Proposes neural SDEs with change points for better time series modeling.
problem Restrictions in modeling time series with distributional shift.
method Generative adversarial networks (GANs) for SDEs and change point detection.
result Jointly learns change points and SDE model parameters.
Neural SDEs model continuous sequences using neural networks.
problem Modeling continuous-time dynamics in sequence data.
method Interprets time-series as samples from a continuous dynamical system, parameterized by Neural SDE.
result Demonstrates superior performance in diverse sequence modeling tasks.
Neural SDEs reduce variance in stochastic simulations.
problem Efficiency of Monte Carlo simulations in finance.
method Use neural SDEs with control variates parameterized by neural networks.
result Prove optimality conditions for variance reduction in SDEs with infinite activity.
TFM trains Neural SDEs without backpropagation, improving clinical time series modeling.
problem Modeling irregularly sampled time series in medicine.
method Trajectory Flow Matching (TFM) using flow matching for generative modeling.
result TFM improves performance on clinical time series datasets.
Model change points in time-series data with neural SDEs and variational autoencoders.
problem Modeling change points in time-series data with neural stochastic differential equations.
method Proposes a novel model formulation and training procedure based on the variational autoencoder framework, alternating between updating neural SDE parameters and change points.
result Demonstrates the expressive power of the proposed model in modeling both classical parametric SDEs and real datasets with distribution shifts.
We developed efficient methods to compute gradients for Neural SDEs, improving training speed and accuracy.
problem Training Neural SDEs requires accurate and efficient computation of gradients, which is challenging due to the complexity of SDEs.
method We introduced a reversible Heun method for solving backwards-in-time SDEs and a Brownian Interval for sampling and reconstructing Brownian motion.
result Our methods significantly improve training speed and accuracy for Neural SDEs, outperforming state-of-the-art techniques.
Bayesian neural SDEs calibrate financial models robustly.
problem Calibrating financial models using neural SDEs for robustness.
method Bayesian framework with prior and likelihood, global approximation theorem, Langevin algorithm.
result Robust bounds on implied volatility surface learned from historical and option data.
Neural-SDE models improve option hedging with lower errors and robustness.
problem Improving option hedging strategies using machine learning.
method Derive sensitivity-based and minimum-variance-based hedging strategies using neural-SDE market models.
result Neural-SDE models achieve lower hedging errors and are more robust than traditional models.
Neural-SDE model accurately simulates option risks.
problem Estimating accurate risk scenarios for option portfolios.
method Arbitrage-free neural-SDE market model for joint option dynamics.
result Models produce more efficient and accurate VaR evaluations.
Combines neural networks with SDEs for robust pricing and hedging.
problem Inadequate financial models lead to undetected and unquantifiable risks.
method Neural SDEs integrating machine learning and classical SDEs.
result Robust bounds for derivative prices and hedging strategies.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…
Improved SDE-BNN model reduces NFEs and accelerates convergence.
problem High computational cost and convergence instability in SDE-BNNs.
method Nesterov's Accelerated Gradient (NAG) method integrated into SDE-BNN framework.
result Significantly reduced number of function evaluations (NFEs) and improved predictive accuracy.
Neural models price financial options without assuming underlying price forms.
problem Pricing financial options under flexible price processes.
method Apply neural SDEs as universal approximators, use Wasserstein distance for training.
result Error in option prices bounded by Wasserstein distance used for training.
Neural SDEs model suicide risk with compact state space constraints.
problem Modeling suicide risk with irregular, noisy, and partially observed data.
method Developed neural SDEs confined to compact state spaces, addressing domain constraints and numerical stability.
result Improved forecasts and optimization dynamics over standard models on EMA datasets.
Improved noise estimation in latent neural SDEs enhances model accuracy.
problem Latent neural SDEs underestimate noise, limiting their stochastic dynamics modeling.
method Explicit additional noise regularization in the loss function.
result Model accurately captures diffusion component of stochastic time series data.
New method learns SDEs without integrators, speeding up computation.
problem Computational expense in learning SDEs using neural networks.
method Importance-sampling estimator for SDEs, leveraging parallelism.
result Lower-variance gradient estimates and massive computation time reductions.
