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.
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.
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.
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.
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.
SDE Matching eliminates simulation for training Latent SDEs, achieving similar performance.
problem Training Latent SDEs with adjoint sensitivity methods is computationally expensive and limited.
method SDE Matching, inspired by Score- and Flow Matching, eliminates simulation for training Latent SDEs.
result SDE Matching achieves performance comparable to adjoint sensitivity methods while reducing computational complexity.
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. This work considers the diffusion limit of suc…
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.
Stochastic normalizing flows use SDEs for efficient training and sampling.
problem Efficient maximum likelihood estimation and variational inference.
method Continuous normalizing flows extended with stochastic differential equations (SDEs) and rough path theory.
result Stochastic normalizing flows enable efficient training and sampling from complex distributions.
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.
Method learns latent SDEs from high-dimensional time series.
problem Learning latent stochastic differential equations from time series data.
method Self-supervised learning with variational autoencoders and Euler-Maruyama approximation.
result Can recover SDE coefficients and latent variables up to isometry with infinite data.
We solve continuous-time latent SDE identifiability using diffusion shifts.
problem Identifiability of latent SDEs in continuous-time time series.
method Environment-induced shifts in diffusion covariance for additive-noise latent SDEs.
result Two diagonal diffusion regimes with distinct variance ratios identify latent coordinates up to permutation and scaling.
Proposes SDE framework for uncertainty quantification in graph neural networks.
problem Lack of uncertainty quantification in graph neural networks.
method Introduces Latent Graph Neural Stochastic Differential Equations (LGNSDE) with Bayesian prior-posterior mechanism and Brownian motion.
result LGNSDEs provide theoretically sensible guarantees for uncertainty estimates and are robust to perturbations.
Simulation-free VI closes the approximation gap in latent SDEs
problem Recovering dynamical systems from noisy observations
method Helmholtz-SDE
result Recovers dynamics more faithfully than prior methods
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.
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.
Efficiently infers latent SDEs with scalable memory and time costs.
problem Inference of latent SDEs with high time and memory complexity.
method Amortized reparametrization of expectations under linear SDEs, coupled with efficient gradient approximation.
result Achieves similar performance to adjoint sensitivities with fewer model evaluations.
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
Develops a method to model neural dynamics with flexible yet interpretable latent states.
problem Capturing complex nonlinear dynamics in neural time series while maintaining interpretability.
method Gaussian Process Switching Linear Dynamical System (gpSLDS) that balances expressiveness and interpretability.
result Favorable performance in comparison to rSLDS on synthetic and real neuroscience data.
Generative models use latent abstractions to create images.
problem Understanding how generative models create high-dimensional data like images.
method Developed a theoretical framework using SDE and information theory.
result Diffusion models can be seen as a non-linear filter driven by latent abstractions.
New method learns latent energy models using particle algorithms.
problem Learning latent variable models with energy priors.
method Continuous-time SDEs for MMLE, particle-based discretization.
result Practical algorithm converges to solve MMLE problem.
AdjointDEIS simplifies diffusion model optimization.
problem Optimizing diffusion models with respect to a differentiable metric.
method Novel bespoke ODE solvers for continuous adjoint equations.
result Continuous adjoint equations simplify to a simple ODE, improving efficiency.
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.
LatentFlow simplifies conditioning of stochastic processes without training.
problem Intractable conditional laws for complex stochastic models.
method Writing stochastic process as latent innovation, reducing conditioning to latent-space inference.
result Exact conditional sampling across various model classes.
Generates consistent IV surfaces using VAEs and SDE models.
problem Creating arbitrage-free IV surfaces from historical data.
method Combining VAEs with SDE models for parameter distribution, sampling, and decoding.
result Superior out-of-sample performance of the refined VAE model.
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.
New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
Enhances deep kernel learning with stochastic latent variables for better model regularization.
problem Weak model regularization in deep kernel learning, especially on small datasets.
method Introduces DLVKL model with stochastic latent variables, NSDE for expressive posterior, and hybrid prior.
result DLVKL-NSDE outperforms existing deep GPs on large datasets.
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.
Quantum algorithm samples from SDEs using DQCs and quantile mechanics.
problem Sampling from solutions of stochastic differential equations.
method Differentiable quantum circuits (DQCs) encoding latent variables, quantile mechanics.
result Quantum algorithm generates time-series from SDEs.
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.
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.
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.
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.