Optimization of model independent gravitational wave search using machine learning

The detection of the first gravitational wave (GW) signal GW150914 [1] commenced the age of the GW astronomy. Since then, the Advanced LIGO [2] and Advanced Virgo [3] network of detectors have identified 11 GW candidates during the first two observing runs (O1 and O2) [4], 40 GW candidates in the first half of the third observing run (O3a) [5], and provided 20 GW public alerts to EM astronomers during the second half of the third observing run (O3b) [6]. With the improving sensitivity of the GW detector network, it is essential to refine the search algorithms used to detect GW signals.

Coherent WaveBurst (cWB) is an algorithm that searches for excess power in the time-frequency domain to identify GW signals in the LIGO-Virgo strain data [7, 8]. Unlike other analysis pipelines which search for binary black hole (BBH) mergers, cWB does not use template waveform models. Instead, the cWB algorithm is model independent, which makes it a valuable tool in the search for poorly modeled or unexpected GW sources. cWB played an integral role in the discovery of the first BBH merger GW150914 [1] and, more recently, in the first direct detection of an intermediate mass black hole (IMBH) GW190521 [9, 10]. Also, cWB has contributed to the detection of 22 BBH events in the O1, O2, and O3a observing runs [4, 5].

The cWB pipeline generates summary statistics for every identified event. These summary statistics describe generic properties of reconstructed events such as the characteristic frequency, duration, cross-correlation between different detectors, and other parameters described in Appendix A. In the standard cWB search framework, we use summary statistics to construct vetoes designed to reject noise events from the analysis and increase the significance of detected GW events. Although this veto procedure generally works well, it risks the removal of GW signal events that lie near the border of the predefined veto thresholds. In addition, designing vetoes is challenging since they need to be redefined for each detector network and are dependent on the run conditions.

Machine learning (ML) offers a novel approach to solving complex problems. Accordingly, the interest of ML techniques in GW astronomy has grown in recent years [11] as ML has been applied to categorize noise artifacts in the GW detector strain data [12, 13, 14], classify GW signals [15, 16], and estimate GW source parameters [17, 18]. ML has already been used in combination with cWB for various other studies [19, 20, 21, 22].

In this paper, we propose to use a decision tree based ensemble learning algorithm called eXtreme-Gradient Boost (XGBoost) [23] to automate the signal-noise classification in cWB and optimize the pipeline sensitivity to BBH mergers. To preserve the waveform independent analysis, we do not attempt to train the ML model directly on the GW strain data. Instead, we utilize cWB to reconstruct events and generate their summary statistics, and then we carefully select a subset of summary statistics used for the construction of the ML model. The end result is the ML-enhanced search pipeline which is resistant to overfitting and provides the robust recovery of GW events with the waveform parameters that could be outside of the training set. We test the cWB pipeline enhanced with XGBoost on publicly available LIGO Hanford and LIGO Livingston strain data from O1 and O2 [24].

The paper is organized as follows. In Section II, we introduce the cWB search pipeline. In Section III, we describe the data used to train and test our ML algorithm. In Section IV, we demonstrate the implementation of ML into the detection procedure and define our new cWB reduced detection statistic. In Section V, we compare the sensitivity of the ML-enhanced cWB search against the sensitivity of the standard cWB search. We report the updated significance of BBH events detected during the O1 and O2 observing runs. Finally, in Section VI, we state the conclusions of our study.

The cWB search algorithm is designed to detect GW signals with minimal assumptions on the signal model [25, 8]. The detector strain data is mapped to the time-frequency domain using the Wilson Daubechies Meyer (WDM) wavelet transform [26] where the data is normalized by the rms of the detector noise. The algorithm then identifies WDM wavelets with excess power above the average fluctuations of the detector noise. The selected nearby wavelets are grouped into clusters. The pipeline generates an event for each selected cluster and reconstructs the signal waveform using the constrained maximum likelihood method [8].

For each event, various summary statistics are estimated by the pipeline which describes the time-frequency structure, signal strength, and coherence across the detector network. The main detection statistic for the cWB generic GW search is the signal-to-noise ratio (SNR) defined for the LIGO detector network as:

Here, $E_{\mathrm{c}}$ denotes the coherent energy estimated by cross-correlating the reconstructed signal waveforms across different detectors, and $\chi^{2}=E_{\mathrm{n}}/N_{\mathrm{df}}$ where $E_{\mathrm{n}}$ is the estimated residual noise energy and $N_{\mathrm{df}}$ is the the number of independent wavelet amplitudes describing the event. The $\chi^{2}$ correction in Equation 1, which is close to unity for genuine GW events, reduces the non-Gaussian noise contribution. For the cWB searches which target BBH events, the detection statistic is modified to favor events which frequency is increasing with time:

where $F_{\mathrm{M}}$ is the event energy fraction and $e_{M}$ is the event ellipticity defined in Ref. [27]. Both parameters $F_{\mathrm{M}}$ and $e_{M}$ are close to unity for BBH events and penalize events which time-frequency evolution is significantly different from the chirping BBH signal.

