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.
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48 results for “Continuous-time SDEs”
Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shiftscs.LG
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.
A new approach models exploration in continuous-time RL using random measures.
problem Modeling exploration in continuous-time reinforcement learning.
method Random measure approach to control execution in continuous-time RL.
result Grid-sampling limit SDE can replace existing models for theoretical analysis and learning algorithms.
New method optimizes SDE models using continuous-time gradient descent.
problem Optimizing over the stationary distribution of SDE models.
method Continuous-time stochastic gradient descent for SDE models.
result Asymptotic convergence to the direction of steepest descent.
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.
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.
Bessel-like birth-death processphysics.soc-ph
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDE…
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.
CT-OT Flow estimates continuous-time dynamics from discrete snapshots.
problem Estimating continuous-time dynamics from temporally aggregated snapshots with noisy or uncertain timestamps.
method Two-stage framework: aligning neighboring intervals via partial optimal transport (POT) and reconstructing a continuous-time distribution through temporal kernel smoothing.
result Reduces distributional and trajectory errors compared with existing methods across synthetic and real datasets.
We establish causal semantics for SDEs and develop methods to reason about them.
problem Understanding causal relationships in systems modeled by stochastic differential equations.
method We introduce a causal graph framework, Markov properties, and do-calculus for SDEs.
result We prove the -separation Markov property and do-calculus for causal SDEs.
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.
Stochastic neural ODEs outperform deterministic ones on image classification tasks.
problem Improving generalization in continuous-time models like neural ODEs.
method Empirical study of stochastically regularized neural ODEs using SDEs.
result Data augmentation negates the benefits of stochastic regularization, making neural ODEs and SDEs nearly equivalent.
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.
Enhances RL for jump processes using MSBVE algorithm.
problem Challenges in continuous-time RL with jumps and noise.
method Introduces MSBVE algorithm to minimize quadratic variation error.
result MSBVE algorithm outperforms MSTDE in jump processes.
We study an agent-based stock market model with heterogeneous agents and friction. Our model is based on that of Foellmer-Schweizer(1993): The process of a stock price in a discrete-time framework is determined by temporary equilibria via agents' excess demand functions, and the diffusion approximation approach is appl…
Generating solution paths of Markovian stochastic differential equations using diffusion modelscs.LG
New AI method generates SDE paths without explicit coefficients.
problem Simulating unknown Markovian SDEs with limited data.
method Uses conditional diffusion models on sample paths.
result Consistently outperforms alternative methods in KL divergence.
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.
The generator gradient estimator is an adjoint state method for stochastic differential equationsmath.OC
New estimator for SDEs is shown to be an adjoint state method.
problem Estimating gradients for overparameterized SDEs efficiently.
method Demonstrates generator gradient estimator as an adjoint state method.
result Generator gradient estimator is an adjoint state method for SDEs.
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.
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.
Paper presents a new approach to a strategic insider equilibrium problem in continuous time.
problem Continuous time Kyle-Back model between insider and market marker.
method Uses forward-backward stochastic differential equations (FBSDEs) for characterization of equilibria.
result Characterizes all equilibria through FBSDEs and shows uniqueness of equilibrium without Markovian restrictions.
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.
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.
HA-SME models SGD dynamics with Hessian info for better escaping behaviors.
problem Capturing the escaping behaviors of SGD from stationary points.
method HA-SME, a novel SDE with Hessian info in drift and diffusion.
result HA-SME achieves best approximation error and recovers SGD dynamics for quadratics.
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…
Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.
problem Approximating solutions to Lévy-driven SDEs for financial derivatives pricing.
method Weak multilevel Monte-Carlo scheme with state space discretization of Lévy processes.
result Efficient approximation of financial derivatives pricing models.
Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep learning settings admits a non-Gaussian, heavy-tailed behavior. This suggests tha…
Continuous-time PCD for MLE with explicit error bounds.
problem Maximum likelihood estimation of unnormalised densities.
method Continuous-time formulation as coupled SDEs, deriving UiT bounds.
result Explicit error bounds between PCD iterates and MLE solution.
A new RG approach connects discrete and continuous time descriptions of Gaussian processes.
problem Discretization of continuous stochastic processes for accurate simulation or model inference.
method Renormalization Group (RG) approach for Gaussian time series generated by auto-regressive models.
result RG fixed points correspond to discretizations of linear SDEs, providing insights into process accuracy.
Work on SGDm under heavy-tailed noise, revealing its generalization properties.
problem Understanding generalization of SGDm under heavy-tailed noise.
method Analysis of continuous-time limit (SDE) and discrete-time SGDm, establishing generalization bounds.
result SGDm can have worse generalization in the presence of heavy-tailed noise for quadratic loss functions.
Paper solves time-inconsistent control problems with BSDEs.
problem Time-inconsistent stochastic control in continuous time.
method Probabilistic representation via BSDEs.
result Equilibrium value function resolved for inconsistent cases.
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.
The choice of how to retain information about past gradients dramatically affects the convergence properties of state-of-the-art stochastic optimization methods, such as Heavy-ball, Nesterov's momentum, RMSprop and Adam. Building on this observation, we use stochastic differential equations (SDEs) to explicitly study t…
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct -optimal stopping tim…
SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationsstat.ML
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 this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our framework guarantees existence of weak solutions of the nonlinear SDEs under the physi…
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
New SDEs use -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced -SDEs with coefficients dependent on current state and solution as random variable.
result Validated new SDE framework for complex stochastic systems.
PMM uses Bayesian inference to generate data from noisy approximations.
problem Creating flexible generative models for various data types.
method Bayesian inference and conjugate pairs of distributions.
result PMM achieves performance competitive with existing generative models.
Study on the smoothness of solutions to a specific type of stochastic differential equation.
problem Regularity of solutions to mean-field -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.
Stochastic differential equation approximation for linear TD(0) under Markovian noise
problem Temporal-difference learning with linear function approximation
method Stochastic differential equation approximation
result Explains the constant-stepsize error floor
The paper develops a method to learn SDE drift functions from sparse, noisy data.
problem Learning SDE drift functions from sparse and noisy data without strong structural assumptions.
method Data-driven approach using a penalized negative log-likelihood functional over RKHS, with an EM algorithm employing SMC for approximations.
result The method enables accurate estimation of SDE drift functions in low-data regimes.
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.
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition,…
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.
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
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.