Hierarchical Veto (hveto) Algorithm

• Hierarchical Veto (hveto) algorithm is a statistical, iterative procedure designed to identify and remove transient noise glitches from gravitational-wave data.
• It systematically applies veto configurations based on time-coincidence analyses with auxiliary channels, minimizing false alarms while preserving live observation time.
• Empirical results from LIGO and KAGRA indicate that hveto significantly enhances data quality by effectively suppressing glitches in burst-type gravitational-wave searches.

The Hierarchical Veto (hveto) algorithm is a statistical, iterative procedure designed for the identification and removal of non-Gaussian transient noise artifacts ("glitches") in the gravitational-wave (GW) strain data of interferometric detectors such as LIGO, Virgo, and KAGRA. Utilizing time-coincidence analyses between the main GW channel and hundreds of auxiliary channels that do not respond to true gravitational waves, hveto produces an ordered set of vetoes that maximally suppress noise-induced false alarms with minimal loss of observation time. The method underpins data-quality assurance protocols for short-duration and unmodeled GW searches, and has been implemented across multiple gravitational-wave observatories (Essick et al., 2013, Smith et al., 2011, Akutsu et al., 26 Jun 2025).

1. Problem Context and Motivation

Noise transients in the GW strain data—typically unmodeled, high-amplitude, and non-Gaussian—pose substantial challenges to transient GW searches. These glitches mimic or obscure real GW signals, increasing false-alarm rates and complicating the detection of astrophysical events, especially for burst-type searches that lack precise waveform templates. Auxiliary channels, which monitor environmental and instrumental states, can themselves exhibit glitches that are causally unrelated to GWs but correlated with noise in the GW data. Identifying and leveraging statistically significant correlations between auxiliary glitches and GW-channel glitches enables the exclusion ("veto") of contaminated data segments, thereby improving search sensitivity (Smith et al., 2011, Essick et al., 2013).

2. Core Algorithmic Structure

The hveto algorithm constructs and applies "veto configurations," systematically removing glitch-associated segments from the GW strain data while tracking live time and statistical significance. A veto configuration $C$ is specified by an auxiliary channel label $a$, a threshold $\theta$ on a channel glitch statistic (typically SNR), a symmetric time window $\Delta t$ around each glitch event, and possible further parameters (e.g., frequency band, epoch). The ordered, hierarchical (step-by-step) application of these configurations constitutes the core of the method (Essick et al., 2013, Smith et al., 2011, Akutsu et al., 26 Jun 2025).

Stepwise Overview:

1. Trigger Generation: Extract "triggers" (candidate transients) in the GW and auxiliary channels via signal-processing pipelines (e.g., Omicron, which uses a Q-transform or wavelet approach).
2. Configuration Formation: For each auxiliary channel, consider a range of SNR thresholds and window sizes to define multiple veto configurations.
3. Significance Calculation: For each configuration, compute the number of GW-channel glitches coincident with auxiliary-channel glitches within their associated windows.
4. Statistical Ranking: Evaluate the statistical significance of observed coincidences under the null hypothesis of independent Poisson (or binomial) processes.
5. Hierarchical Application: At each round, select the configuration with highest significance ("round winner"), apply its vetoes, remove the corresponding GW-channel events and live time, and iterate on the reduced dataset.
6. Termination: Stop when no configuration exceeds a preset significance threshold or additional vetoes would produce excessive dead time.

This approach yields a non-redundant, minimal set of vetoes with maximal impact on glitch reduction and minimal loss of analysis time (Essick et al., 2013, Smith et al., 2011).

3. Statistical Foundations and Significance Measures

The hveto algorithm quantifies the relevance of each veto configuration using hypothesis-testing frameworks predicated on Poisson or binomial statistics. Given $N_\mathrm{GW}$ total GW triggers over live time $T$, $N_\mathrm{aux}$ auxiliary triggers, a window $\Delta t$, and $n_\mathrm{coinc}$ observed coincidences, the expectation under uncorrelated rates is $$\langle n_\mathrm{C} \rangle = N_\mathrm{GW}\, N_\mathrm{aux}\, \Delta t / T$$ or, equivalently, $a$0, with $a$1 the cumulative veto segment duration and $a$2 the GW-trigger rate.

