可微分的颗粒滤波器提供一种灵活的机制，可以通过从观察到的数据学习来自适应地培训动态和测量模型。然而，大多数现有的可分辨率粒子过滤器位于引导粒子过滤框架内，并且无法将信息从最新观察中纳入，以构建更好的建议。在本文中，我们利用条件标准化流动构建可分解粒子过滤器的提案分布，丰富了提案分布可以代表的分配家庭。此外，归一化流量在动态模型的结构中并入，导致更具表现力的动态模型。我们展示了在视觉跟踪任务中提出的条件归一化流动的可微分粒子过滤器的性能。

颗粒滤波方法广泛应用于非线性非高斯状态空间模型内的顺序状态估计。然而，传统的颗粒过滤方法在高维状态空间模型中遭受重量退化。目前，有许多方法可以提高高维状态空间模型中粒子滤波的性能。其中，更先进的方法是通过实施复合Metropolis-Hasting（MH）内核来构建顺序Makov Chian Monte Carlo（SMCMC）框架。在本文中，我们提出了离散的示出ZAG采样器，并在SMCMC框架内的复合MH内核的细化阶段应用Zig-Zag采样器，其在联合拉伸阶段中的可逆颗粒流动实现。通过挑战复杂的高维过滤实施例的数值实验，我们评估所提出的方法的性能。无限的实验表明，在高维状态估计例中，所提出的方法提高了估计精度并增加了与最先进的过滤方法相比的接收比率。

它已被广泛记录说粒子过滤器中的采样和重采样步骤不能差异化。介绍{\ itshape Reparameterisisisisisation技巧}以允许采样步骤重新重整为可微分功能。我们扩展{\ itshape Reparameterisisisation Trick}以包括重采样的随机输入，因此在此步骤之后限制了梯度计算中的不连续性。了解先前和可能性的梯度允许我们运行粒子马尔可夫链蒙特卡罗（P-MCMC）并在估算参数时使用No-U转样采样器（螺母）作为提案。我们将大都市调整后的Langevin算法（MALA）进行比较，汉密尔顿蒙特卡罗与不同数量的步骤和坚果。我们考虑两个状态空间模型，并表明坚果改善了马尔可夫链的混合，可以在较少的计算时间内产生更准确的结果。

本文介绍了用于增量平滑和映射（NF-ISAM）的归一化流，这是一种新型算法，用于通过非线性测量模型和非高斯因素来推断SLAM问题中完整的后验分布。NF-ISAM利用了神经网络的表达能力，并将正常的流量训练以建模和对完整的后部进行采样。通过利用贝叶斯树，NF-ISAM启用了类似于ISAM2的有效增量更新，尽管在更具挑战性的非高斯环境中。我们证明了NF-ISAM使用数据关联模棱两可的仅范围的SLAM问题来证明NF-ISAM比最先进的点和分布估计算法的优势。NF-ISAM在描述连续变量（例如位置）和离散变量（例如数据关联）的后验信仰方面提出了卓越的准确性。

Passive monitoring of acoustic or radio sources has important applications in modern convenience, public safety, and surveillance. A key task in passive monitoring is multiobject tracking (MOT). This paper presents a Bayesian method for multisensor MOT for challenging tracking problems where the object states are high-dimensional, and the measurements follow a nonlinear model. Our method is developed in the framework of factor graphs and the sum-product algorithm (SPA). The multimodal probability density functions (pdfs) provided by the SPA are effectively represented by a Gaussian mixture model (GMM). To perform the operations of the SPA in high-dimensional spaces, we make use of Particle flow (PFL). Here, particles are migrated towards regions of high likelihood based on the solution of a partial differential equation. This makes it possible to obtain good object detection and tracking performance even in challenging multisensor MOT scenarios with single sensor measurements that have a lower dimension than the object positions. We perform a numerical evaluation in a passive acoustic monitoring scenario where multiple sources are tracked in 3-D from 1-D time-difference-of-arrival (TDOA) measurements provided by pairs of hydrophones. Our numerical results demonstrate favorable detection and estimation accuracy compared to state-of-the-art reference techniques.

