Estimates log-likelihood of interacting particle systems using virtual particles.
problem Inconsistent estimation of finite-particle log-likelihood in large particle systems.
method Stochastic gradient estimate using continuous trajectory and virtual particle systems.
result Convergence to stationary points of limiting mean-field system's log-likelihood.
A new stochastic algorithm approximates optimal distributions without requiring propagation of chaos.
problem Optimizing functionals over probability distributions using finite particle systems.
method Virtual particle stochastic approximation, viewed as a form of stochastic gradient descent in the Wasserstein space.
result The algorithm's output converges to the optimal distribution and produces i.i.d. samples.
New method for online learning in interacting particle systems.
problem Parameter estimation in stochastic interacting particle systems.
method Stochastic approximation of gradient of asymptotic log likelihood using continuous observations.
result Convergence to stationary points of asymptotic log-likelihood under suitable assumptions.
We present the particle stochastic approximation EM (PSAEM) algorithm for learning of dynamical systems. The method builds on the EM algorithm, an iterative procedure for maximum likelihood inference in latent variable models. By combining stochastic approximation EM and particle Gibbs with ancestor sampling (PGAS), PS…
New method learns particle system potentials from unlabeled data.
problem Learning potentials of interacting particle systems from unlabeled data with trajectory information missing.
method Introduces a self-test loss function based on stochastic evolution equation.
result Method outperforms baseline methods in robust estimation of large, high-dimensional systems.
This paper studies when particle filtering is efficient for planning in partially observed systems.
problem The efficiency of particle filtering for planning in partially observed linear dynamical systems.
method Coupling of ideal and approximate sequences to bound particle complexity.
result Polynomially many particles suffice for stable systems to approximate optimal planning.
New method generates equilibrium glass configurations efficiently.
problem Sampling equilibrium configurations of amorphous materials is slow and difficult.
method Riemannian stochastic interpolation framework combining Riemannian stochastic interpolant and equivariant flow matching.
result Enforcing geometric and symmetry constraints significantly improves generative performance.
Study infers interaction kernels from multiple particle trajectories.
problem Inferring interaction kernels from multiple particle trajectories in stochastic systems.
method Nonparametric inference approach based on regularized maximum likelihood estimator.
result Consistent estimator with near-optimal learning rate independent of state space dimension.
Deep density methods improve filtering in high-dimensional systems.
problem Nonlinear filtering in high-dimensional systems.
method Two deep density methods based on Feynman-Kac formulas and neural networks.
result Logarithmic deep backward stochastic differential equation filter outperforms classical methods in high dimensions.
Paper studies systemic robustness in financial networks using particle systems.
problem Budget control and default risk in regional financial networks.
method Mean-field particle system approach, McKean-Vlasov equations, asymptotic analysis.
result Systemic robustness measured by the proportion of surviving entities in large particle systems.
Method identifies IPS governing equations from particle data efficiently.
problem Identify governing equations of interacting particle systems efficiently.
method Combines mean-field theory and WSINDy for large N and M. result Converges with rate O(N−1/2) for N≥100. Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
Study simulates Heston-type local stochastic volatility model using particle method.
problem Simulate calibrated Heston-type local stochastic volatility model with non-standard coefficients.
method Monte Carlo particle method, Euler-Maruyama scheme, full truncation Euler scheme.
result Strong convergence of Euler-Maruyama scheme with rate 1/2 in time, up to a logarithmic factor.
Paper studies particle method for LSV model calibration, proving convergence and error bounds.
problem Calibration of local-stochastic volatility models with open well-posedness question.
method Regularized Euler--Maruyama scheme for particle approximation of McKean--Vlasov dynamics.
result Strong convergence of the Euler--Maruyama scheme with rate 1/2 in step-size.
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random Batch Method (RBM) for interacting particle systems proposed by Jin et al to the …
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian particle system, in which …
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
Two SVGD variants achieve fast convergence with provable guarantees.
problem Understanding and improving SVGD's performance with finite particles.
method Introducing virtual particles and novel stochastic approximations.
result Provable fast convergence rates for finite-particle SVGD variants.
New AD methods improve likelihood estimation for partially observed systems.
problem Estimating likelihood functions for partially observed nonlinear systems.
method Embedding AD particle filter methods in a theoretical framework, developing new algorithms for likelihood maximization.
result Mean squared error significantly lower than existing algorithms.
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.
Unified ML approach for SDEs in bounded domains.
problem Challenges in simulating SDEs with particle exit phenomena.
method Hybrid approach combining diffusion model and exit prediction network.
result Accurate modeling of interior dynamics and boundary interactions.
GER learns particle dynamics from unpaired snapshots using physics-informed GANs.
problem Learning particle dynamics from unpaired snapshots with physics constraints.
method Physics-informed generative model to fit particle ensemble distributions.
result Inferred dynamics of particle ensembles governed by SODEs up to 100 dimensions.
