Improving significance of binary black hole mergers in Advanced LIGO data using deep learning: Confirmation of GW151216

We present a novel machine learning (ML) based strategy to search for binary black hole (BBH) mergers in data from ground-based gravitational wave (GW) observatories. This is the first ML-based search that not only recovers all the compact binary coalescences (CBCs) in the first GW transients catalog (GWTC-1), but also makes a clean detection of GW151216, which was not significant enough to be included in the catalog. Moreover, we achieve this by only adding a new coincident ranking statistic (MLStat) to a standard analysis that was used for GWTC-1. In CBC searches, reducing contamination by terrestrial and instrumental transients, which create a loud noise background by triggering numerous false alarms, is crucial to improving the sensitivity for detecting true events. The sheer volume of data and a large number of expected detections also prompts the use of ML techniques. We perform transfer learning to train “InceptionV3,” a pretrained deep neural network, along with curriculum learning to distinguish GW signals from noisy events by analyzing their continuous wavelet transform (CWT) maps. MLStat incorporates information from this ML classifier into the coincident search likelihood used by the standard pycbc search. This leads to at least an order of magnitude improvement in the inverse false-alarm-rate (IFAR) for the previously “low significance” events GW151012, GW170729, and GW151216. We also perform the parameter estimation of GW151216 using seobnrv4hm_rom. We carry out an injection study to show that MLStat brings substantial improvement to the detection sensitivity of Advanced LIGO for all compact binary coalescences. The average improvement in the sensitive volume is $\sim 10\%$ for low chirp masses ($0.8–5{\mathrm{M}}_{\odot }$) and $\sim 30\%$ for higher masses ($5–50{\mathrm{M}}_{\odot }$). Performance in the lower masses may become even better if the training set for the ML classifier, currently restricted to black hole binaries with component masses in the range $2–98{\mathrm{M}}_{\odot }$ only, is expanded to include binaries with neutron stars. Considering the impressive ability of the statistic to distinguish signals from glitches, the list of marginal events from MLStat could be quite reliable for astrophysical population studies and further follow-up. This work demonstrates the immense potential and readiness of MLStat for finding new sources in current data and the possibility of its adaptation in similar searches.

Figure 1

Confusion matrix (in percent) for the combined validation data from all the levels of curriculum learning for 17 transient classes. The performance of CBC class is of particular importance to MLStat.

Figure 2

The receiver operating characteristic curves for different chirp mass bins obtained by comparing simulated injections against randomly chosen noise triggers from Hanford and Livingston data. Log scales are used to visualize the differences better. Masses for the noise triggers are taken from the respective templates triggering them. As some injections lie out of the training range, the performance in the $0.8–5{\mathrm{M}}_{\odot }$ chirp mass bin is suboptimal as compared to other bins.

Figure 3

Ratio of the sensitive volume-time (VT) estimates with MLStat and base statistic for different IFAR thresholds and four chirp mass bins obtained from the injection study is shown in the top panel. The bottom panel combines the higher mass bins to reduce the error bars, showing an average $\sim 10\%$ improvement in sensitive volume for low chirp masses ($<5{\mathrm{M}}_{\odot }$) and overall $\sim 30\%$ improvement for higher chirp masses.

Figure 4

Significance improvement for GW151012 (left) and GW170729 (right): Cumulative histograms of foreground events in base statistic (yellow) and MLStat (blue) along with the expected background plotted against the inverse false-alarm rate. Shaded regions show the sigma intervals for Poisson uncertainty. The loudness of first $\sim 20$ foreground events with MLStat in O2 is not a systematic bias and is rather an effect of the low number statistics which has been observed with other statistics before (see Fig. 2 and Fig. 3 in [9]). With MLStat, IFAR value of the most significant foreground event GW151012 (GW170729) improves from 5.84 (0.73) years to 218.1 (55.8) years. We also observed that the event sequence according to IFAR values was considerably shuffled in MLStat. The second most significant event viz., 151016, in O1 chunk has IFAR 0.21 years.

Figure 5

Significance improvement for GW151216: With MLStat, IFAR value of GW151216 improves from 0.0173 years to 1.453 years making it the most significant foreground event of the chunk.

Figure 6

Comparative search results with MLStat and base statistic for the chunk containing GW151216 (marked by star). Notice the reduced background and a better separated foreground with MLStat.

Figure 7

CWT maps of events that gain significance with MLStat. Whitened strain data of duration one second, bandpassed between 16 Hz and 512 Hz, is used to generate the grayscale images that are fed to the classifier.

Figure 8

Bayesian parameter estimation posteriors for the event GW151216 using seobnrv4hm_rom waveform model. We can clearly see the evidence for unequal masses with component masses of ${46.8}_{-17.7}^{+12.5}{\mathrm{M}}_{\odot }$ and ${23.6}_{-9.6}^{+5.6}{\mathrm{M}}_{\odot }$ and nonzero spin with ${\chi }_{\mathrm{eff}}$ of ${0.56}_{-0.5}^{+0.23}$ and luminosity distance of ${2269}_{-1033}^{+1193}\mathrm{Mpc}$. The corresponding sky localisation map is also overlaid.