Deep signature/log-signature FBSDE algorithm improves accuracy and training time.
problem Solving FBSDEs with state and path dependent features.
method Incorporates deep signature/log-signature transformation into RNN model.
result Improves accuracy and training time compared to existing methods.
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
problem Computing expected signatures in semimartingale models.
method Revisits and provides new formulae for computing expected signatures in a general semimartingale setting.
result Log-transform of expected signatures simplifies complexity, leading to signature cumulants.
Semi-supervised GANs with log-signatures improve credit card fraud detection.
problem Detecting fraud in large, complex financial transaction data streams.
method Conditional GANs with Bayesian inference and log-signatures for robust feature encoding.
result Consistent improvements over benchmarks in global and domain-specific metrics.
A new method compares unaligned datasets using log-Euclidean signatures of SPD matrices.
problem Efficiently comparing datasets with unknown alignment.
method Diffusion operators, Riemannian geometry, log-Euclidean metric.
result LES distance recovers meaningful structural differences, outperforming existing methods.
Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble th…
Paper combines RNN and signatures for learning functions on streamed multimodal data.
problem Learning functions on streamed multimodal data.
method Hybrid Logsig-RNN algorithm combining signatures and RNN.
result Hybrid algorithm achieves outstanding accuracy with superior efficiency and robustness.
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.
Kernel for Lévy rough paths derived from PDE system.
problem Computing similarity measures for Lévy rough paths.
method Developed a PDE system for the expected signature of inhomogeneous Lévy processes.
result Gaussian martingales' expected signature kernel satisfies a Goursat PDE.
Framework combines random features with CDEs for efficient time-series learning.
problem Efficient training of time-series models with strong inductive bias.
method Random Fourier CDEs and Random Rough DEs using continuous-time reservoirs and log-ODE discretization.
result Unified perspective on random-feature reservoirs and path-signature theory.
Improved graph matching algorithm robust to noise.
problem Finding a bijection between vertex sets of two graphs.
method Uses multistage signature vectors to match vertices.
result Recover matching exactly with high probability for α≤1/(loglogn)C. Study on martingale property and moment explosions in signature volatility models.
problem Analyzing the martingale property and moment explosions in signature volatility models.
method Fine analysis of the explosion time of a signature stochastic differential equation.
result The price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative.
Average signature of 2-bridge knots approximates sqrt(2c/π).
problem Estimating the average signature and 4-genus of 2-bridge knots.
method Developed a model for 2-bridge knot diagrams indexed by crossing number, and used it to derive upper bounds for the average 4-genus.
result Upper bound for the average 4-genus of a 2-bridge knot is 9.75c/log c.
This paper presents a novel deep learning based method for automatic malware signature generation and classification. The method uses a deep belief network (DBN), implemented with a deep stack of denoising autoencoders, generating an invariant compact representation of the malware behavior. While conventional signature…
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.
LogAnMeta detects anomalies from log events using meta learning.
problem Poor performance of current log anomaly detection on new or unseen anomalies.
method Meta-learning-based hybrid few-shot classifier trained in an episodic manner.
result Demonstrates efficacy of LogAnMeta on detecting anomalies with few samples.
Study proves Alexander polynomials of certain 4-braid knots satisfy a conjecture and gives formulas for log-concave sequences.
problem Proving the Alexander polynomials of certain 4-braid knots satisfy Fox's Trapezoidal Conjecture.
method Analyzes families of alternating 4-braids and n-braids, providing explicit formulas and verifying log-concavity. result Explicit formulas for signature and first 4 coefficients of Alexander polynomials, showing log-concavity.
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.
New algorithms compute Volterra signature efficiently for time series analysis.
problem Efficient computation of Volterra signature with matrix-valued kernels.
method Decomposed Chen-type convolution relation, introduced FFT-based and exact recursion algorithms.
result Efficient algorithms for Volterra signature computation with various complexities.
Holomorphic torsion invariant for log-Enriques surfaces derived from Borcherds products.
problem Holomorphic torsion invariant for log-Enriques surfaces.
method Introduced a holomorphic torsion invariant using Borcherds products.
result The invariant is given by the Petersson norm of an explicit Borcherds product.
New method for curve comparison using iterated integrals and moving frames.
problem Comparing curves robustly to noise and transformations.
method Moving frame method paired with log-signature transform.
result Algorithmic construction of invariants for curve equivalence under rigid motions.
The paper introduces a new volatility model using Fourier techniques for pricing and hedging.
problem Pricing and hedging of financial derivatives with stochastic volatility.
method A Fourier-based approach to price and hedge European and path-dependent options in a stochastic volatility model.
result The model includes and extends popular volatility models like Stein-Stein, Bergomi, and Heston.
Generative model prices basket options efficiently.
problem Real-time pricing of basket options with varying market inputs.
method Truncated path signatures and Mixture Density Networks (MDN) for learning the terminal density.
result The model produces small pricing errors and matches Monte Carlo simulations closely.
