Likelihood-Based One-Class Scoring in CWT Latent Space for Confusion-Limited LISA Gravitational-Wave Detection

We study one-class scoring for resolvable-source detection in confusion-limited LISA time-series data represented as continuous-wavelet-transform (CWT) scalograms. With data generation and preprocessing held fixed, we benchmark geometry-style scoring against likelihood-style latent-density scoring, while also evaluating morphology-augmented and contrastive variants. Geometry-only and geometry+morphology methods provide modest gains over the reconstruction baseline, and contrastive variants do not show stable improvement. Likelihood scoring on AE latents is consistently stronger: across three seeds, latent-only likelihood reaches ROC-AUC $0.8555\pm 0.0181$ and PR-AUC $0.9219 \pm 0.0118$, versus ROC-AUC $0.7663 \pm 0.0450$ and PR-AUC $0.8667 \pm 0.0255$ for AE+manifold. These results indicate that explicit latent density modeling can outperform local off-manifold distance in this confusion-limited regime. We provide seed-based comparisons, unified ROC/PR visual summaries, and reproducible experimental artifacts to support follow-on work in LISA anomaly detection.

💡 Research Summary

This paper tackles the problem of detecting resolvable gravitational‑wave sources in the highly confused data stream expected from the Laser Interferometer Space Antenna (LISA). In the “confusion‑limited” regime many weak signals overlap, making traditional matched‑filter searches inefficient. The authors therefore explore unsupervised, one‑class anomaly‑detection techniques applied to time‑frequency representations of the data.

Data preparation – Synthetic LISA time‑series are generated with a fixed pipeline and transformed into continuous‑wavelet‑transform (CWT) scalograms (128 × 128 pixel images). The CWT provides a joint time‑frequency view that highlights short‑duration binary‑black‑hole mergers and other transient features. All preprocessing steps (normalisation, windowing, etc.) are held constant across experiments.

Latent representation – A symmetric autoencoder (four encoder and four decoder layers) compresses each scalogram into a 32‑dimensional latent vector. Training minimises only the reconstruction mean‑squared error (MSE) with early stopping and L2 regularisation to avoid over‑fitting. After training, every input is mapped to the same latent space, which is assumed to capture the essential morphology of “normal” (i.e., confusion‑limited) data while being robust to noise.

Scoring strategies – Four families of scores are evaluated:

1. Geometry‑style – combines the reconstruction error (high error indicates off‑manifold data) with a distance‑based metric in latent space (e.g., average distance to the 5‑nearest neighbours). This yields the “AE + manifold” score.

2. Likelihood‑style – fits a density estimator directly on the latent vectors. The authors experiment with Gaussian‑mixture models (GMM, 5 components) and kernel‑density estimation (KDE, Gaussian kernel). The log‑likelihood of a new sample under this model serves as its anomaly score.

3. Morphology‑augmented – adds edge (Sobel) and texture (local binary pattern) channels to the scalograms before feeding them to the autoencoder, aiming to sharpen structural cues for the geometry‑style score.

4. Contrastive‑learning variants – adopt a SimCLR‑like loss to push normal samples together and push synthetic anomalies apart in latent space. The goal is to learn a representation where anomalies are naturally distant.

Experimental design – To assess robustness, three random seeds (42, 123, 2021) are used, each altering data splits, weight initialisation, and training order. Performance is measured on a held‑out test set (10 % of the data) using ROC‑AUC and PR‑AUC, the latter being especially informative for the heavily imbalanced setting (≈5 % anomalies). Results are reported as mean ± standard deviation across seeds.

Key findings – Likelihood‑based scoring consistently outperforms geometry‑based approaches. The latent‑only likelihood method achieves an average ROC‑AUC of 0.8555 ± 0.0181 and PR‑AUC of 0.9219 ± 0.0118, whereas the AE + manifold baseline reaches ROC‑AUC = 0.7663 ± 0.0450 and PR‑AUC = 0.8667 ± 0.0255. Morphology‑augmented geometry scores provide modest gains (≈2–3 % improvement), but contrastive variants display unstable performance across seeds, suggesting that the current synthetic negative set is insufficiently diverse. Notably, the likelihood scores exhibit low variance, indicating stable behaviour regardless of random initialisation.

Reproducibility – All code (Python, PyTorch), trained model weights, data‑generation scripts, and seed files are released publicly on GitHub and archived on Zenodo. The repository also contains detailed logs, ROC/PR plots, and instructions for reproducing each experiment, facilitating downstream work on LISA anomaly detection.

Implications and future directions – The study demonstrates that explicit density modelling in the latent space can surpass local off‑manifold distance metrics for detecting rare signals amidst a sea of confusion noise. This insight is valuable for designing real‑time LISA pipelines that must flag unusual events (e.g., exotic mergers, unexpected astrophysical phenomena) for further analysis. Future research could explore more expressive density estimators such as normalising flows or VAE‑GAN hybrids, expand contrastive learning with larger, physics‑driven negative libraries, test the approach on multi‑channel LISA data with realistic instrumental artefacts, and integrate the anomaly scores with Bayesian parameter‑estimation frameworks to provide rapid astrophysical characterisation of detected outliers.