The paper introduces a new class of algorithms that embed existing automatic differentiation (AD) particle filter methods, enabling a bias‑variance tradeoff and reducing mean squared error in likelihood estimation for partially observed nonlinear stochastic dynamical systems. Unlike prior approaches, these algorithms only require a differentiable simulator of the latent dynamics, not explicit transition probabilities. Numerical experiments demonstrate that a hybrid method—using AD to refine a coarse solution from iterated filtering—outperforms current state‑of‑the‑art techniques on a challenging scientific benchmark.
arXiv:2609.30498v1 Announce Type: cross Abstract: Sequential inference estimates latent states from noisy and incomplete observations. Particle Filters (PFs), a class of Monte Carlo methods based on...
arXiv:2510. 25693v3 Announce Type: replace-cross Abstract: State-space models (SSMs) are a widely used tool in time series analysis.
The paper introduces the Belief Flow Filter (BFF), a generative filtering framework that encodes the evolving posterior distribution directly into flow matching model weights and updates them via test‑time gradient descent. By avoiding particle representations and Gaussian assumptions, BFF aligns structurally with Bayesian filtering and targets the recursive filtering operator. Empirical results on five physical systems—including chaotic dynamics, sparse observations, and a tokamak plasma estimation task—show that BFF outperforms existing methods in most benchmark metrics.
The paper introduces Differentiable Systematic Resampling (DSR), a temperature-controlled relaxation of systematic resampling that maintains the CDF-ordered, banded structure while allowing full gradient flow. DSR converges to exact systematic resampling as temperature approaches zero and the authors prove a pointwise exponential convergence rate for the induced bias. Compared to optimal-transport-based differentiable resampling, DSR avoids iterative solvers and has substantially lower computational overhead, achieving comparable or superior filtering and dynamics learning performance on stochastic dynamical systems and real-world handwriting data.
arXiv:2607. 01012v1 Announce Type: new Abstract: Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications.
arXiv:2407. 20432v3 Announce Type: replace Abstract: Bayesian inference methods such as Markov Chain Monte Carlo (MCMC) typically require repeated computations of the likelihood function, but in some scenarios this is infeasible and alternative methods are needed.
arXiv:2607. 12095v1 Announce Type: cross Abstract: Sensor-rich data-driven applications increasingly use Bayesian approaches to infer latent states of dynamic systems from noisy sensor measurements and physical models.
arXiv:2510. 12311v2 Announce Type: replace-cross Abstract: We develop interacting particle algorithms for learning latent variable models with energy-based priors.
arXiv:2608. 02844v1 Announce Type: cross Abstract: We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients.
arXiv:2604.07169v3 Announce Type: replace-cross Abstract: Bayesian filtering and smoothing are central to data assimilation in nonlinear dynamical systems. Recent advances in deep generative models p...
arXiv:2606. 01468v1 Announce Type: cross Abstract: Due to their explicit priors and ability to model uncertainty, Bayesian methods have played a major role in dynamical latent variable modeling of single-cell neural recordings.
The paper explores how to use gradients of simulator outputs with respect to input parameters to improve Bayesian inference for expensive simulators. By incorporating gradient information into Gaussian process surrogate models, the authors show that Bayesian optimization can converge faster under a limited simulation budget. They find that reverse‑mode differentiation yields efficiency gains, while forward‑mode does not offset its computational cost, especially when the number of parameters exceeds the output dimensionality.