforcement learning. The theory is compared with an adaptive network model that assumes people make inferences by integrating information according to a connectionist network. The network's weights are modified by error correction learning. The theories were tested against each other in 2 experimental studies. Study 1 showed that people substantially improved their inferences through feedback, which was appropriately predicted by the strategy selection learning theory. Study 2 examined a dynamic environment in which the strategies' performances changed. In this situation a quick adaptation to the new situation was not observed; rather, individuals got stuck on the strategy they had successfully applied previously. This "inertia effect" was most strongly predicted by the strategy selection learning theory.

Adult↗

PubMed2001

A microbial population-species interface: nested cladistic and coalescent inference with multilocus data.

Using sequence data from seven nuclear loci in 385 isolates of the haploid, plant parasitic, ascomycete fungus, Sclerotinia, divergence times of populations and of species were distinguished. The evolutionary history of haplotypes on both population and species scales was reconstructed using a combination of parsimony, maximum likelihood and coalescent methods, implemented in a specific order. Analysis of site compatibility revealed recombination blocks from which alternative (marginal) networks were inferred, reducing uncertainty in the network due to recombination. Our own modifications of Templeton and co-workers' cladistic inference method and a coalescent approach detected the same phylogeographic processes. Assuming neutrality and a molecular clock, the boundary between divergent populations and species is an interval of time between coalescence (to a common ancestor) of populations and coalescence of species.

Ascomycota↗

PubMed2006

BIOREL: the benchmark resource to estimate the relevance of the gene networks.

The progress of high-throughput methodologies in functional genomics has lead to the development of statistical procedures to infer gene networks from various types of high-throughput data. However, due to the lack of common standards, the biological significance of the results of the different studies is hard to compare. To overcome this problem we propose a benchmark procedure and have developed a web resource (BIOREL), which is useful for estimating the biological relevance of any genetic network by integrating different sources of biological information. The associations of each gene from the network are classified as biologically relevant or not. The proportion of genes in the network classified as "relevant" is used as the overall network relevance score. Employing synthetic data we demonstrated that such a score ranks the networks fairly in respect to the relevance level. Using BIOREL as the benchmark resource we compared the quality of experimental and theoretically predicted protein interaction data.

Computational Biology↗

PubMed2004

Inferring dynamic architecture of cellular networks using time series of gene expression, protein and metabolite data.

MOTIVATION: High-throughput technologies have facilitated the acquisition of large genomics and proteomics datasets. However, these data provide snapshots of cellular behavior, rather than help us reveal causal relations. Here, we propose how these technologies can be utilized to infer the topology and strengths of connections among genes, proteins and metabolites by monitoring time-dependent responses of cellular networks to experimental interventions. RESULTS: We demonstrate that all connections leading to a given network node, e.g. to a particular gene, can be deduced from responses to perturbations none of which directly influences that node, e.g. using strains with knock-outs to other genes. To infer all interactions from stationary data, each node should be perturbed separately or in combination with other nodes. Monitoring time series provides richer information and does not require perturbations to all nodes. Overall, the methods we propose are capable of deducing and quantifying functional interactions within and across cellular gene, signaling and metabolic networks. SUPPLEMENTARY INFORMATION: Supplementary material is available at http://www.dbi.tju.edu/bioinformatics2004.pdf

Algorithms↗

PubMedDate not supplied

Medical expert systems based on causal probabilistic networks.

Causal probabilistic networks (CPNs) offer new methods by which you can build medical expert systems that can handle all types of medical reasoning within a uniform conceptual framework. Based on the experience from a commercially available system and a couple of large prototype systems, it appears that CPNs are now an attractive alternative to other methods. A CPN is an intensional model of a domain, and it is therefore conceptually much closer to qualitative reasoning systems and to simulation systems than to rule-based or logic-based systems. Recent progress in Bayesian inference in networks has yielded computationally efficient methods. The inference method used follows the fundamental axioms of probability theory, and gives a sound framework for causal and diagnostic (deductive and abductive) reasoning under uncertainty. Experience with the prototypes indicates that it may be possible to use decision theory as a rational approach to test planning and therapy planning. The way in which knowledge is acquired and represented in CPNs makes it easy to express 'deep knowledge' for example in the form of physiological models, and the facilities for learning make it possible to make a smooth transition from expert opinion to statistics based on empirical data.

Artificial Intelligence↗

PubMed2026

Causal assessment of Bayesian gene regulatory networks from single-cell transcriptomics.

Gene regulatory network (GRN) inference is an essential tool for revealing dysregulated relationships between genes in different cell types from single-cell transcriptomic (SCT) data. GRNs based on Bayesian networks (BNs) learned from SCT data can elucidate directed regulatory relationships representing complex disease mechanisms and their interplay through graphical modeling. However, software for learning BNs from SCT data is not widely available, nor is software for evaluating the BNs' structural accuracy in representing causal relationships between genes. Here, we describe the scstruc R package. This package provides a suite of BN structure learning algorithms specifically designed to handle SCT data, to evaluate the resulting networks based on the causal relationships they represent regardless of the availability of established molecular interaction networks, and to compare regulatory relationships between conditions. We demonstrated that scstruc can identify biologically relevant differential regulatory relationships between groups on a per-cell basis.

Bayesian networks↗

PubMed2006

Reconstructing the evolutionary history of polyploids from multilabeled trees.

In recent studies, phylogenetic networks have been derived from so-called multilabeled trees in order to understand the origins of certain polyploids. Although the trees used in these studies were constructed using sophisticated techniques in phylogenetic analysis, the presented networks were inferred using ad hoc arguments that cannot be easily extended to larger, more complicated examples. In this paper, we present a general method for constructing such networks, which takes as input a multilabeled phylogenetic tree and outputs a phylogenetic network with certain desirable properties. To illustrate the applicability of our method, we discuss its use in reconstructing the evolutionary history of plant allopolyploids. We conclude with a discussion concerning possible future directions. The network construction method has been implemented and is freely available for use from http://www.uea.ac.uk/ approximately a043878/padre.html.