Novel method for SDE calibration from sparse data using neural flows.
problem Calibrating SDEs from sparse, noisy observations.
method Characterization of posterior SDE using neural networks trained to solve a PDE with multiplicative updates.
result Significant improvement in scalability and accuracy compared to classical methods.
We develop a variational framework for SDEs driven by fractional noise.
problem Capturing long-term dependencies in SDEs driven by fractional noise.
method Markov approximation of fractional Brownian motion, variational inference, neural networks.
result Efficient variational inference of posterior path measures for neural-SDEs.
Sig-SDE model integrates signatures with SDEs for financial data.
problem Calibrating models to exotic financial products with non-linear dependencies.
method Integrating signatures from stochastic analysis with neural SDEs.
result Sig-SDE provides theoretical guarantees for convergence.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabl…
This paper bridges the gap between ODE and SDE in diffusion models using Fokker-Planck equations.
problem Empirical evidence shows that ODE-based samples from score-based diffusion models are inferior to SDE-based samples.
method The paper rigorously describes dynamics and approximations in training score-based diffusion models, linking them to Fokker-Planck equations.
result Adding a regularisation term based on the Fokker-Planck residual can close the gap between ODE- and SDE-induced distributions.
The paper analyzes convergence of neural SDEs as sample size increases.
problem Understanding the limiting behavior of neural SDEs as sample size grows.
method Analyzes Hamilton-Jacobi-Bellman equation and uses stochastic maximum principle.
result Convergence of minima and optimal parameters of neural SDEs as sample size increases.
NSFs learn SDE transition laws for efficient sampling.
problem Efficiently sampling between arbitrary time points in SDEs.
method Conditional normalising flows with architectural constraints.
result Up to two orders of magnitude speed-ups at large time gaps.
NANSDE-Net models time series with memory using neural ARMA-type noise.
problem Modeling time series with long- or short-memory characteristics.
method Developed NANSDE-Net, a generative model that incorporates Neural Network-kernel ARMA-type noise.
result NANSDE-Net matches or outperforms existing models in reproducing long- and short-memory features of data.
Paper introduces non-adversarial training for Neural SDEs using signature kernel scores.
problem Stability and mode collapse issues in adversarial training of Neural SDEs.
method Uses signature kernel scores as objective function for non-adversarial training.
result Non-adversarial training leads to better performance and more stable models.
New method for Bayesian inference of Lévy-driven SDEs with jumps.
problem Bayesian inference for Lévy-driven SDEs is challenging due to discontinuities and heavy tails.
method Neural exponential tilting framework for variational inference.
result Accurately captures jump dynamics and reliable posterior inference in heavy-tailed regimes.
Delay-SDE-net models time series with memory and uncertainty, outperforming other models.
problem Accurately modeling time series with memory and uncertainty.
method Stochastic delay differential equations (SDDEs) neural network model with aleatoric and epistemic uncertainty.
result The Delay-SDE-net consistently outperforms other models in predicting time series values and uncertainties.
Develops a nonparametric model for arbitrage-free pricing of illiquid derivatives.
problem Modeling joint dynamics of liquid vanilla options for arbitrage-free pricing of illiquid derivatives.
method Derives a state space for prices respecting underlying financial constraints using neural networks and imposes constraints to preserve no-arbitrage conditions.
result Neural SDE models are guaranteed to satisfy a set of linear inequalities and validated with numerical experiments.
Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE), usually rely on a completely deterministic feed-forward operation. This work pr…
Neural networks improve financial derivative pricing accuracy.
problem Improving accuracy in financial derivative pricing.
method Use neural networks to model drift and volatility in SDE models, optimize using SGD for European options and PDE for American options.
result Neural network models outperform traditional models in pricing derivatives.
SDE-Net quantifies uncertainty in deep nets using stochastic dynamics.
problem Uncertainty quantification in deep neural networks.
method Viewing DNN transformations as state evolution of a stochastic dynamical system, introducing a Brownian motion term for epistemic uncertainty.
result SDE-Net outperforms existing methods in uncertainty estimation across various tasks.
Paper introduces FDM for efficient training of Neural SDEs.
problem Training Neural SDEs using existing methods is computationally expensive and unstable.
method Developed a novel scoring rule called Finite Dimensional Matching (FDM) to bypass signature kernels and reduce training complexity.
result FDM achieves superior performance in terms of computational efficiency and generative quality.