GW detector data is hindered by noise artifacts known as glitches, and consequently, some noise events are reconstructed by the pipeline and leak into the analysis. In the standard cWB analysis, we apply a series of vetoes to target and remove these glitches. This approach, henceforth known as the veto method, improves the significance of candidate GW events by reducing excess background. The veto method consists of applying a priori defined veto thresholds on a set of the cWB summary statistics. This procedure discretely classifies generated events into one of the two categories: signal-like events and noise-like events. Events that fall into the noise-like category are removed from the analysis. This process could inevitably result in discarding borderline GW events which do not pass the veto thresholds and at the same time makes the pipeline vulnerable to the high SNR glitches which do pass the vetoes. Designing vetoes in the multidimensional space of the summary statistics is challenging, and furthermore, requires re-tuning of the veto thresholds for each detector network configuration and each observing run.

In the standard cWB setup, the veto method is tuned separately to improve the search sensitivity to stellar-mass BBH mergers ($M_{\mathrm{tot}}\lesssim 100\,M_{\odot}$) and IMBH binary mergers ($M_{\mathrm{tot}}\gtrsim 100\,M_{\odot}$). While the GW waveforms of these two classes are conceptually similar, the corresponding GW signals observed in the LIGO frequency band are quite different. A GW signal originating from the stellar-mass BBH merger usually exhibits the full inspiral-merger-ringdown waveform, whereas GW signals from IMBH binary mergers are short in duration and contain mostly the merger-ringdown waveform, with the inspiral signal buried inside the low-frequency seismic noise. As a result, we utilize two configurations of the cWB search tuned for these systems: the BBH configuration which targets stellar-mass BBH mergers, and the IMBH configuration which targets IMBH binary mergers [10]. IMBH binaries are expected to merge at lower frequencies compared to the stellar-mass BBH mergers, and so the corresponding cWB search configurations apply different vetoes to account for the difference in the signal morphology.

We analyze publicly available strain data from Advanced LIGO’s first two observational runs [24]. Here, we only examine data from the LIGO Hanford and LIGO Livingston detectors, with the inclusion of Virgo data left for future work. To train and test our ML model, we require a representative set of noise events and signal events.

Noise events (background) are generated by systematically time-shifting the data from one detector with respect to other detectors in the detector network. Each time shift is chosen to be greater than the time of flight between detectors to exclude true astrophysical signals. This process is repeated multiple times for various time lags, and we count the number of background events generated over the total accumulated background time. For the O1 run, we accumulated approximately 16,000 years and 4,000 years of the background time for the BBH and IMBH searches, respectively. For the O2 run, we accumulated approximately 11,000 years of background for each search.

To generate a representative set of the signal events, we add (inject) simulated GW signals to the detector data and reconstruct them with cWB. In this work, we investigate four sets of simulated signals: (i) a quasi-circular spin-aligned stellar-mass BBH set, (ii) a quasi-circular IMBH binary set, (iii) an eccentric BBH set, and (iv) a quasi-circular precessing BBH set. Only the first two simulation sets of the quasi-circular signals were used for ML training, whereas the remaining two sets are used to test the robustness of the ML implementation. In all four cases, the binary orientation parameters (sky location, inclination angle) for every simulated waveform are randomly drawn from uniform distributions. The redshift $z$ is drawn from a uniform distribution in co-moving volume, assuming Planck 2015 cosmology [28].

To simulate the stellar-mass BBH set, we use the SEOBNRv3 [29] and SEOBNRv4 [30] waveform approximants. These waveform approximants include only the dominant ($\ell=2,m=2$) harmonic mode. The source frame total mass for these simulations ranges from approximately $5\,M_{\odot}$ to $100\,M_{\odot}$, and the mass ratio $q=m_{2}/m_{1}$ ranges from approximately 1/4 to 1. Component black hole spins are aligned with the orbital plane.

For the IMBH binary set, we use numerical relativity waveforms which include higher-order harmonics. We consider 17 massbins, as used in Ref. [31], which range in source frame total mass from $120\,M_{\odot}$ to $800\,M_{\odot}$, with mass ratios ranging from 1 to 1/10.

For the high mass, eccentric BBH set, we also use numerical relativity waveforms [32, 33]. We consider 28 massbins which range in total mass from $100\,M_{\odot}$ to $250\,M_{\odot}$, mass ratio equal to 1, with eccentricities ranging from 0.66 to 0.99.

For the precessing stellar-mass BBH set, we use the SEOBNRv4PHM [34] waveform approximant, which includes precession and higher-order harmonic modes. The source frame total mass ranges from $4\,M_{\odot}$ to $200\,M_{\odot}$, with mass ratios ranging from 1 to 1/20. Component black hole spins are isotropically distributed.