粒子过滤是针对多种顺序推断任务的标准蒙特卡洛方法。粒子过滤器的关键成分是一组具有重要性权重的粒子，它们可以作为某些随机过程的真实后验分布的代理。在这项工作中，我们提出了连续的潜在粒子过滤器，该方法将粒子过滤扩展到连续时域。我们证明了如何将连续的潜在粒子过滤器用作依赖于学到的变异后验的推理技术的通用插件替换。我们对基于潜在神经随机微分方程的不同模型家族进行的实验表明，在推理任务中，连续时间粒子滤波在推理任务中的卓越性能，例如似然估计和各种随机过程的顺序预测。

顺序蒙特卡洛（SMC）是状态空间模型的推理算法，通过从一系列中间目标分布进行采样来近似后验。目标分布通常被选择为过滤分布，但是这些忽略了未来观察结果的信息，从而导致推理和模型学习的实际和理论局限性。我们介绍了SIXO，这种方法将学习近似平滑分布的目标，并结合了所有观测值的信息。关键思想是使用密度比估计来拟合将过滤分布扭曲到平滑分布中的功能。然后，我们将SMC与这些学习的目标一起使用，以定义模型和建议学习的变异目标。六体的产量可证明更紧密的对数边缘下限，并在各种域中提供了更准确的后验推断和参数估计。

The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on four examples, two linear in one and twenty dimensions and two nonlinear in one dimension. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.

A track-before-detect (TBD) particle filter-based method for detection and tracking of low observable objects based on a sequence of image frames in the presence of noise and clutter is studied. At each time instance after receiving a frame of image, first, some preprocessing approaches are applied to the image. Then, it is sent to the detection and tracking algorithm which is based on a particle filter. Performance of the approach is evaluated for detection and tracking of an object in different scenarios including noise and clutter.

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.

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 particle methods. Recent methods addressing this problem typically differentiate through time in a particle filter, which requires workarounds to the non-differentiable resampling step, that yield biased or high variance gradient estimates. By contrast, we exploit Fisher's identity to obtain a particle-based approximation of the score function (the gradient of the log likelihood) that yields a low variance estimate while only requiring stepwise differentiation through the transition and observation models. We apply our method to real data collected from autonomous vehicles (AVs) and show that it learns better models than existing techniques and is more stable in training, yielding an effective smoother for tracking the trajectories of vehicles around an AV.

标准化流动，扩散归一化流量和变形自动置换器是强大的生成模型。在本文中，我们提供了一个统一的框架来通过马尔可夫链处理这些方法。实际上，我们考虑随机标准化流量作为一对马尔可夫链，满足一些属性，并表明许多用于数据生成的最先进模型适合该框架。马尔可夫链的观点使我们能够将确定性层作为可逆的神经网络和随机层作为大都会加速层，Langevin层和变形自身偏移，以数学上的声音方式。除了具有Langevin层的密度的层，扩散层或变形自身形式，也可以处理与确定性层或大都会加热器层没有密度的层。因此，我们的框架建立了一个有用的数学工具来结合各种方法。

Wasserstein-Fisher-Rao（WFR）距离是一个指标家族，用于评估两种ra措施的差异，这同时考虑了运输和重量的变化。球形WFR距离是WFR距离的投影版本，以实现概率措施，因此配备了WFR的ra尺度空间可以在概率测量的空间中，用球形WFR视为公式锥。与Wasserstein距离相比，在球形WFR下对大地测量学的理解尚不清楚，并且仍然是持续的研究重点。在本文中，我们开发了一个深度学习框架，以计算球形WFR指标下的大地测量学，并且可以采用学习的大地测量学来生成加权样品。我们的方法基于球形WFR的Benamou-Brenier型动态配方。为了克服重量变化带来的边界约束的困难，将基于反向映射的kullback-leibler（KL）发散术语引入成本函数。此外，引入了使用粒子速度的新的正则化项，以替代汉密尔顿 - 雅各比方程的动态公式中的潜力。当用于样品生成时，与先前的流量模型相比，与给定加权样品的应用相比，我们的框架可能对具有给定加权样品的应用有益。

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling the random numbers of the next model in the stack, we obtain a type of normalizing flow suitable for density estimation, which we call Masked Autoregressive Flow. This type of flow is closely related to Inverse Autoregressive Flow and is a generalization of Real NVP. Masked Autoregressive Flow achieves state-of-the-art performance in a range of general-purpose density estimation tasks.