Algorithms↗

PubMed2005

A causal inference approach for constructing transcriptional regulatory networks.

MOTIVATION: Transcriptional regulatory networks specify the interactions among regulatory genes and between regulatory genes and their target genes. Discovering transcriptional regulatory networks helps us to understand the underlying mechanism of complex cellular processes and responses. METHOD: This paper describes a causal inference approach for constructing transcriptional regulatory networks using gene expression data, promoter sequences and information on transcription factor (TF) binding sites. The method first identifies active TFs in each individual experiment using a feature selection approach. TFs are viewed as "treatments" and gene expression levels as "responses". For every TF and gene pair, a marginal structural model is built to estimate the causal effect of the TF on the expression level of the gene. The model parameters can be estimated using the G-computation procedure or the IPTW estimator. The P-value associated with the causal parameter in each of these models is used to measure how strongly a TF regulates a gene. These results are further used to infer the overall regulatory network structures. RESULTS: Our analysis of yeast data suggests that the method is capable of identifying significant transcriptional regulatory interactions and the corresponding regulatory networks. AVAILABILITY: The software is under development.

Algorithms↗

PubMed2002

A duplication growth model of gene expression networks.

MOTIVATION: There has been considerable interest in developing computational techniques for inferring genetic regulatory networks from whole-genome expression profiles. When expression time series data sets are available, dynamic models can, in principle, be used to infer correlative relationships between gene expression levels, which may be causal. However, because of the range of detectable expression levels and the current quality of the data, the predictive nature of such inferred, quantitative models is questionable. Network models derived from simple rate laws offer an intermediate level analysis, going beyond simple statistical analysis, but falling short of a fully quantitative description. This work shows how such network models can be constructed and describes the global properties of the networks derived from such a model. These global properties are statistically robust and provide insights into the design of the underlying network. RESULTS: Several whole-genome expression time series data sets from yeast microarray experiments were analyzed using a Markov-modeling method (Dewey and Galas, FUNC: Integr. Genomics, 1, 269-278, 2001) to infer an approximation to the underlying genetic network. We found that the global statistical properties of all the resulting networks are similar. The overall structure of these biological networks is distinctly different from that of other recently studied networks such as the Internet or social networks. These biological networks show hierarchical, hub-like structures that have some properties similar to a class of graphs known as small world graphs. Small world networks exhibit local cliquishness while exhibiting strong global connectivity. In addition to the small world properties, the biological networks show a power law or scale free distribution of connectivities. An inverse power law, N(k) approximately k(-3/2), for the number of vertices (genes) with k connections was observed for three different data sets from yeast. We propose network growth models based on gene duplication events. Simulations of these models yield networks with the same combination of global graphical properties that we inferred from the expression data.

Algorithms↗

PubMed2002

Quantifying gene networks with regulatory strengths.

A gene network is the collection of regulatory relationships between all genes in a genome. Gene networks are high-level descriptions of cellular biochemistry and show the phenomenological interactions between gene activities. These interactions are mediated by proteins and metabolites. In the gene network approach, only the transcriptome is considered and all biochemistry underlying gene-gene interactions is only implicitly present. In a previous work, we presented a method for inferring gene networks from experimental data, quantifying gene-gene interactions with regulatory strengths. Here, we show how to express these regulatory strengths in terms of properties of the whole biochemical network.

Gene Expression Profiling↗

PubMed2005

Haplotype structure and phylogenetic shadowing of a hypervariable region in the CAPN10 gene.

It has been proposed that variation in calpain 10 (CAPN10) contributes to the risk of type 2 diabetes (T2D). A previous survey of CAPN10 in ethnically diverse populations revealed an intronic region with a significant excess of polymorphism levels relative to inter-species sequence divergence, suggesting that this region was the target of long-standing balancing selection. Based on the thrifty genotype hypothesis, variation that increases risk to T2D in contemporary humans at one time conferred a survival advantage in ancestral populations. Thus, the signature of positive natural selection in a T2D candidate gene could identify a genomic region containing variation that influences disease susceptibility. Here, we investigate this hypothesis by re-sequencing the CAPN10 region with unusual polymorphism levels in T2D cases and controls (n=91) from a Mexican American (MA) population, and by using networks to infer the evolutionary relationships between the major haplotypes. Haplotype tag SNPs (htSNPs) were then selected in each population sample and in MA cases and controls. By placing the htSNPs on the haplotype network, we investigate how cross-population differences in CAPN10 genetic architecture may affect the detection of the disease association. Interestingly, despite the small scale of our case-control study, we observe a nearly significant signal of association between T2D and variation in the putative target of balancing selection. Finally, we use phylogenetic shadowing across 10 primate species to search for conserved non-coding elements that may affect the expression and function of CAPN10. These elements are postulated to be the targets of long-standing balancing selection.

Animals↗

PubMed2004

Finding optimal models for small gene networks.

Finding gene networks from microarray data has been one focus of research in recent years. Given search spaces of super-exponential size, researchers have been applying heuristic approaches like greedy algorithms or simulated annealing to infer such networks. However, the accuracy of heuristics is uncertain, which--in combination with the high measurement noise of microarrays--makes it very difficult to draw conclusions from networks estimated by heuristics. We present a method that finds optimal Bayesian networks of considerable size and show first results of the application to yeast data. Having removed the uncertainty due to the heuristic methods, it becomes possible to evaluate the power of different statistical models to find biologically accurate networks.

Algorithms↗