skip to main content


Title: Variational Approximation based Model Selection for Microbial Network Inference
Microbial associations are characterized by both direct and indirect interactions between the constituent taxa in a microbial community, and play an important role in determining the structure, organization, and function of the community. Microbial associations can be represented using a weighted graph (microbial network) whose nodes represent taxa and edges represent pairwise associations. A microbial network is typically inferred from a sample-taxa matrix that is obtained by sequencing multiple biological samples and identifying the taxa counts in each sample. However, it is known that microbial associations are impacted by environmental and/or host factors. Thus, a sample-taxa matrix generated in a microbiome study involving a wide range of values for the environmental and/or clinical metadata variables may in fact be associated with more than one microbial network. Here we consider the problem of inferring multiple microbial networks from a given sample-taxa count matrix. Each sample is a count vector assumed to be generated by a mixture model consisting of component distributions that are Multivariate Poisson Log-Normal. We present a variational Expectation Maximization algorithm for the model selection problem to infer the correct number of components of this mixture model. Our approach involves reframing the mixture model as a latent variable model, treating only the mixing coefficients as parameters, and subsequently approximating the marginal likelihood using an evidence lower bound framework. Our algorithm is evaluated on a large simulated dataset generated using a collection of different graph structures (band, hub, cluster, random, and scale-free).  more » « less
Award ID(s):
2051283
NSF-PAR ID:
10323782
Author(s) / Creator(s):
;
Editor(s):
Singh, Mona
Date Published:
Journal Name:
Journal of computational biology
ISSN:
1066-5277
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ABSTRACT Host-associated microbial communities are shaped by extrinsic and intrinsic factors to the holobiont organism. Environmental factors and microbe-microbe interactions act simultaneously on the microbial community structure, making the microbiome dynamics challenging to predict. The coral microbiome is essential to the health of coral reefs and sensitive to environmental changes. Here, we develop a dynamic model to determine the microbial community structure associated with the surface mucus layer (SML) of corals using temperature as an extrinsic factor and microbial network as an intrinsic factor. The model was validated by comparing the predicted relative abundances of microbial taxa to the relative abundances of microbial taxa from the sample data. The SML microbiome from Pseudodiploria strigosa was collected across reef zones in Bermuda, where inner and outer reefs are exposed to distinct thermal profiles. A shotgun metagenomics approach was used to describe the taxonomic composition and the microbial network of the coral SML microbiome. By simulating the annual temperature fluctuations at each reef zone, the model output is statistically identical to the observed data. The model was further applied to six scenarios that combined different profiles of temperature and microbial network to investigate the influence of each of these two factors on the model accuracy. The SML microbiome was best predicted by model scenarios with the temperature profile that was closest to the local thermal environment, regardless of the microbial network profile. Our model shows that the SML microbiome of P. strigosa in Bermuda is primarily structured by seasonal fluctuations in temperature at a reef scale, while the microbial network is a secondary driver. IMPORTANCE Coral microbiome dysbiosis (i.e., shifts in the microbial community structure or complete loss of microbial symbionts) caused by environmental changes is a key player in the decline of coral health worldwide. Multiple factors in the water column and the surrounding biological community influence the dynamics of the coral microbiome. However, by including only temperature as an external factor, our model proved to be successful in describing the microbial community associated with the surface mucus layer (SML) of the coral P. strigosa . The dynamic model developed and validated in this study is a potential tool to predict the coral microbiome under different temperature conditions. 
    more » « less
  2. Summary

    An important problem in modern forensic analyses is identifying the provenance of materials at a crime scene, such as biological material on a piece of clothing. This procedure, which is known as geolocation, is conventionally guided by expert knowledge of the biological evidence and therefore tends to be application specific, labour intensive and often subjective. Purely data-driven methods have yet to be fully realized in this domain, because in part of the lack of a sufficiently rich source of data. However, high throughput sequencing technologies can identify tens of thousands of fungi and bacteria taxa by using DNA recovered from a single swab collected from nearly any object or surface. This microbial community, or microbiome, may be highly informative of the provenance of the sample, but data on the spatial variation of microbiomes are sparse and high dimensional and have a complex dependence structure that render them difficult to model with standard statistical tools. Deep learning algorithms have generated a tremendous amount of interest within the machine learning community for their predictive performance in high dimensional problems. We present DeepSpace: a new algorithm for geolocation that aggregates over an ensemble of deep neural network classifiers trained on randomly generated Voronoi partitions of a spatial domain. The DeepSpace algorithm makes remarkably good point predictions; for example, when applied to the microbiomes of over 1300 dust samples collected across continental USA, more than half of geolocation predictions produced by this model fall less than 100 km from their true origin, which is a 60% reduction in error from competing geolocation methods. Moreover, we apply DeepSpace to a novel data set of global dust samples collected from nearly 30 countries, finding that dust-associated fungi alone predict a sample's country of origin with nearly 90% accuracy.

