pySigLib speeds up signature-based computations on CPUs and GPUs.
problem Efficient signature-based computations on large datasets and long sequences.
method Optimised Python library for CPU and GPU, novel differentiation scheme.
result Accurate gradients at a fraction of the runtime of existing libraries.
The paper develops methods for novelty detection on path space using signature-based statistics.
problem Novelty detection on path space as a hypothesis testing problem.
method Signature-based test statistics, transportation-cost inequalities, CVaR, one-class SVM algorithms.
result Established lower bounds on type-II error and general power bounds. The study identifies volatility models from path geometry using signature-based methods.
problem Identifying different stochastic volatility models from observed data.
method Mapping volatility trajectories into a feature space via truncated path signatures and applying a gradient boosting classifier.
result The method achieves high classification accuracy across various volatility dynamics and parameter settings.
New methods for volatility modeling using rough paths and signatures.
problem Calibrating implied volatility surfaces in various stochastic models.
method Analytical approximations and signature-based models based on rough path theory.
result Signature-based models achieve comparable accuracy to analytical expansions and can capture more complex dynamics.
Develops a new trading strategy for statistical arbitrage with path-dependent signals.
problem Optimal execution in statistical arbitrage strategies with dynamic predictive signals.
method Signature-based framework modeling alpha and trading speed as linear functionals of truncated signature of market path.
result Fitted policy achieves higher return on turnover compared to a z-score benchmark.
Paper tackles DR problem with scalable signature-based approach.
problem Memory and computation cost issues in DR solutions.
method Signature-based features, novel distance approximator.
result Proposes scalable DR solution with reduced estimation uncertainty.
Two signature-based methods solve optimal stopping in non-Markovian frameworks.
problem Optimal stopping in non-Markovian frameworks, particularly pricing American options.
method Primal and dual formulations using linear functionals of rough path signatures.
result Both primal and dual methods converge and provide numerical examples.
Sig-DEG speeds up diffusion models by distilling them into faster approximations.
problem Computational intensity of diffusion models at inference time.
method Signature-based differential equation generation to summarize Brownian motion.
result Sig-DEG reduces inference steps by an order of magnitude while maintaining generation quality.
Paper develops approximation and statistical theory for signature-based path regression.
problem Understanding how fast signatures approximate continuous path functionals.
method Develops \(L^2\) approximation rate for smooth functionals of Itô diffusions and establishes consistency of statistical learning procedures.
result Signature-based methods improve prediction over handcrafted features in various real-data applications.
Nowadays, advanced intrusion detection systems (IDSs) rely on a combination of anomaly detection and signature-based methods. An IDS gathers observations, analyzes behavioral patterns, and reports suspicious events for further investigation. A notorious issue anomaly detection systems (ADSs) and IDSs face is the possib…
The model uses signatures to accurately calibrate SPX and VIX options without jumps or rough volatility.
problem Joint calibration of SPX and VIX options without jumps or rough volatility.
method The approach uses a stochastic volatility model with signatures of polynomial diffusions to price and calibrate SPX and VIX options.
result Highly accurate calibration results for SPX and VIX options without adding jumps or rough volatility.
Mobile technologies offer opportunities for higher resolution monitoring of health conditions. This opportunity seems of particular promise in psychiatry where diagnoses often rely on retrospective and subjective recall of mood states. However, getting actionable information from these rather complex time series is cha…
New methods price American options in rough volatility models.
problem Pricing American options under rough volatility.
method Integrating deep-signature and signature-kernel learning into optimal stopping problem solutions.
result Performance comparison in rough Heston and rough Bergomi models.
Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent technological advances allow the prospective reporting of mood in real time enabl…
Validates economic scenarios using statistical tests on stochastic processes.
problem Ensuring the accuracy of real-world economic scenario models.
method Applies Chevyrev and Oberhauser's (2022) signature and maximum mean distance test to various stochastic processes.
result Demonstrates the test's effectiveness across different path properties relevant to financial modeling.
Information systems have widely been the target of malware attacks. Traditional signature-based malicious program detection algorithms can only detect known malware and are prone to evasion techniques such as binary obfuscation, while behavior-based approaches highly rely on the malware training samples and incur prohi…
The study explains why signature methods work in commodity futures term structure classification.
problem Lack of interpretability in signature methods for term structure classification.
method Introducing signature perturbations to explain the success of signature-based classification.
result The volatility of the convenience yield is the major discriminant for commodity markets classification.
Novel model for predicting event intensities from static and time series data.
problem Predicting event intensities from static and irregularly sampled time series data.
method Neural controlled differential equations and signature-based CoxSig model.
result The CoxSig model provides theoretical learning guarantees and performs well on various datasets.
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a "sequentialized" version of any static kernel. The…
A new algorithm for high-dimensional hedging problems.
problem High-dimensional, path-dependent hedging problems.
method Signature-based algorithm using operator-valued kernels and geometric rough paths.
result Theoretical guarantees on existence and uniqueness of a global minimum.
Expected signatures map data streams to lower dimensions, improving ML performance.
problem Leveraging model-free embeddings for domain-agnostic machine learning.
method Expected signatures map data streams to lower dimensions, with convergence results bridging empirical and theoretical estimators.
result A modified expected signature estimator with lower mean squared error for martingale processes.
New method uses path signatures for efficient likelihood estimation in time-series data.
problem Intractable likelihood functions in complex dynamic models.
method Kernel classifier based on path signatures for sequential data.
result Path signatures yield highly performant classifiers, even with low sample numbers.
Study local expansions of continuous-time processes using Ito signature properties.
problem Analyzing local expansions of continuous-time processes and their moments.
method Using the Ito signature, a basis of iterated integrals, to conduct expansions of the process' characteristic function.
result Explicit coefficients and stochastic representations for asymptotics as time shrinks or diverges.