New algorithm tames non-linear growth in stochastic optimization.
problem Computational challenges in E-step of EM framework.
method Employing interacting particle systems and taming techniques to create tIPLA.
result Non-asymptotic convergence error estimates in Wasserstein-2 distance for tIPLA.
The paper studies how noise synchronizes tokens in deep transformer models.
problem Understanding synchronization in deep learning models with noise.
method Proves convergence to a stochastic particle system and identifies the limiting SDE.
result The limiting model displays synchronization by noise and exponential dissipation of interaction energy.
Develops a new algorithm for estimating model parameters using interacting particle systems.
problem Estimating parameters of latent variable models.
method Interacting Particle Langevin Algorithm (IPLA) based on Langevin diffusion.
result Nonasymptotic optimisation error bounds for the estimator.
A new particle filter uses diffusion models to improve state estimation from noisy data.
problem Sequentially estimating the state of a dynamical system from noisy and incomplete observations.
method Uses a diffusion model to simulate and predict system dynamics, incorporating noisy observations to refine predicted states.
result An unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic process, and MCMC moves to propose new values for the parameters. We show how p…
New model captures state-dependent variability in partially observed systems.
problem Structured stochasticity not captured by constant-variance models.
method State-coupled stochastic volatility framework with particle expectation-maximization.
result Model consistently reduces recovery bias under partial observation.
It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose deterministic jump intensity is called local intensity. The Stochastic Local Intensity (SLI) models such as the one proposed by Arnsdorf and Halperin…
In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with a limited number of particles. Particles are pushed forward from the prior to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between…
In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in the timestep and second order in the spatial gri…
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample …
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with t…
Paper explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.
problem Bayesian inference and Markov chain Monte Carlo methods.
method Stein variational gradient descent (SVGD) with deterministic and stochastic dynamics.
result Identifies Stein-Fisher information as the leading order contribution in the long-time and many-particle regime.
Paper uses averaging from many particle filters to approximate posterior predictive distributions.
problem Approximating posterior predictive distributions efficiently and accurately.
method Particle swarm filter algorithm that averages many particle filter approximations.
result Law of large numbers and central limit theorem support the method's effectiveness.
Interacting particle methods are increasingly used to sample from complex and high-dimensional distributions. These stochastic particle integration techniques can be interpreted as an universal acceptance-rejection sequential particle sampler equipped with adaptive and interacting recycling mechanisms. Practically, the…
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein gradient flows. With a rigorous non-asymptotic convergence theory developed recently…
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.
This paper presents a new interacting particle system and uses it as a spin model for financial market microstructure. The asymptotic analysis of this stochastic process exhibits a lower bound to the contemporaneous measurement of price and trading volume under the invariant measure in the `frozen' phase of the supercr…
IBPF algorithm tackles high-dimensional parameter learning for complex systems.
problem Learning high-dimensional parameters in complex, partially observed, and nonlinear systems.
method Iterated Block Particle Filter (IBPF) for graphical state space models.
result IBPF algorithm consistently beats the curse of dimensionality across various experiments.
The collective phenomena of a liquid market is characterized in terms of a particle system scenario. This physical analogy enables us to disentangle intrinsic features from purely stochastic ones. The latter are the result of environmental changes due to a `heat bath' acting on the many-asset system, quantitatively des…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate…
Study on deep multi-head self-attention dynamics, proving homogenized limits under specific scalings.
problem Understanding the behavior of deep multi-head self-attention models as depth increases.
method Random model of deep multi-head self-attention, viewing depth as time, and analyzing the residual stream as a particle system.
result Homogenized limit of the dynamics, leading to deterministic or stochastic behavior depending on scaling, with implications for representation collapse.
iDEM generates samples from Boltzmann densities without data.
problem Generating statistically independent samples from unnormalized distributions.
method Iterative algorithm using energy and gradient for diffusion-based sampler training.
result iDEM achieves state-of-the-art performance and trains faster than existing methods.
Coercivity condition ensures learning of interacting particle systems.
problem Ensuring identifiability of interaction functions in learning systems of interacting particles.
method Equivalence of coercivity condition to strictly positive definiteness of an integral kernel.
result For ergodic systems, the integral kernel is strictly positive definite, satisfying the coercivity condition.
Quasi-equilibrium models for aggregate variables are widely-used throughout finance and economics. The validity of such models depends crucially upon assuming that the systems' participants behave both independently and in a Markovian fashion. We present a simplified market model to demonstrate that herding effects bet…
New method improves Euler approximation for local stochastic volatility models.
problem Well-posedness of Euler approximation for local stochastic volatility models.
method Start with a well-defined Euler approximation to the formal McKean-Vlasov equation, followed by a half-step scheme.
result Showed weak order one for the Euler discretization, plus error terms.
We investigate unification of two systems of identical elements having different dimensions which may be of interest for both physics and economics. Characteristic parameters as well as explicit formulae for the temperature (in economics - capital turnover) and dimension of the united system are obtained as functions o…