SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
problem Sampling partially known densities or using gradients in probabilistic models.
method Smoothed Particle Hydrodynamics (SPH) for modeling fluid dynamics to approximate target densities.
result SPH-ParVI provides fast, flexible, scalable, and deterministic sampling for Bayesian inference and generative models.
Impute missing events in continuous-time sequences using particle smoothing.
problem Missing events in continuous-time sequences.
method Particle smoothing with trainable bidirectional LSTM proposals.
result Imputed sequences have low Bayes risk compared to ground truth.
This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.
problem Optimizing functions of probability measures with displacement convex properties.
method Particle gradient descent applied to displacement convex functions with theoretical guarantees.
result Finite number of particles and computations are sufficient to find optimal solutions for displacement convex functions.
A new method for generating samples without training, using smoothed score matching.
problem Generating samples efficiently and without training.
method Moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD).
result The method enables fast, robust, training-free sampling with competitive sample fidelity and diversity.
SVO improves particle diversity and variational bounds in filtering SMC.
problem Improving variational bounds in particle filtering with limited samples.
method Introduces Particle Smoothing Variational Objectives (SVO) for smoothed approximate posterior through subsampling.
result SVO outperforms filtered objectives with fewer Monte Carlo samples on nonlinear systems.
We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run fo…
Proves some flat spacetimes can't be extended smoothly.
problem Proving smooth extension of certain FLRW spacetimes.
method Utilizing Sbierski's C0-inextendibility techniques. result Proves C0-inextendibility of spatially flat FLRW spacetimes. We prove that any hyperbolic end with particles (cone singularities along infinite curves of angles less than π) admits a unique foliation by constant Gauss curvature surfaces. Using a form of duality between hyperbolic ends with particles and convex globally hyperbolic maximal (GHM) de Sitter spacetime with particle…
dSMC improves parallel processing of state-space models.
problem Processing multiple observations efficiently in state-space models.
method A parallel-in-time particle smoother that reduces complexity to log(T).
result dSMC achieves O(log(T)) time complexity on parallel architectures.
Study particle dynamics in non-differentiable fractal spaces.
problem Understanding motion in non-smooth, probabilistic geometries.
method Use fiber bundle theory to characterize multivalued geodesic trajectories.
result Developed a hybrid theory combining surface and stochastic process theories.
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…
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
The paper analyzes rates for a modified gradient descent method using Stein variational gradients.
problem Improving the accuracy of gradient descent methods for complex target distributions.
method Derives finite-particle rates for regularized Stein variational gradient descent (R-SVGD).
result Establishes explicit non-asymptotic bounds for time-averaged empirical measures.
A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.
problem Improving generative modeling by addressing non-conservatism issues.
method Proposes a conservative drifting method using kernel density estimator gradients to address non-conservatism.
result Proves finite-particle convergence rates for the conservative method, providing explicit quadrature constants.
This work develops a particle system to approximate Fisher-Rao gradient flows in mean-field optimization.
problem Optimizing probability measures in neural network contexts.
method Constructing an interacting particle system approximating Fisher-Rao gradient flows.
result Propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimization.
Gaussian Process Hydrodynamics approximates fluid flow equations using probabilistic kernels.
problem Approximating fluid flow equations with fewer particles and uncertainty estimates.
method Lagrangian particle-based approach with Gaussian Process (GP) prior and physics-informed kernels.
result GPH requires fewer particles and provides uncertainty estimates.
Unified framework for photon and massive particle hypersurfaces in stationary spacetimes.
problem Understanding photon and massive particle hypersurfaces in stationary spacetimes.
method Unified framework using Killing-invariant timelike hypersurfaces and associated Finsler structures.
result Conditions for a hypersurface to be a photon or massive particle hypersurface are established.
A new algorithm for optimizing probability distributions converges linearly.
problem Optimizing functionals over families of probability distributions.
method Variational transport: particle-based algorithm approximating Wasserstein gradient descent.
result Variational transport converges linearly to the global minimum of the objective functional.
We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward a…
SIFG uses noisy particles to efficiently sample from complex distributions.
problem Efficient sampling from complex distributions using particle-based methods.
method SIFG introduces a semi-implicit functional gradient flow with Gaussian noise to improve sampling efficiency and accuracy.
result SIFG achieves strong theoretical convergence guarantees and efficient sampling.
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify variou…
Study controlled contagion with state-dependent killing, proving a comparison principle.
problem Analyzing controlled McKean--Vlasov contagion with state-dependent killing.
method Proof of a comparison principle using Wasserstein smooth-gauge comparison and killing-jump absorption estimates.
result Established a comparison principle for the two-population killed-particle HJB.