     
    more » « less
  3. Obeid, Iyad Selesnick (Ed.)
    Electroencephalography (EEG) is a popular clinical monitoring tool used for diagnosing brain-related disorders such as epilepsy [1]. As monitoring EEGs in a critical-care setting is an expensive and tedious task, there is a great interest in developing real-time EEG monitoring tools to improve patient care quality and efficiency [2]. However, clinicians require automatic seizure detection tools that provide decisions with at least 75% sensitivity and less than 1 false alarm (FA) per 24 hours [3]. Some commercial tools recently claim to reach such performance levels, including the Olympic Brainz Monitor [4] and Persyst 14 [5]. In this abstract, we describe our efforts to transform a high-performance offline seizure detection system [3] into a low latency real-time or online seizure detection system. An overview of the system is shown in Figure 1. The main difference between an online versus offline system is that an online system should always be causal and has minimum latency which is often defined by domain experts. The offline system, shown in Figure 2, uses two phases of deep learning models with postprocessing [3]. The channel-based long short term memory (LSTM) model (Phase 1 or P1) processes linear frequency cepstral coefficients (LFCC) [6] features from each EEG channel separately. We use the hypotheses generated by the P1 model and create additional features that carry information about the detected events and their confidence. The P2 model uses these additional features and the LFCC features to learn the temporal and spatial aspects of the EEG signals using a hybrid convolutional neural network (CNN) and LSTM model. Finally, Phase 3 aggregates the results from both P1 and P2 before applying a final postprocessing step. The online system implements Phase 1 by taking advantage of the Linux piping mechanism, multithreading techniques, and multi-core processors. To convert Phase 1 into an online system, we divide the system into five major modules: signal preprocessor, feature extractor, event decoder, postprocessor, and visualizer. The system reads 0.1-second frames from each EEG channel and sends them to the feature extractor and the visualizer. The feature extractor generates LFCC features in real time from the streaming EEG signal. Next, the system computes seizure and background probabilities using a channel-based LSTM model and applies a postprocessor to aggregate the detected events across channels. The system then displays the EEG signal and the decisions simultaneously using a visualization module. The online system uses C++, Python, TensorFlow, and PyQtGraph in its implementation. The online system accepts streamed EEG data sampled at 250 Hz as input. The system begins processing the EEG signal by applying a TCP montage [8]. Depending on the type of the montage, the EEG signal can have either 22 or 20 channels. To enable the online operation, we send 0.1-second (25 samples) length frames from each channel of the streamed EEG signal to the feature extractor and the visualizer. Feature extraction is performed sequentially on each channel. The signal preprocessor writes the sample frames into two streams to facilitate these modules. In the first stream, the feature extractor receives the signals using stdin. In parallel, as a second stream, the visualizer shares a user-defined file with the signal preprocessor. This user-defined file holds raw signal information as a buffer for the visualizer. The signal preprocessor writes into the file while the visualizer reads from it. Reading and writing into the same file poses a challenge. The visualizer can start reading while the signal preprocessor is writing into it. To resolve this issue, we utilize a file locking mechanism in the signal preprocessor and visualizer. Each of the processes temporarily locks the file, performs its operation, releases the lock, and tries to obtain the lock after a waiting period. The file locking mechanism ensures that only one process can access the file by prohibiting other processes from reading or writing while one process is modifying the file [9]. The feature extractor uses circular buffers to save 0.3 seconds or 75 samples from each channel for extracting 0.2-second or 50-sample long center-aligned windows. The module generates 8 absolute LFCC features where the zeroth cepstral coefficient is replaced by a temporal domain energy term. For extracting the rest of the features, three pipelines are used. The differential energy feature is calculated in a 0.9-second absolute feature window with a frame size of 0.1 seconds. The difference between the maximum and minimum temporal energy terms is calculated in this range. Then, the first derivative or the delta features are calculated using another 0.9-second window. Finally, the second derivative or delta-delta features are calculated using a 0.3-second window [6]. The differential energy for the delta-delta features is not included. In total, we extract 26 features from the raw sample windows which add 1.1 seconds of delay to the system. We used the Temple University Hospital Seizure Database (TUSZ) v1.2.1 for