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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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…
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.
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.
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.
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.
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.
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.
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.
Dynamic Structural Causal Models handle time-dependent systems with cycles and latent confounding.
problem Representing and analyzing systems of Stochastic Differential Equations (SDEs) with DSCMs.
method Define time-splitting and subsampling operations to analyze DSCMs of SDEs, and apply existing causal discovery algorithms to time-series data.
result DSCMs provide a graphical Markov property for SDEs and enable identification of time-dependent causal effects.
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.
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.
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.
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.
DDPM encoder matches optimal transport for natural images.
problem Understanding theoretical properties of DDPM latent space.
method Showed DDPM encoder matches optimal transport for common distributions.
result DDPM encoder map coincides with optimal transport map for natural images.
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolu…
New SDEs use G-Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced G-SDEs with coefficients dependent on current state and solution as random variable. result Validated new SDE framework for complex stochastic systems.
Study on the smoothness of solutions to a specific type of stochastic differential equation.
problem Regularity of solutions to mean-field G-SDEs. method Analysis of first and second order Fréchet differentiability in the random initial condition.
result Established the Fréchet differentiability of the solution and specified the corresponding equations.
New SDE model for continuous-time reinforcement learning.
problem Modeling exploration in continuous-time reinforcement learning.
method Introduced grid-sampling SDE as a proxy model.
result Wellposedness of the SDE in the presence of jumps.
This paper uses SDEs to analyze GANs training and long-run behavior.
problem Understanding the training process and long-run behavior of GANs.
method Established SDE approximations for GANs training and analyzed long-run behavior via invariant measures.
result The long-run behavior of GANs training can be studied via the invariant measures of its SDE approximations.
The paper identifies generators of linear SDEs with noise types.
problem Identifying the generator of linear SDEs from their solution distribution.
method Deriving sufficient and necessary conditions for additive noise, and sufficient conditions for multiplicative noise.
result Generic conditions for identifying the generator of linear SDEs with both types of noise.
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.
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.
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.
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.
We explain how Itô Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be used to derive graphical representations of Itô SDEs. We show how jets can be used…
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.
New geometric SDEs and discretizations on Riemannian manifolds with error bounds.
problem Modeling diffusion processes on Riemannian manifolds with geometric SDEs.
method Introduced a new construction of geometric SDEs and provided non-asymptotic error bounds.
result First non-asymptotic error bound for geometric Euler-Murayama discretization.
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.
New method identifies SDE drift and diffusion from temporal data.
problem Learning SDE parameters from temporal data, especially in noisy or incomplete data.
method Entropy-regularized optimal transport, APPEX algorithm.
result Can almost always recover drift and diffusion from temporal marginals.
New algorithm optimizes nonlinear SDEs online with convergence guarantees.
problem Optimizing nonlinear stochastic differential equations (SDEs) is computationally challenging.
method Forward propagation algorithm that solves an SDE derived using forward differentiation.
result Convergence theorem for nonlinear dissipative SDEs with bounds on stochastic fluctuations.
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.
We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the SDEs and is strongly convergent with rate one. Moreover, we show that this general …
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a use…