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Title: Stratified Random Sampling over Streaming and Stored Data
Stratified random sampling (SRS) is a widely used sampling technique for approximate query processing. We consider SRS on continuously arriving data streams, and make the following contributions. We present a lower bound that shows that any streaming algorithm for SRS must have (in the worst case) a variance that is Ω(r) factor away from the optimal, where r is the number of strata. We present S-VOILA, a streaming algorithm for SRS that is locally variance-optimal. Results from experiments on real and synthetic data show that S-VOILA results in a variance that is typically close to an optimal offline algorithm, which was given the entire input beforehand. We also present a variance-optimal offline algorithm VOILA for stratified random sampling. VOILA is a strict generalization of the well-known Neyman allocation, which is optimal only under the assumption that each stratum is abundant, i.e. has a large number of data points to choose from. Experiments show that VOILA can have significantly smaller variance (1.4x to 50x) than Neyman allocation on real-world data.
Authors:
; ; ; ;
Award ID(s):
1725702 1527541
Publication Date:
NSF-PAR ID:
10110905
Journal Name:
Advances in Database Technology - 22nd International Conference on Extending Database Technology (EDBT)
Page Range or eLocation-ID:
25-36
Sponsoring Org:
National Science Foundation
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    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 EEGmore »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. 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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. 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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.« less
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  4. Summary Sequential Monte Carlo algorithms are widely accepted as powerful computational tools for making inference with dynamical systems. A key step in sequential Monte Carlo is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been used in practice, including multinomial resampling, residual resampling, optimal resampling, stratified resampling and optimal transport resampling. In one-dimensional cases, we show that optimal transport resampling is equivalent to stratified resampling on the sorted particles, and both strategies minimize the resampling variance as well as the expected squared energy distance between the original and resampled empirical distributions. For general $d$-dimensional cases, we show that if the particles are first sorted using the Hilbert curve, the variance of stratified resampling is $O(m^{-(1+2/d)})$, an improvement over the best previously known rate of $O(m^{-(1+1/d)})$, where $m$ is the number of resampled particles. We show that this improved rate is optimal for ordered stratified resampling schemes, as conjectured in Gerber et al. (2019). We also present an almost-sure bound on the Wasserstein distance between the original and Hilbert-curve-resampled empirical distributions. In light of these results, we show that for dimension $d>1$ the mean square error of sequential quasi-Monte Carlo with $n$ particlesmore »can be $O(n^{-1-4/\{d(d+4)\}})$ if Hilbert curve resampling is used and a specific low-discrepancy set is chosen. To our knowledge, this is the first known convergence rate lower than $o(n^{-1})$.« less
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Participants completed a set of individual questionnaires related to science reasoning skills and attitudes toward science prior to watching a 45-minute mock armed-robbery trial. The trial included various pieces of evidence and testimony, including forensic experts testifying about mitochondrial DNA evidence (mtDNA; based on Hans et al. 2011 materials). Participants were then given 45 minutes to deliberate. The deliberations were video recorded and transcribed to text for analysis. We analyzed the deliberation content for discussions related to the scientific evidence presented during trial. We hypothesized that those with stronger scientific and numeric reasoning skills, higher need for cognition, and more positive views towards science would discuss scientific evidence more than their counterparts during deliberation. 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We used word count to operationalize the extent to which each juror discussed scientific information. First we calculated the total word count for each complete jury deliberation transcript. Based on the above coding scheme we determined the number of words each juror spent discussing scientific information. To compare across juries, we wanted to account for the differing length of deliberation; thus, we calculated each juror’s scientific deliberation word count as a proportion of their jury’s total word count. Results On average, jurors discussed the science for about 4% of their total deliberation (SD=4%, range 0-22%). We regressed proportion of the deliberation jurors spend discussing scientific information on the four individual difference measures (i.e., SRS, NFC, WNS, ATS). Using the adjusted R-squared, the measures significantly accounted for 5.5% of the variability in scientific information deliberation discussion, SE=0.04, F(4, 199)=3.93, p=0.004. When controlling for all other variables in the model, the Scientific Reasoning Scale was the only measure that remained significant, b=0.003, SE=0.001, t(203)=2.02, p=0.045. To analyze how much variability each measure accounted for, we performed a stepwise regression, with NFC entered at step 1, ATS entered at step 2, WNS entered at step 3, and SRS entered at step 4. At step 1, NFC accounted for 2.4% of the variability, F(1, 202)=5.95, p=0.02. At step 2, ATS did not significantly account for any additional variability. At step 3, WNS accounted for an additional 2.4% of variability, ΔF(1, 200)=5.02, p=0.03. Finally, at step 4, SRS significantly accounted for an additional 1.9% of variability in scientific information discussion, ΔF(1, 199)=4.06, p=0.045, total adjusted R-squared of 0.055. Discussion This study provides additional support for previous findings that scientific reasoning skills affect the way jurors comprehend and use scientific evidence. It expands on previous findings by suggesting that these individual differences also impact the way scientific evidence is discussed during juror deliberations. In addition, this study advances the literature by identifying Scientific Reasoning Skills as a potentially more robust explanatory individual differences variable than more well-studied constructs like Need for Cognition in jury research. Our next steps for this research, which we plan to present at AP-LS as part of this presentation, incudes further analysis of the deliberation content (e.g., not just the mention of, but the accuracy of the references to scientific evidence in discussion). We are currently coding this data with a software program called Noldus Observer XT, which will allow us to present more sophisticated results from this data during the presentation. Learning Objective: Participants will be able to describe how individual differences in scientific reasoning skills affect how much jurors discuss scientific evidence during deliberation.« less