developing the online system [10]. The statistics for this dataset are shown in Table 1. A channel-based LSTM model was trained using the features derived from the train set using the online feature extractor module. A window-based normalization technique was applied to those features. In the offline model, we scale features by normalizing using the maximum absolute value of a channel [11] before applying a sliding window approach. Since the online system has access to a limited amount of data, we normalize based on the observed window. The model uses the feature vectors with a frame size of 1 second and a window size of 7 seconds. We evaluated the model using the offline P1 postprocessor to determine the efficacy of the delayed features and the window-based normalization technique. As shown by the results of experiments 1 and 4 in Table 2, these changes give us a comparable performance to the offline model. The online event decoder module utilizes this trained model for computing probabilities for the seizure and background classes. These posteriors are then postprocessed to remove spurious detections. The online postprocessor receives and saves 8 seconds of class posteriors in a buffer for further processing. It applies multiple heuristic filters (e.g., probability threshold) to make an overall decision by combining events across the channels. These filters evaluate the average confidence, the duration of a seizure, and the channels where the seizures were observed. The postprocessor delivers the label and confidence to the visualizer. The visualizer starts to display the signal as soon as it gets access to the signal file, as shown in Figure 1 using the “Signal File” and “Visualizer” blocks. Once the visualizer receives the label and confidence for the latest epoch from the postprocessor, it overlays the decision and color codes that epoch. The visualizer uses red for seizure with the label SEIZ and green for the background class with the label BCKG. Once the streaming finishes, the system saves three files: a signal file in which the sample frames are saved in the order they were streamed, a time segmented event (TSE) file with the overall decisions and confidences, and a hypotheses (HYP) file that saves the label and confidence for each epoch. The user can plot the signal and decisions using the signal and HYP files with only the visualizer by enabling appropriate options. For comparing the performance of different stages of development, we used the test set of TUSZ v1.2.1 database. It contains 1015 EEG records of varying duration. The any-overlap performance [12] of the overall system shown in Figure 2 is 40.29% sensitivity with 5.77 FAs per 24 hours. For comparison, the previous state-of-the-art model developed on this database performed at 30.71% sensitivity with 6.77 FAs per 24 hours [3]. The individual performances of the deep learning phases are as follows: Phase 1’s (P1) performance is 39.46% sensitivity and 11.62 FAs per 24 hours, and Phase 2 detects seizures with 41.16% sensitivity and 11.69 FAs per 24 hours. We trained an LSTM model with the delayed features and the window-based normalization technique for developing the online system. Using the offline decoder and postprocessor, the model performed at 36.23% sensitivity with 9.52 FAs per 24 hours. The trained model was then evaluated with the online modules. The current performance of the overall online system is 45.80% sensitivity with 28.14 FAs per 24 hours. Table 2 summarizes the performances of these systems. The performance of the online system deviates from the offline P1 model because the online postprocessor fails to combine the events as the seizure probability fluctuates during an event. The modules in the online system add a total of 11.1 seconds of delay for processing each second of the data, as shown in Figure 3. In practice, we also count the time for loading the model and starting the visualizer block. When we consider these facts, the system consumes 15 seconds to display the first hypothesis. The system detects seizure onsets with an average latency of 15 seconds. Implementing an automatic seizure detection model in real time is not trivial. We used a variety of techniques such as the file locking mechanism, multithreading, circular buffers, real-time event decoding, and signal-decision plotting to realize the system. A video demonstrating the system is available at: https://www.isip.piconepress.com/projects/nsf_pfi_tt/resources/videos/realtime_eeg_analysis/v2.5.1/video_2.5.1.mp4. The final conference submission will include a more detailed analysis of the online performance of each module. ACKNOWLEDGMENTS Research reported in this publication was most recently supported by the National Science Foundation Partnership for Innovation award number IIP-1827565 and the Pennsylvania Commonwealth Universal Research Enhancement Program (PA CURE). