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.
Deep signature algorithm for pricing path-dependent options.
problem Pricing path-dependent options with complex payoff functions.
method Extended backward scheme for state-dependent FBSDEs with reflections, incorporating signature layer for path-dependent FBSDEs.
result Convergence analysis of the algorithm with explicit dependence on truncation order and neural network approximation errors.
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 develops a deep signature approach for option pricing under non-Markovian stochastic volatility models.
problem Pricing options under non-Markovian stochastic volatility models is challenging due to the dependence on historical paths.
method Reformulate the asset dynamics as a rough stochastic differential equation and represent rough paths via signatures. Apply standard analytical tools to solve the transformed equation.
result The deep signature approach provides a theoretically grounded and computationally efficient framework for option pricing.
Path signatures improve hedging of exotic derivatives in non-Markovian models.
problem Hedging exotic derivatives under non-Markovian stochastic volatility models.
method Investigates path signatures in deep and shallow learning contexts, comparing neural networks and regression approaches.
result Path signatures outperform LSTM in most cases and yield more accurate results in hedging.
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been treated as a fixed feature transformation, on top of which a model may be built. We propose a novel approach which combines the advantages o…
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.
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…
Paper generates synthetic radar signatures for motion classification.
problem Lack of large training datasets for radar-based human activity recognition.
method Adversarial learning for synthetic data generation, kinematic sifting for consistency.
result 93% overall accuracy achieved on diverse aspect angles.
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.
New method solves optimal stopping problems using rough path signatures.
problem Optimal stopping problems in finance and other fields.
method Using rough path signatures and deep neural networks.
result Solves optimal stopping problems efficiently under minimal assumptions.
New algorithm reduces MFGs with common noise complexity.
problem Prohibitive computational cost in solving MFGs with common noise.
method Signatured deep fictitious play based on rough path theory.
result Significantly reduced computational complexity and improved efficiency.
Paper introduces non-linearity signature to measure deep neural network performance.
problem Difficulty in explaining performance differences among similar DNN architectures.
method Affine Optimal Transport mappings to measure non-linearity.
result Signature provides better understanding of DNN inner workings.
New method uses LSTM and signature theory to solve complex financial PDEs.
problem Solving path-dependent PDEs for financial derivatives pricing.
method Combining LSTM networks and rough paths theory.
result Efficient algorithms for pricing and hedging path-dependent derivatives.
Algorithm classifies market regimes using time series signatures.
problem Classifying different market conditions from time series data.
method Utilizes path signatures and a metric structure for clustering.
result Established a connection between regime separation and point clustering.
SigMA uses signatures and attention to estimate parameters in fBm-driven SDEs.
problem Estimating parameters in SDEs driven by fBm is challenging due to non-Markovian and semimartingale issues.
method SigMA integrates path signatures with multi-head self-attention, using convolutional and MLP layers.
result SigMA outperforms other methods in accuracy, robustness, and model compactness.
The area of Handwritten Signature Verification has been broadly researched in the last decades, but remains an open research problem. The objective of signature verification systems is to discriminate if a given signature is genuine (produced by the claimed individual), or a forgery (produced by an impostor). This has …
The area of Handwritten Signature Verification has been broadly researched in the last decades, but remains an open research problem. In offline (static) signature verification, the dynamic information of the signature writing process is lost, and it is difficult to design good feature extractors that can distinguish g…
Deep IDA integrates multi-view data to classify COVID-19 severity, identifying molecular signatures.
problem Understanding the complexity of COVID-19 severity from multi-view clinical and molecular data.
method Deep IDA learns nonlinear projections to maximize view associations and class separations, with feature ranking.
result Deep IDA outperforms other methods in classifying COVID-19 severity and identifies interpretable molecular signatures.
Transformer model improves asset allocation by unifying forecasting and optimization.
problem Separation of forecasting and optimization leads to suboptimal portfolios.
method Signature Informed Transformer using path signatures and specialized attention.
result Direct minimization of Conditional Value at Risk improves performance.
A Python package for GPU-accelerated signature kernel computation.
problem Efficient computation of signature kernels for sequential data.
method GPU-accelerated algorithms and tensor sketches.
result New algorithm outperforms existing methods.
Signature Isolation Forest removes constraints from FIF by using rough path theory's signature transform.
problem Challenges in FIF's linear inner product and dictionary choices leading to unreliable results.
method Introduces Signature Isolation Forest using rough path theory's signature transform to remove linearity constraints.
result Demonstrates relevance of methods through numerical experiments and real-world applications.
Research on Offline Handwritten Signature Verification explored a large variety of handcrafted feature extractors, ranging from graphology, texture descriptors to interest points. In spite of advancements in the last decades, performance of such systems is still far from optimal when we test the systems against skilled…
Signature kernel handles sequential data with theoretical and practical advantages.
problem Handling sequential data efficiently and accurately.
method Positive definite kernel based on stochastic analysis with efficient computation.
result Strong empirical performance and theoretical guarantees.
