Differentiable Particle Filtering using Optimal Placement Resampling
1 Department of Control for Transportation；Vehicle Systems, Faculty of Transportation Engineering；Vehicle Engineering, Budapest University of Technology
Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating the marginal data (observation) likelihood. A good proposal distribution and a good resampling scheme are crucial to obtain low variance estimates. However, traditional methods like multinomial resampling introduce nondifferentiability in PF-based loss functions for parameter estimation, prohibiting gradient-based learning tasks. This work proposes a differentiable resampling scheme by deterministic sampling from an empirical cumulative distribution function. We evaluate our method on parameter inference tasks and proposal learning.
Stanford（斯坦福大学）；Google AI（谷歌人工智能）；Robotics at Google（谷歌机器人）
Resampling is a key component of sample-based recursive state estimation in particle filters. Recent work explores differentiable particle filters for end-to-end learning. However, resampling remains a challenge in these works, as it is inherently non-differentiable. We address this challenge by replacing traditional resampling with a learned neural network resampler. We present a novel network architecture, the particle transformer, and train it for particle resampling using a likelihood-based loss function over sets of particles. Incorporated into a differentiable particle filter, our model …
Aalto University（阿尔托大学）；University of Oxford（牛津大学）
Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter …
University of Liverpool（利物浦大学）；Uppsala University（乌普萨拉大学）
It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The {\itshape reparameterisation trick} was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the {\itshape reparameterisation trick} to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when esti…
University of British Columbia（不列颠哥伦比亚大学）；Inverted AI；Mila
Particle filters are not compatible with automatic differentiation due to the presence of discrete resampling steps. While known estimators for the score function, based on Fisher's identity, can be computed using particle filters, up to this point they required manual implementation. In this paper we show that such estimators can be computed using automatic differentiation, after introducing a simple correction to the particle weights. This correction utilizes the stop-gradient operator and does not modify the particle filter operation on the forward pass, while also being cheap and easy to c…
Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly: as the latent dimensionality grows, they require exponentially many samples to retain the benefits of importance weighting. While sequential Monte-Carlo (SMC) can address this problem, it is prohibitively slow because the resampling step imposes sequential structure which cannot be parallelised, and moreover, resampling is non-differentiable which is problem…
Columbia University（哥伦比亚大学）；Flatiron Institute（弗莱提荣研究所）；Aalto University（阿尔托大学）
We propose Pathfinder, a variational method for approximately sampling from differentiable log densities. Starting from a random initialization, Pathfinder locates normal approximations to the target density along a quasi-Newton optimization path, with local covariance estimated using the inverse Hessian estimates produced by the optimizer. Pathfinder returns draws from the approximation with the lowest estimated Kullback-Leibler (KL) divergence to the true posterior. We evaluate Pathfinder on a wide range of posterior distributions, demonstrating that its approximate draws are better than tho…
We present a new method, PARsing And visual GrOuNding (ParaGon), for grounding natural language in object placement tasks. Natural language generally describes objects and spatial relations with compositionality and ambiguity, two major obstacles to effective language grounding. For compositionality, ParaGon parses a language instruction into an object-centric graph representation to ground objects individually. For ambiguity, ParaGon uses a novel particle-based graph neural network to reason about object placements with uncertainty. Essentially, ParaGon integrates a parsing algorithm into a p…
Deep neural networks (DNNs) are found to be vulnerable to adversarial attacks, and various methods have been proposed for the defense. Among these methods, adversarial training has been drawing increasing attention because of its simplicity and effectiveness. However, the performance of the adversarial training is greatly limited by the architectures of target DNNs, which often makes the resulting DNNs with poor accuracy and unsatisfactory robustness. To address this problem, we propose DSARA to automatically search for the neural architectures that are accurate and robust after adversarial tr…
Multi-object state estimation is a fundamental problem for robotic applications where a robot must interact with other moving objects. Typically, other objects' relevant state features are not directly observable, and must instead be inferred from observations. Particle filtering can perform such inference given approximate transition and observation models. However, these models are often unknown a priori, yielding a difficult parameter estimation problem since observations jointly carry transition and observation noise. In this work, we consider learning maximum-likelihood parameters using p…
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Criteo AI Labs（Criteo人工智能实验室）
We consider the task of feature selection for reconstruction which consists in choosing a small subset of features from which whole data instances can be reconstructed. This is of particular importance in several contexts involving for example costly physical measurements, sensor placement or information compression. To break the intrinsic combinatorial nature of this problem, we formulate the task as optimizing a binary mask distribution enabling an accurate reconstruction. We then face two main challenges. One concerns differentiability issues due to the binary distribution. The second one c…
