The iisignature library: efficient calculation of iterated-integral signatures and log signatures

Reizenstein, Jeremy; Graham, Benjamin

doi:10.48550/arxiv.1802.08252

Cited by 11 publications

(14 citation statements)

References 9 publications

(18 reference statements)

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“…We note that the signature and the signature kernel can be easily computed on real time series using existing python libraries (Lyons, 2010;Reizenstein & Graham, 2018).…”

Section: Variational Orthogonal Signature Featuresmentioning

confidence: 99%

SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data

Lemercier¹,

Salvi²,

Cass³

et al. 2021

Preprint

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Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework for Gaussian Processes (GPs) on sequential data. Our contribution is twofold. First, we construct inducing variables underpinning the sparse approximation so that the resulting evidence lower bound (ELBO) does not require any matrix inversion. Second, we show that the gradients of the GP signature kernel are solutions of a hyperbolic partial differential equation (PDE). This theoretical insight allows us to build an efficient backpropagation algorithm to optimize the ELBO. We showcase the significant computational gains of SigGPDE compared to existing methods, while achieving state-of-the-art performance for classification tasks on large datasets of up to 1 million multivariate time series.

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“…We note that the signature and the signature kernel can be easily computed on real time series using existing python libraries (Lyons, 2010;Reizenstein & Graham, 2018).…”

Section: Variational Orthogonal Signature Featuresmentioning

confidence: 99%

SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data

Lemercier¹,

Salvi²,

Cass³

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…In terms of applications, some examples where the signature method has seen use include character recognition (Yang et al, 2016a,b;Reizenstein, 2019;Toth and Oberhauser, 2019), human action recognition (Li et al, 2017;Yang et al, 2017;Liao et al, 2019), and medicine (Arribas et al, 2018;Morrill et al, 2019;Howison et al, 2020). These applications have also prompted the creation of high performance software (Reizenstein and Graham, 2018;Kidger and Lyons, 2020).…”

Section: Related Workmentioning

confidence: 99%

A Generalised Signature Method for Multivariate Time Series Feature Extraction

Morrill¹,

Fermanian²,

Kidger³

et al. 2020

Preprint

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The 'signature method' refers to a collection of feature extraction techniques for multimodal sequential data, derived from the theory of controlled differential equations. Variations exist as many authors have proposed modifications to the method, so as to improve some aspect of it. Here, we introduce a generalised signature method that contains these variations as special cases, and groups them conceptually into augmentations, windows, transforms, and rescalings. Within this framework we are then able to propose novel variations, and demonstrate how previously distinct options may be combined. We go on to perform an extensive empirical study on 26 datasets as to which aspects of this framework typically produce the best results. Combining the top choices produces a canonical pipeline for the generalised signature method, which demonstrates state-of-the-art accuracy on benchmark problems in multivariate time series classification. * Equal contribution Preprint. Under review.

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“…, x n , where x contains n observations, and the ith observation x i , i ∈ [n], is assumed to be a d-dimensional column vector at the ith time point, one needs to convert it to a continuous R d -valued path via piecewise linear interpolation or other transforms in order to compute signature. The availability of Python packages iisignature [19] and esig allows easy calculation of signature, where the linear interpolation is implemented automatically by the packages.…”

Section: Signature Featuresmentioning

confidence: 99%

“…To ensure comparability of our results, we predicted raw ASRM/QIDS scores. For our own comparison, we also made more coarse-grained predictions according to the categories for QIDS: none (1-5), mild (6-10), moderate (11)(12)(13)(14)(15), severe (16)(17)(18)(19)(20) and very severe (21)(22)(23)(24)(25)(26)(27) [20], and for ASRM: none (0-5), mild (6)(7)(8)(9), moderate (10)(11)(12)(13), severe (14)(15)(16)(17) and very severe (17)(18)(19)(20).…”

Section: Score Predictionmentioning

confidence: 99%

Deriving information from missing data: implications for mood prediction

Lyons

Saunders

2020

Preprint

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The availability of mobile technologies has enabled the efficient collection prospective longitudinal, ecologically valid self-reported mood data from psychiatric patients. These data streams have potential for improving the efficiency and accuracy of psychiatric diagnosis as well predicting future mood states enabling earlier intervention. However, missing responses are common in such datasets and there is little consensus as to how this should be dealt with in practice. A signature-based method was used to capture different elements of self-reported mood alongside missing data to both classify diagnostic group and predict future mood in patients with bipolar disorder, borderline personality disorder and healthy controls. The missing-response-incorporated signature-based method achieves roughly 66% correct diagnosis, with f1 scores for three different clinic groups 59% (bipolar disorder), 75% (healthy control) and 61% (borderline personality disorder) respectively. This was significantly more efficient than the naive model which excluded missing data. Accuracies of predicting subsequent mood states and scores were also improved by inclusion of missing responses. The signature method provided an effective approach to the analysis of prospectively collected mood data where missing data was common and should be considered as an approach in other similar datasets. 1

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The iisignature library: efficient calculation of iterated-integral signatures and log signatures

Cited by 11 publications

References 9 publications

SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data

SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data

A Generalised Signature Method for Multivariate Time Series Feature Extraction

Deriving information from missing data: implications for mood prediction

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