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.
Automatic Offline Handwritten Signature Verification has been researched over the last few decades from several perspectives, using insights from graphology, computer vision, signal processing, among others. In spite of the advancements on the field, building classifiers that can separate between genuine signatures and…
Backdoors can be implanted in neural models of source code, and we detect and remove them.
problem Vulnerability of neural models to backdoors in source code.
method Defined and implemented various backdoor classes, adapted robust statistics algorithms, and detected poisoned data through spectral signatures.
result Demonstrated the ease of injecting and removing backdoors in neural models of source code.
Deep neural features identify unique vehicles from dash-cam feeds.
problem Identifying unique vehicles in dash-cam feeds for self-driving cars.
method Used pretrained YOLO network feature maps to create deep integrated feature signatures (DIFS) for 700 images of 35 vehicles and 340 images of 17 vehicles.
result Correctly identified unique vehicles at 96.7% for high resolution data and 86.8% for lower resolution data.
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.
We compute the average Tristram---Levine signature of any graph link with positive weights in a three sphere, generalizing the results of Kirby and Melvin. The main tools are the Neumann's algorithm for computing the equivariant signatures of graph links and the Reciprocity Law for Dedekind sums.
A novel signature method improves sequential data prediction accuracy.
problem Improving prediction accuracy for sequential and temporal data.
method Signature method based on rough path theory, with a specific embedding called lead-lag.
result Lead-lag embedding consistently outperforms other embeddings across various datasets and algorithms.
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 paper calculates knot invariants using Blanchfield forms and obstructs sliceness.
problem Computing and obstructing the sliceness of knots.
method Algorithmic computation of twisted signature invariants using twisted Blanchfield forms and satellite formulas.
result Illustrated algorithm for (2,q)-torus knots and obstruction of sliceness for certain knots. We use GANs and signatures to approximate conditional laws in filtering and prediction of diffusion processes.
problem Approximating conditional laws for diffusion processes with noisy observations.
method Conditional GANs combined with signatures for approximation.
result Efficient approximation of conditional laws for diffusion processes.
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.
In his Ph.D. thesis, Burak Ozbagci described an algorithm computing signatures of Lefschetz fibrations where the input is a factorization of the monodromy into a product of Dehn twists. In this note, we give a reformulation of Ozbagci's algorithm which becomes much easier to implement. Our main tool is Wall's non-addit…
We give an explicit construction of linearly independent families of knots arbitrarily deep in the (n)-solvable filtration of the knot concordance group using the ρ^1-invariant. A difference between previous constructions of infinite rank subgroups in the concordance group and ours is that the deepest infecting knots i…
Novel time series forecasting method using sliding window signatures.
problem Challenges in forecasting nonlinear and delayed time series data.
method Ridge regression with signature features calculated on sliding windows.
result Signature features effectively encode temporal and nonlinear dependencies, leading to accurate forecasts.
Methods for learning feature representations for Offline Handwritten Signature Verification have been successfully proposed in recent literature, using Deep Convolutional Neural Networks to learn representations from signature pixels. Such methods reported large performance improvements compared to handcrafted feature …
Deep networks learn clean structure before memorizing corrupted labels, leaving a spectral signature in gradient centered scatter.
problem Deep networks' transition from learning clean structure to memorizing corrupted labels under label noise.
method Analysis of the centered scatter of per-example last-layer gradients to identify Fisher Rank Inflation.
result Fisher Rank Inflation is a spectral signature of memorization under label noise, with effective rank expanding during memorization.
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.
Proposes a simple method to represent and manipulate concepts using polynomials and moment statistics.
problem Lack of a mathematical framework to define and operate on concepts.
method Characterizes concepts as zero sets of polynomials and uses moment statistics for representation; proposes a dictionary-based method to learn hierarchical structures.
result Signature of concepts can be used to discover common structures and recursively produce higher-level concepts.
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.
We provide an introduction to the signature method, focusing on its theoretical properties and machine learning applications. Our presentation is divided into two parts. In the first part, we present the definition and fundamental properties of the signature of a path. The signature is a sequence of numbers associated …
Bayesian time series forecasting improves by dynamically adapting to recent information.
problem Lack of forgetting mechanism in signature kernel for time series forecasting.
method Introducing a novel forgetting mechanism for signature features using Random Fourier Decayed Signature Features (RFDSF) with Gaussian processes (GPs).
result Demonstrates superior performance compared to other GP-based alternatives and state-of-the-art probabilistic time series forecasting algorithms.
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.
The paper values variable annuities using complex stochastic models and deep learning.
problem Valuation of variable annuities with early surrender options under non-Markovian models.
method Developed a deep signature Least Squares Monte Carlo approach to handle path-dependent continuation values.
result Fair fees increase with Hurst parameters of stock volatility and mortality force.