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the official views of any of these organizations. REFERENCES [1] A. Craik, Y. He, and J. L. Contreras-Vidal, “Deep learning for electroencephalogram (EEG) classification tasks: a review,” J. Neural Eng., vol. 16, no. 3, p. 031001, 2019. https://doi.org/10.1088/1741-2552/ab0ab5. [2] A. C. Bridi, T. Q. Louro, and R. C. L. Da Silva, “Clinical Alarms in intensive care: implications of alarm fatigue for the safety of patients,” Rev. Lat. Am. Enfermagem, vol. 22, no. 6, p. 1034, 2014. https://doi.org/10.1590/0104-1169.3488.2513. [3] M. Golmohammadi, V. Shah, I. Obeid, and J. Picone, “Deep Learning Approaches for Automatic Seizure Detection from Scalp Electroencephalograms,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York, New York, USA: Springer, 2020, pp. 233–274. https://doi.org/10.1007/978-3-030-36844-9_8. [4] “CFM Olympic Brainz Monitor.” [Online]. Available: https://newborncare.natus.com/products-services/newborn-care-products/newborn-brain-injury/cfm-olympic-brainz-monitor. [Accessed: 17-Jul-2020]. [5] M. L. Scheuer, S. B. Wilson, A. Antony, G. Ghearing, A. Urban, and A. I. Bagic, “Seizure Detection: Interreader Agreement and Detection Algorithm Assessments Using a Large Dataset,” J. Clin. Neurophysiol., 2020. https://doi.org/10.1097/WNP.0000000000000709. [6] A. Harati, M. Golmohammadi, S. Lopez, I. Obeid, and J. Picone, “Improved EEG Event Classification Using Differential Energy,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium, 2015, pp. 1–4. https://doi.org/10.1109/SPMB.2015.7405421. [7] V. Shah, C. Campbell, I. Obeid, and J. Picone, “Improved Spatio-Temporal Modeling in Automated Seizure Detection using Channel-Dependent Posteriors,” Neurocomputing, 2021. [8] W. Tatum, A. Husain, S. Benbadis, and P. Kaplan, Handbook of EEG Interpretation. New York City, New York, USA: Demos Medical Publishing, 2007. [9] D. P. Bovet and C. Marco, Understanding the Linux Kernel, 3rd ed. O’Reilly Media, Inc., 2005. https://www.oreilly.com/library/view/understanding-the-linux/0596005652/. [10] V. Shah et al., “The Temple University Hospital Seizure Detection Corpus,” Front. Neuroinform., vol. 12, pp. 1–6, 2018. https://doi.org/10.3389/fninf.2018.00083. [11] F. Pedregosa et al., “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011. https://dl.acm.org/doi/10.5555/1953048.2078195. [12] J. Gotman, D. Flanagan, J. Zhang, and B. Rosenblatt, “Automatic seizure detection in the newborn: Methods and initial evaluation,” Electroencephalogr. Clin. Neurophysiol., vol. 103, no. 3, pp. 356–362, 1997. https://doi.org/10.1016/S0013-4694(97)00003-9. 
    more » « less
  4. Summary

    Community detection in networks is a key exploratory tool with applications in a diverse set of areas, ranging from finding communities in social and biological networks to identifying link farms in the World Wide Web. The problem of finding communities or clusters in a network has received much attention from statistics, physics and computer science. However, most clustering algorithms assume knowledge of the number of clusters k. We propose to determine k automatically in a graph generated from a stochastic block model by using a hypothesis test of independent interest. Our main contribution is twofold; first, we theoretically establish the limiting distribution of the principal eigenvalue of the suitably centred and scaled adjacency matrix and use that distribution for our test of the hypothesis that a random graph is of Erdős–Rényi (noise) type. Secondly, we use this test to design a recursive bipartitioning algorithm, which naturally uncovers nested community structure. Using simulations and quantifiable classification tasks on real world networks with ground truth, we show that our algorithm outperforms state of the art methods.

     
    more » « less
  5. Abstract Motivation Droplet-based single-cell RNA-seq (dscRNA-seq) data are being generated at an unprecedented pace, and the accurate estimation of gene-level abundances for each cell is a crucial first step in most dscRNA-seq analyses. When pre-processing the raw dscRNA-seq data to generate a count matrix, care must be taken to account for the potentially large number of multi-mapping locations per read. The sparsity of dscRNA-seq data, and the strong 3’ sampling bias, makes it difficult to disambiguate cases where there is no uniquely mapping read to any of the candidate target genes. Results We introduce a Bayesian framework for information sharing across cells within a sample, or across multiple modalities of data using the same sample, to improve gene quantification estimates for dscRNA-seq data. We use an anchor-based approach to connect cells with similar gene-expression patterns, and learn informative, empirical priors which we provide to alevin’s gene multi-mapping resolution algorithm. This improves the quantification estimates for genes with no uniquely mapping reads (i.e. when there is no unique intra-cellular information). We show our new model improves the per cell gene-level estimates and provides a principled framework for information sharing across multiple modalities. We test our method on a combination of simulated and real datasets under various setups. Availability and implementation The information sharing model is included in alevin and is implemented in C++14. It is available as open-source software, under GPL v3, at https://github.com/COMBINE-lab/salmon as of version 1.1.0. 
    more » « less