Novel method uses Gaussian process to estimate particle sizes from scattering data.
problem Estimating particle size distributions from noisy optical scattering measurements.
method Constrained Gaussian process regression with normalization constraints.
result Accurately reconstructs particle size distributions from noisy data.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of vi…
A new algorithm reduces bias in estimating model parameters.
problem Efficient estimation of model parameters in non-linear state-space models.
method Parisian particle Gibbs (PPG) algorithm for bias reduction in online learning.
result Non-asymptotic bounds on bias and variance for PPG.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Smooth deformations of a Minkowski type metric in a four-dimensional space-time manifold are considered. Deformations of the basic spin-tensorial fields associated with this metric are calculated and their application to calculating the energy-momentum tensor of a massive spin 1/2 particle is shown.
Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization …
We present a 1-parameter family of finite action solutions to the S0(2,1) Hitchin's equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multi-particle generalization of our basic solutions.
Develops a gradient flow for Muon optimizer, a method for optimization.
problem Optimization of complex systems with matrix-valued parameters.
method Gradient flow on probability measures induced by regularized Muon optimizer.
result Derives continuous-time limits and proves Hamiltonian dissipation.
Smooth Schrödinger Bridges improve trajectory inference by smoothing Gaussian processes.
problem Improving trajectory inference in applications like particle tracking.
method Generalizes Schrödinger Bridge problem to smooth Gaussian processes, solving the problem on phase space.
result The method outperforms existing methods on real datasets.
Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping we demonstrate that the steady parameters associated with the physical environment det…
We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then consider geometric consequences of this stochastic representation. Based on this …
This paper analyzes error bounds for biased SMC samplers in conditional sampling.
problem Analyzing error bounds for biased SMC samplers in conditional sampling.
method Develops a non-asymptotic error analysis for SMC samplers with biased mutation kernels.
result Derives the first non-asymptotic error bound for conditional sampling with score-based diffusion models.
A computer vision approach improves neutral particle detection in particle flow algorithms.
problem Optimal reconstruction of particle content and kinematics in calorimeter images.
method Computer vision techniques applied to calorimeter images, using deep learning and super-resolution.
result Significantly improved reconstruction of neutral particle calorimeter energy deposits.
Jointly estimates flow fields and particle properties from Lagrangian data.
problem Estimating flow fields and particle properties from sparse, noisy Lagrangian data.
method Data assimilation framework coupling Eulerian and Lagrangian models.
result Joint estimation of flow fields and particle properties in various flow regimes.
Develops a novel ML smoothing method for incomplete data in state-space models.
problem Estimating states in stochastic systems with incomplete information.
method Introduces score function and conditional observed information matrices for incomplete data, and uses them to derive the ML smoother.
result The ML smoother provides more accurate state estimates with lower standard errors compared to the standard ML state estimator.
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.
New sampling and diffusion models methods introduced without density function assumptions.
problem Sampling and diffusion models without regularity assumptions.
method Inspired by reverse diffusion process, novel sampling and diffusion algorithms.
result Explicit convergence rate and dimension-free particle approximation convergence result.
New optimization method for sampling from unknown density measures.
problem Sampling from measures with unknown normalization constants.
method Mollified Interaction Energy Descent (MIED) method.
result Gradient flow of MIE converges to chi-square divergence.
The excluded area between a pair of two-dimensional hard particles with given relative orientation is the region in which one particle cannot be located due to the presence of the other particle. The magnitude of the excluded area as a function of the relative particle orientation plays a major role in the determinatio…
We study a simplification of GAN training: the problem of transporting particles from a source to a target distribution. Starting from the Sobolev GAN critic, part of the gradient regularized GAN family, we show a strong relation with Optimal Transport (OT). Specifically with the less popular dynamic formulation of OT …
Differentiable resampling improves particle filter performance.
problem Non-differentiability of traditional resampling in particle filters.
method Introduced a neural network resampler (particle transformer) trained with a likelihood-based loss function.
result Learned resampling outperforms traditional methods on synthetic and real-world tasks.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
Optimal weights improve particle-based approximations of discrete distributions.
problem Improving particle-based approximations of discrete distributions.
method Proving optimality of weights and showing how to compute them efficiently.
result Optimal weights can be computed from existing particle-based methods without extra costs.
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…
Extends Newton's minimal resistance problem to Riemannian surfaces.
problem Minimal resistance on Riemannian surfaces.
method Derive resistance functional, analyze constrained minimization.
result Smooth extremals are loxodromes, global minimizers characterized.