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.

提出了一种可微分的重采样方案，通过从经验累积分布函数进行确定性采样，用于粒子滤波器的参数推断和提议学习任务。

利用最优放置重采样的可微粒子滤波

Differentiable Particle Filtering using Optimal Placement Resampling

We investigate the low-dimensional structure of deterministic transformations
between random variables, i.e., transport maps between probability measures. In
the context of statistics and machine learning, these transformations can be
used to couple a tractable "reference" measure (e.g., a standard Gaussian) with
a target measure of interest. Direct simulation from the desired measure can
then be achieved by pushing forward reference samples through the map. Yet
characterizing such a map---e.g., representing and evaluating it---grows
challenging in high dimensions. The central contribution of this paper is to
establish a link between the Markov properties of the target measure and the
existence of low-dimensional couplings, induced by transport maps that are
sparse and/or decomposable. Our analysis not only facilitates the construction
of transformations in high-dimensional settings, but also suggests new
inference methodologies for continuous non-Gaussian graphical models. For
instance, in the context of nonlinear state-space models, we describe new
variational algorithms for filtering, smoothing, and sequential parameter
inference. These algorithms can be understood as the natural
generalization---to the non-Gaussian case---of the square-root
Rauch-Tung-Striebel Gaussian smoother.

通过探究概率分布之间的确定性变换结构，我们建立了目标分布的马尔可夫特性与较低维耦合间的联系，从而解决高维情形下的非高斯图模型推断问题，并提出了相应的方案。

通过低维耦合进行推断

Inference via low-dimensional couplings

We consider approximate maximum likelihood parameter estimation in nonlinear
state-space models. We discuss both direct optimization of the likelihood and
expectation--maximization (EM). For EM, we also give closed-form expressions
for the maximization step in a class of models that are linear in parameters
and have additive noise. To obtain approximations to the filtering and
smoothing distributions needed in the likelihood-maximization methods, we focus
on using Gaussian filtering and smoothing algorithms that employ sigma-points
to approximate the required integrals. We discuss different sigma-point schemes
based on the third, fifth, seventh, and ninth order unscented transforms and
the Gauss--Hermite quadrature rule. We compare the performance of the methods
in two simulated experiments: a univariate nonlinear growth model as well as
tracking of a maneuvering target. In the experiments, we also compare against
approximate likelihood estimates obtained by particle filtering and extended
Kalman filtering based methods. The experiments suggest that the higher-order
unscented transforms may in some cases provide more accurate estimates

研究用于非线性状态空间模型的近似极大似然参数估计，讨论了直接最大化似然和 EM 算法，使用 sigma 点来近似所需积分的高斯滤波和平滑算法，比较了不同阶的 unscented 变换以及高斯 - 埃尔米特积分规则得出的方法在两个模拟实验中的表现

基于卡尔曼滤波器和平滑器的非线性动态系统参数估计

Sigma-Point Filtering and Smoothing Based Parameter Estimation in  Nonlinear Dynamic Systems

We investigate nonlinear state-space models without a closed-form transition
density, and propose reformulating such models over their latent noise
variables rather than their latent state variables. In doing so the tractable
noise density emerges in place of the intractable transition density. For
importance sampling methods such as the auxiliary particle filter, this enables
importance weights to be computed where they could not be otherwise. As case
studies we take two multivariate marine biogeochemical models and perform state
and parameter estimation using the particle marginal Metropolis-Hastings
sampler. For the particle filter within this sampler, we compare several
proposal strategies over noise variables, all based on lookaheads with the
unscented Kalman filter. These strategies are compared using conventional means
for assessing Metropolis-Hastings efficiency, as well as with a novel metric
called the conditional acceptance rate for assessing the consequences of using
an estimated, and not exact, likelihood. Results indicate the utility of
reformulating the model over noise variables, particularly for fast-mixing
process models.

通过对潜在噪声变量而非潜在状态变量进行重新表述的方法，我们研究了没有闭合形式转移的非线性状态空间模型。研究发现，这种转化实现了可计算的噪声密度以代替不可计算的转移密度，可作为辅助粒子滤波器等重要性抽样方法中的重要权重计算。通过两个多元海洋生物地球化学模型的实例探讨粒子边缘 Metropolis-Hastings 采样器的状态和参数估计问题。结果表明，对于快速混合过程模型来说，重新表述噪声变量的模型非常有用。