mlsanityData to 7 Oct 2026

Novelty detection on path space

arXiv 2512.03243 ↗First posted 2 Dec 2025stat.ML cs.LG math.PRcited by 0

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Abstract (arXiv)

We frame novelty detection on path space as a hypothesis testing problem with signature-based test statistics. Using transportation-cost inequalities of Gasteratos and Jacquier (2023), we obtain tail bounds for false positive rates that extend beyond Gaussian measures to laws of RDE solutions with smooth bounded vector fields, yielding estimates of quantiles and p-values. Exploiting the shuffle product, we derive exact formulae for smooth surrogates of conditional value-at-risk (CVaR) in terms of expected signatures, leading to new one-class SVM algorithms optimising smooth CVaR objectives. We then establish lower bounds on type-II error for alternatives with finite first moment, giving general power bounds when the reference measure and the alternative are absolutely continuous with respect to each other. Finally, we evaluate numerically the type-I error and statistical power of signature-based test statistic, using synthetic anomalous diffusion data and real-world molecular biology data.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 36 of its 82 references that are in the map. First posted on arXiv 2 Dec 2025.

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References · 36

  1. 2020Neural Rough Differential Equations for Long Time Seriescited by 140
  2. 2021Testing for Outliers with Conformal p-valuescited by 133
  3. 2022Deep Learning for Time Series Anomaly Detection: A Surveycited by 130
  4. 2016Kernels for sequentially ordered datacited by 83
  5. 2019Deep Signature Transformscited by 75
  6. 2024Theoretical Foundations of Deep Selective State-Space Modelscited by 73
  7. 2020The Signature Kernel is the solution of a Goursat PDEcited by 58
  8. 2018Signature moments to characterize laws of stochastic processescited by 54
  9. 2021Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamicscited by 46
  10. 2020Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPUcited by 45
  11. 2018The iisignature library: efficient calculation of iterated-integral signatures and log signaturescited by 38
  12. 2023Non-adversarial training of Neural SDEs with signature kernel scorescited by 36
24 more
  1. 2020A Data-driven Market Simulator for Small Data Environmentscited by 34
  2. 2022Signature Methods in Machine Learningcited by 33
  3. 2020Distribution Regression for Sequential Datacited by 31
  4. 2020A Kernel Two-Sample Test for Functional Datacited by 27
  5. 2021Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processescited by 27
  6. 2023Neural signature kernels as infinite-width-depth-limits of controlled ResNetscited by 25
  7. 2023Unsupervised anomaly detection algorithms on real-world data: how many do we need?cited by 20
  8. 2019Functional Isolation Forestcited by 19
  9. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  10. 2021SK-Tree: a systematic malware detection algorithm on streaming trees via the signature kernelcited by 16
  11. 2025Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Modelscited by 16
  12. 2023A Neural RDE approach for continuous-time non-Markovian stochastic control problemscited by 13
  13. 2023New directions in the applications of rough path theorycited by 12
  14. 2023Signature Methods in Stochastic Portfolio Theorycited by 11
  15. 2024Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signalscited by 9
  16. 2020Dimensionless Anomaly Detection on Multivariate Streams with Variance Norm and Path Signaturecited by 8
  17. 2021Unsupervised learning of anomalous diffusion datacited by 8
  18. 2025Rough kernel hedgingcited by 7
  19. 2024Sparse Signature Coefficient Recovery via Kernelscited by 5
  20. 2025pySigLib -- Fast Signature-Based Computations on CPU and GPUcited by 5
  21. 2024Novelty Detection on Radio Astronomy Data using Signaturescited by 4
  22. 2025ParallelFlow: Parallelizing Linear Transformers via Flow Discretizationcited by 3
  23. 2024Signature Isolation Forestcited by 1
  24. 2025Path Signatures Enable Model-Free Mapping of RNA Modificationscited by 1

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