Paper characterizes DLN distribution, its properties, and estimation methods.
problem No specific problem stated, focuses on DLN distribution properties.
method Characterization of PDF, CDF, moments; generalization to N-dimensions; methods to handle double-exponential nature.
result Characterization of DLN distribution and its properties, including estimation methods.
We have analyzed the risks of possible development of bubbles in the Swiss residential real estate market. The data employed in this work has been collected by comparis.ch, and carefully cleaned from duplicate records through a procedure based on supervised machine learning methods. The study uses the log periodic powe…
Study uses topological signatures to quantify financial market complexity.
problem Capturing temporal organization beyond volatility measures.
method Null validated topological approach using L1 norm of persistence landscapes. result Persistence landscape norms reveal dynamical structure during market stress.
The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface Z over CP1. We show that for the ∂ˉ-operator along the fiber the logarithm of the regularized determinant −1/2logdet′(∂ˉ∗∂ˉ) satisfies the anomaly equation of the …
We consider the problem of separating error messages generated in large distributed data center networks into error events. In such networks, each error event leads to a stream of messages generated by hardware and software components affected by the event. These messages are stored in a giant message log. We consider …
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade models to unravel the possi…
Deep neural RDEs improve portfolio optimization accuracy and risk sensitivity.
problem High-dimensional, path-dependent valuation and control problems.
method Coupling truncated log-signatures with a neural RDE backbone.
result Improved accuracy, tail fidelity, and training stability across various financial models.
Neural RDEs extend CDEs to irregular time series.
problem Modeling long irregular time series efficiently.
method Representing time series through log-signature and solving RDEs.
result Significant training speed-ups and improved model performance.
Dead-Direction Signatures (DDS) provide a cheap, closed-form spectral reading of a network's singular complexity.
problem Estimating the complexity of deep networks through their loss singularities.
method DDS replaces the SGLD posterior chain with spectral linear algebra.
result DDS observables rank-track the network's singular complexity at the framework-predicted sign.
A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, whi…
Random flat bundles on surfaces have least eigenvalues at least 1/4.
problem Equidistribution of flat bundles on random surfaces.
method Hide--Magee method and probabilistic prime geodesic theorem.
result Flat unitary bundles have least eigenvalue at least 1/4 with high probability.
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.
A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifol…
Maximum Levine-Tristram signature of torus knots follows a reduction formula.
problem Determining the maximum Levine-Tristram signature for torus knots.
method Proved a reduction formula analogous to Gordon-Litherland-Murasugi's classical signature result.
result Maximum Levine-Tristram signature of torus knots satisfies a reduction formula.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
problem Invalidity of existing inverse theorems for mesh group-planes.
method Classification of three and five point meshes, analysis of joint invariant signatures.
result Valid conditions for the Signature-inverse Theorem in mesh group-planes.
Introduces flat discrete signatures for financial data analysis.
problem Representing financial data for machine learning without continuous transformation.
method Introduced flat discrete signatures and discrete signatures, generalizing flat discrete signatures.
result Flat discrete signatures can represent quadratic variation relevant in finance.
This is a sequel to the paper "The signature package on Witt spaces, I. Index classes" by the same authors. In the first part we investigated, via a parametrix construction, the regularity properties of the signature operator on a stratified Witt pseudomanifold, proving, in particular, that one can define a K-homology …
We define the Analytical signature, the Hodge signature and the de Rham signature for a foliated manifold with boundary with foliation transverse to the boundary. We show that all these signatures coincide and a Hirzebruch formula is valid.
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.
The paper examines the consistency of Lasso regression applied to signature analysis of time series data.
problem Consistency of Lasso regression in signature analysis of time series data.
method The paper studies the consistency of Lasso regression applied to signature analysis of time series data, both theoretically and numerically.
result The Lasso regression is consistent both asymptotically and in finite sample for certain types of time series and processes.
Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.
problem Computing signatures of torus links and their cores.
method Use Neumann's equivariant signatures and rewrite Hirzebruch's formula for torus links (without cores) in terms of integral points in a parallelogram.
result Rewritten Hirzebruch's formula for torus links with cores using integral points in a parallelogram.
This paper extends the C*-signature to non-Witt spaces using noncommutative geometric methods.
problem Extending the signature to non-Witt spaces with noncommutative geometric methods.
method Noncommutative geometric methods, combinatorial framework, and comparison with analytical signature.
result Constructing the C*-signature on non-Witt spaces.
Paper generalizes path signature using fractional calculus for improved machine learning.
problem Improving path signature for machine learning applications.
method Introduces two new signatures inspired by fractional calculus and machine learning considerations.
result Significant accuracy improvements in handwritten digit recognition.
We present a novel method for extracting cancer signatures by applying statistical risk models (http://ssrn.com/abstract=2732453) from quantitative finance to cancer genome data. Using 1389 whole genome sequenced samples from 14 cancers, we identify an "overall" mode of somatic mutational noise. We give a prescription …
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.
Efficiently computes sparse signature coefficients using kernels.
problem Lack of efficient methods for sparse signature coefficients.
method Signature kernels and PDE-based methods.
result Sparse groups of signature coefficients can be isolated effectively.