The probability of $a$3 or more coincidences arising by chance is:

$a$4

with the significance statistic defined by $a$5 (Essick et al., 2013, Smith et al., 2011, Akutsu et al., 26 Jun 2025). High values of $a$6 indicate strong, potentially causal correlations. In contexts such as KAGRA, a binomial model is sometimes preferred, with the key parameters:

• $a$7 (chance coincidence probability per auxiliary trigger)
• $a$8, where $a$9 is the cumulative binomial probability (Akutsu et al., 26 Jun 2025).

4. Implementation Flow and Pseudocode

A high-level pseudocode description, as used in both LIGO and KAGRA implementations, is summarized below (Essick et al., 2013, Smith et al., 2011, Akutsu et al., 26 Jun 2025):

$N_\mathrm{GW}$2

Typical complexity per iteration is $\theta$0, though efficient time-indexing can reduce cost (Essick et al., 2013).

5. Performance Metrics and Empirical Results

Performance is evaluated in terms of glitch-removal efficiency and induced deadtime. Let $\theta$1 denote the fraction of GW-channel glitches removed, and $\theta$2 the fractional deadtime:

$\theta$3

(Essick et al., 2013). Receiver Operating Characteristic (ROC) curves plotting $\theta$4 versus $\theta$5 provide visualization and optimization guidance.

Empirical studies report:

• In LIGO S5/VSR1: Single-detector $\theta$6–$\theta$7 at $\theta$8; coincident background reduction $\theta$9–$\Delta t$0 at $\Delta t$1 (Essick et al., 2013).
• On LIGO Livingston (2010): hveto removed $\Delta t$2 of h(t)-channel triggers at $\Delta t$3 deadtime, with efficiency/deadtime ratios $\Delta t$4 for early rounds (Smith et al., 2011).
• In KAGRA O3GK (2023): hveto with SNR threshold $\Delta t$5, $\Delta t$6–$\Delta t$7 s, and significance cut $\Delta t$8 removed $\Delta t$9 main-channel glitches by $N_\mathrm{GW}$0 auxiliary channels; $N_\mathrm{GW}$1 of these could be visually classified as blip, helix, line, scratchy, dot, or scattered-light glitches (Akutsu et al., 26 Jun 2025).

The method typically achieves most of its effect after a small number of rounds (1–3), with diminishing returns and increasing deadtime beyond that point.

6. Algorithmic Choices, Parameters, and Operational Considerations

Optimal performance relies on well-chosen thresholds and window lengths tailored to the detector environment and expected coupling timescales. SNR cuts define analysis sensitivity; stricter cuts reduce accidental coincidences but may miss low-amplitude correlations. Time windows must capture the temporal extent of glitches; too wide, they increase deadtime, too narrow, and true couplings may be missed (Essick et al., 2013, Akutsu et al., 26 Jun 2025).

Auxiliary channels are pre-vetted for "safety" (no known GW response via hardware injections). Veto segments are merged as necessary to avoid redundant deadtime. When overlapping with test-injections or hardware-safety-flagged intervals, vetoes are excluded by construction (Smith et al., 2011, Essick et al., 2013).

Cross-validation techniques (e.g., round-robin time binning) can guard against overfitting. Over-training may arise if too many configurations or insufficiently varied data are used (Essick et al., 2013).

7. Extensions, Strengths, and Limitations

Strengths of hveto include its transparency, automation, statistical rigor, and generalizability to new feature sets (e.g., frequency, morphology). The hierarchical ranking prevents redundant or overlapping vetoes and provides detailed statistical significance per configuration, allowing traceable and minimal deadtime vetoing (Essick et al., 2013, Smith et al., 2011).

Limitations stem from the Poisson (or binomial) independence assumption—significant non-stationarity in trigger rates can bias assessments of significance. The method's sensitivity is dictated by the richness of the configuration grid; sparse coverage can plateau performance. Algorithmic efficiency becomes a concern for very large channel and trigger counts.

Extensions include real-time adaptation of thresholds/windows, incorporation of multivariate or machine-learning-based vetoes, joint optimization for multi-channel coincidences, and Bayesian model-selection to distinguish between astrophysical and instrumental origins for glitches (Essick et al., 2013).

In practice, hveto constitutes a foundational method for real-time and offline data quality assurance in GW observatories. Application to KAGRA O3GK led to effective glitch suppression and explicit morphological linkage of vetoed glitches to detector subsystems, exemplifying its broader diagnostic utility (Akutsu et al., 26 Jun 2025).