Novel signature approach for pricing and hedging path-dependent options with market frictions.
problem Pricing and hedging path-dependent options with market frictions.
method Signature approach, mean-quadratic variation criterion, non-standard infinite-dimensional Riccati equations, time-augmented signature, non-Markovian stochastic control problem.
result Effective hedging strategies in frictional markets with low-truncated signature approximations.
A new graph signature invariant to graph automorphisms.
problem Graph symmetry and feature generation.
method Power spectrum signature derived from squared graph Fourier transform.
result Power spectrum signature is stable under graph perturbations.
Develops a kernel-based framework for dynamic trading strategies.
problem Optimizing portfolios with temporal dependencies in asset dynamics.
method Parameterizes trading strategies as functions in RKHS, enabling flexible, non-Markovian approaches.
result Significantly outperforms classical Markovian methods in synthetic and market-data examples.
Estimates path-valued data using signature metrics and local kernels.
problem Nonparametric regression and classification for path-valued data.
method Combines signature transform and local kernel regression.
result Establishes convergence bounds and demonstrates competitive accuracy.
Universal approximation for rough paths and Lévy processes.
problem Approximating continuous functionals of càdlàg paths.
method Linear functionals of time-extended signatures.
result Universal approximation theorem for continuous functionals of càdlàg paths.
Malware currently presents a number of serious threats to computer users. Signature-based malware detection methods are limited in detecting new malware samples that are significantly different from known ones. Therefore, machine learning-based methods have been proposed, but there are two challenges these methods face…
The paper explores asset price models using signatures of underlying processes, providing methods for calibration and pricing.
problem Developing asset price models that can approximate classical models and learn parameters from various data sources.
method Using linear functions of the signature of a primary underlying process, the paper provides conditions for absence of arbitrage and tractable option pricing formulas.
result The linearity of the model allows for fast and accurate calibrations from time-series and implied volatility data.
Detects anomalies in stock and crypto data with high accuracy.
problem Identifying rare or unexpected events in time series data.
method Uses signature or randomized signature methods for anomaly detection.
result Achieves F1 scores up to 88% in identifying pump and dump attempts.
The increasing scale and sophistication of cyberattacks has led to the adoption of machine learning based classification techniques, at the core of cybersecurity systems. These techniques promise scale and accuracy, which traditional rule or signature based methods cannot. However, classifiers operating in adversarial …
A new VWAP execution method using transformer and signature features.
problem Asset-specific model training and complex temporal dependencies.
method Combining transformer-based design with path signatures for capturing geometric features.
result GFT-Sig model achieves superior performance in VWAP loss metrics.
A hybrid framework for American option pricing under time-varying rough volatility.
problem Pricing American options under time-varying rough volatility.
method Signature method combined with gradient-boosted ensemble for Hurst parameter estimation, regime switch, and Random Fourier Features for acceleration.
result The proposed hybrid framework improves performance over fixed-roughness baselines and reduces duality gaps in some regimes.
With the rapid proliferation and increased sophistication of malicious software (malware), detection methods no longer rely only on manually generated signatures but have also incorporated more general approaches like machine learning detection. Although powerful for conviction of malicious artifacts, these methods do …
Paper builds ML classifier to detect crypto-ransomware.
problem Detecting crypto-ransomware with high accuracy and low false positives.
method Behavior-based detection using input/output activities and file-content entropy. Deep-learning classifier with adversarial research and Integrated Gradient method for explanation.
result Deep-learning classifier achieves high accuracy and low false positive rate in detecting crypto-ransomware.
Generative model for TPPs using signatures and distributional discrepancies.
problem Limitations of signature methods for TPPs and lack of global sequence-level loss in neural models.
method Introduce interarrival embedding to lift jump paths to continuous paths of bounded variation, enabling signature methods for discrete event sequences. Develop sigTPP, a signature-based generative model trained on path-level loss.
result sigTPP achieves the best average rank across multiple metrics and outperforms or is within a standard error of the strongest baseline in 64% of dataset-metric pairs.
New imputation strategies improve signature models for irregular time series.
problem Applying signature models to irregular time series requires continuous path construction.
method Characterized imputation as a problem, evaluated various strategies, proposed GP-PoM.
result Gaussian process adapters improve predictive performance and robustness.
The ability to visually re-identify objects is a fundamental capability in vision systems. Oftentimes, it relies on collections of visual signatures based on descriptors, such as SIFT or SURF. However, these traditional descriptors were designed for a certain domain of surface appearances and geometries (limited relief…
To save manual effort, developers often translate programs from one programming language to another, instead of implementing it from scratch. Translating application program interfaces (APIs) used in one language to functionally equivalent ones available in another language is an important aspect of program translation…
Detects backdoors in outsourced models by replicating training steps across multiple servers.
problem Detecting backdoors in models trained on cloud providers without prior knowledge.
method Replicate training steps across multiple servers to identify deviations and malicious updates.
result 99.6% accuracy in identifying backdoored models out of 50% malicious providers.
Scalable machine learning with path signatures for time series and graphs.
problem Challenges in real-world time series and graph data.
method Combines rough path theory with probabilistic, deep, and kernel methods.
result Scalable models for time series and graph data.
Path signatures reveal community structure in coupled oscillators' dynamics.
problem Detecting communities in multivariate dynamical processes from time series data.
method Path signatures, a mathematical framework encoding geometric and temporal properties of continuous paths.
result Achieved exact recovery of structural communities from observed time series in multiple KSBM instances.
Signatures simplify analysis of evolving data streams.
problem Understanding and analyzing irregular, non-stationary data streams.
method Mathematical signatures reduce noise and preserve key information.
result Signatures manage the exponential scaling of data complexity.