本文提出并讨论了多个目标跟踪方法的实现，它能够处理目标交互，防止由于劫持而防止跟踪器失败。参考方法使用Markov链蒙特卡罗（MCMC）采样步骤来评估过滤器并构建有效的提案密度以产生新的样品。该密度基于每个时间步骤生成的Markov随机字段（MRF）集成了目标交互项。 MRFS模拟目标之间的相互作用，以减少典型粒子滤波器在跟踪多个目标时遭受的跟踪模糊性。在受限空间中包含20个相互作用蚂蚁的662灰度帧的测试序列用于测试所提出的方法和基于一个重要的自动粒子过滤器，以建立性能比较。结果表明，使用MRF建模目标交互的实现方法成功地校正了独立，交互不知道粒子过滤器的许多跟踪误差。

我们提出了连续重复的退火流传输蒙特卡洛（CRAFT），该方法结合了顺序的蒙特卡洛（SMC）采样器（本身是退火重要性采样的概括）与使用归一化流量的变异推断。直接训练了归一化的流量，可用于使用KL差异进行每个过渡，以在退火温度之间运输。使用归一化流/SMC近似值估算了此优化目标。我们从概念上展示并使用多个经验示例，这些示例可以改善退火流运输蒙特卡洛（Arbel等，2021），并在其上建造，也可以在基于马尔可夫链蒙特卡洛（MCMC）基于基于的随机归一化流（Wu等人。2020）。通过将工艺纳入粒子MCMC中，我们表明，这种学识渊博的采样器可以在具有挑战性的晶格场理论示例中获得令人印象深刻的准确结果。

非线性状态空间模型是一种强大的工具，可以在复杂时间序列中描述动态结构。在一个流的媒体设置中，当一次处理一个样本的情况下，状态的同时推断及其非线性动力学在实践中提出了重大挑战。我们开发了一个小说在线学习框架，利用变分推理和顺序蒙特卡罗，这使得灵活和准确的贝叶斯联合过滤。我们的方法提供了滤波后的近似，这可以任意地接近针对广泛的动态模型和观察模型的真正滤波分布。具体地，所提出的框架可以使用稀疏高斯过程有效地近似于动态的后验，允许潜在动力学的可解释模型。每个样本的恒定时间复杂性使我们的方法能够适用于在线学习场景，适用于实时应用。

退火重要性采样（AIS）是一种流行的算法，用于估计深层生成模型的棘手边际可能性。尽管AIS可以保证为任何一组超参数提供无偏估计，但共同的实现依赖于简单的启发式方法，例如初始和目标分布之间的几何平均桥接分布，这些分布在计算预算有限时会影响估计性性能。由于使用Markov过渡中的大都市磨碎（MH）校正步骤，因此对完全参数AI的优化仍然具有挑战性。我们提出一个具有灵活中间分布的参数AIS过程，并优化桥接分布以使用较少数量的采样步骤。一种重新聚集方法，它允许我们优化分布序列和Markov转换的参数，该参数适用于具有MH校正的大型Markov内核。我们评估了优化AIS的性能，以进行深层生成模型的边际可能性估计，并将其与其他估计器进行比较。

基于标准化流的算法是由于有希望的机器学习方法，以便以可以使渐近精确的方式采样复杂的概率分布。在格子场理论的背景下，原则上的研究已经证明了这种方法对标量理论，衡量理论和统计系统的有效性。这项工作开发了能够使用动力学蜕皮的基于流动的理论采样的方法，这对于应用于粒子物理标准模型和许多冷凝物系的晶格场理论研究是必要的。作为一种实践演示，这些方法应用于通过Yukawa相互作用耦合到标量场的无大量交错的费米子的二维理论的现场配置的采样。