SING improves state inference in latent SDE models for better drift function estimation.
problem Intractable posterior inference in latent SDE models.
method Natural gradient variational inference.
result SING provides faster and more reliable inference in latent SDE models.
New method speeds up SDE inference by matching moments to FPK equation.
problem Efficiency of sampling schemes in high-dimensional SDEs.
method Direct approximation of Fokker-Planck-Kolmogorov equation by matching moments.
result Fast, scalable inference in high-dimensional latent spaces.
Deep learning accelerates Monte Carlo SDE simulations with large time steps.
problem Accurate simulation of SDEs with large time steps.
method Polynomial chaos expansion with neural network learned stochastic collocation points.
result Data-driven scheme achieves strong convergence in Monte Carlo simulations.
A new framework models uncertainty in structured temporal data using SDEs and neural networks.
problem Uncertainty quantification in machine learning applications involving structured and temporal data.
method Integrates stochastic differential equations (SDEs) with deep generative models in a variational autoencoder framework.
result Improves uncertainty quantification in machine learning applications involving structured and temporal data.
Proposes methods to include distributional information in MV-SDEs for better modeling of interacting particle systems.
problem Modeling the behavior of an infinite number of interacting particles with distributional information.
method Semi-parametric methods and estimators for MV-SDEs.
result Explicitly including distributional dependence improves performance in modeling temporal data with interaction.
Deep learning estimates time-varying Markov model parameters.
problem Estimating time-dependent parameters in Markov models.
method Reframes parameter estimation as an optimization problem using maximum likelihood.
result Real solution close to SDE with neural network-derived parameters under specific conditions.
Generative model uses SDEs to transform data distributions.
problem Creating data from complex distributions.
method Stochastic differential equations (SDEs) for data transformation.
result Achieved record-breaking performance in image generation.
SCOTCH learns system structure from irregular time series using neural SDEs.
problem Learning system structure from irregular time series data.
method SCOTCH uses neural stochastic differential equations (SDE) with variational inference.
result SCOTCH improves structure learning performance on synthetic and real-world datasets.
Neural network models accurately price assets in rough Bergomi model.
problem Accurately pricing assets in the rough Bergomi model with hidden parameters.
method Used a neural SDE to learn the forward variance curve, proposing a numerical scheme for simulation.
result The learned forward variance curve calibrates asset prices and option prices simultaneously.
Faster training of neural ODEs using Gauß-Legendre quadrature.
problem Training neural ODEs is slow due to solving ODEs numerically.
method Use Gauß-Legendre quadrature to solve integrals faster than ODE-based methods.
result Faster training of neural ODEs, especially for large models.
Study on neural network initialization with shaped infinite depth-and-width networks.
problem Understanding the distribution of random covariance matrices in shaped infinite-depth-and-width networks.
method Introduced the Neural Covariance SDE to model the distribution of the random covariance matrix.
result Identified the precise scaling of the activation function necessary for a non-trivial limit.
A new method simulates implied volatility surfaces for multiple assets.
problem Generating consistent market scenarios for multiple asset implied volatilities.
method Combining functional data analysis and neural SDEs with a penalty for model misspecification.
result Simulated market scenarios are consistent with historical features and lie within the sub-manifold of essentially free static arbitrage.
Study models deep learning training dynamics using locally elastic SDEs to reveal feature separability.
problem Understanding how deep learning models separate features from different classes during training.
method Modeling deep learning training using locally elastic SDEs with a drift term reflecting backpropagation impact.
result Local elasticity in SDEs leads to linear separability of features, resulting in vanishing training loss.
Neural networks estimate SDEs with jump noise using a Tamed-Milstein scheme.
problem Estimating drift and diffusion functions in SDEs with jump noise.
method Tamed-Milstein scheme with neural networks as non-parametric approximators.
result Flexible estimation of complex nonlinear dynamics in systems with state-dependent noise.
Neural Diffusion Intensity Models simplify Cox processes inference.
problem Intractable nonparametric estimation and posterior inference of latent stochastic intensity in Cox processes.
method Variational framework using neural SDEs, with theoretical guarantee of ELBO maximization coinciding with maximum likelihood estimation.
result Accurate recovery of latent intensity dynamics and posterior paths with significant speedup.