The veto method used in the standard cWB search categorizes events into two discrete bins: signal events and noise events. Here, the veto method effectively acts as a decision tree with only two leaves, where the summary statistics for a given event are compared against various rules at each decision node until the event is classified as either a signal event or a noise event. Since this method produces a discrete outcome, it unavoidably removes signal events which do not pass all veto thresholds.

We propose using ML, which produces continuous ranking criteria for all reconstructed events, to replace the veto method. Binary classification is a standard problem in the ML literature. Moreover, many prominent ML algorithms are based on the decision tree structure, which we expect is well suited for the cWB classification problem.

We use the boosted decision tree based ML algorithm called XGBoost [23]. In XGBoost, instead of using a single decision tree to classify events, an ensemble of decision trees is generated. A decision tree is used as the base learner, and subsequent learners (trees) are formed based on the residual errors obtained after each iteration (boosting). This process is expected to be more accurate and more robust than using a single decision tree used by the veto method. A continuous score is calculated by taking the weighted average of output, obtained from each decision tree in the ensemble. The final output $P_{\mathrm{XGB}}$ is computed by taking the sigmoid of the continuous score, where a value close to zero denotes a noise-like event and a value close to one denotes a signal-like event.

To construct the ML model, we select a subset of 14 summary statistics estimated by cWB as input features for the ML algorithm. Selected summary statistics describe the signal strength and the correlation across the detectors ($\eta_{\mathrm{0}}$, $c_{\mathrm{c}}$, $n_{\mathrm{f}}$), the quality of the likelihood fit ($E_{\mathrm{c}}/L$, $\chi^{2}$), the time-frequency evolution of the event ($\Delta T_{\mathrm{s}}$, $\Delta F_{\mathrm{s}}$, $f_{0}$, $\mathcal{M}$, $e_{\mathrm{M}}$) and the two different estimators for the number of cycles in the reconstructed waveform ($Q_{\mathrm{a}}$, $Q_{\mathrm{p}}$). The detailed list of selected summary statistics and their definitions can be found in Appendix A.

In this section, we present the results of the ML-enhanced cWB search and compare its sensitivity to the standard cWB search. The significance of a given candidate event is estimated by its false alarm rate (FAR). It is computed by counting the number of background events with the equal or higher value of the detection statistic than for the candidate event, divided by the total background time.

For the ML-enhanced cWB search, FAR is calculated by using the reduced detection statistic $\eta_{\mathrm{r}}$ (Equation 3). Whereas for the standard cWB BBH search, we first remove vetoed events and then calculate FAR by using the $\eta_{\mathrm{1}}$ detection statistic (Equation 2). We compare the performance of the different cWB searches by comparing their detection efficiency defined as the number of detected simulated events with FAR equal to or less than a given threshold, divided by the total number of recovered simulation events.

In conclusion, we introduce a novel method to automate the noise rejection in cWB with ML, and we demonstrate that the ML-enhanced cWB search has improved sensitivity to the BBH mergers. Unlike the standard cWB search, which decimates noise events with the veto method, the ML-enhanced search uses a continuous ranking statistic and does not remove any events. Instead, it penalizes noise events with the newly designed detection statistic $\eta_{\mathrm{r}}$, which combines the correlated network SNR with the penalty factor based on the signal-noise classification provided by the XGBoost model. This new detection statistic $\eta_{\mathrm{r}}$ is resistant to loud noise glitches and allows cWB identification of BBH events with higher significance.

For the stellar-mass BBH mergers, the detection efficiency of the ML-enhanced cWB search is improved by 26% compared to the standard cWB search (at FAR less than $1\,\mathrm{yr}^{-1}$). Similarly, for the simulation set of IMBH binary mergers, the detection efficiency is improved by 16%. While we do not claim any new BBH detections in the O1 and O2 data, we do improve the detection confidence of the previously identified GW candidates and recovered the GW170809 event missed by the standard cWB search.

The ML-enhanced cWB search is capable of detecting BBH signals well outside of the training set. We demonstrate the improved pipeline sensitivity to the highly eccentric BBH mergers despite only being trained on the quasi-circular IMBH signals. We also found the search to be agnostic to other binary waveform properties including precession, high mass ratio, and higher-order harmonic modes. Waveforms with similar time-frequency morphology, but not predicted by general relativity should also be detectable.

The ML-enhanced BBH search is a promising addition to the cWB pipeline for future planned observing runs, where we expect numerous BBH detections. While in this study, we use only the LIGO Hanford and LIGO Livingston detector network, in future work we will expand the ML-enhanced search to the other detector networks which include Virgo and Kagra detectors. This will further improve the cWB sensitivity to the BBH mergers. The ML-enhanced pipeline could be also used for the low latency cWB searches in the future observing runs.