Learning dynamical systems from sparse observations is critical in numerous
fields, including biology, finance, and physics. Even if tackling such problems
is standard in general information fusion, it remains challenging for
contemporary machine learning models, such as diffusion models. We introduce a
method that integrates conditional particle filtering with ancestral sampling
and diffusion models, enabling the generation of realistic trajectories that
align with observed data. Our approach uses a smoother based on iterating a
conditional particle filter with ancestral sampling to first generate plausible
trajectories matching observed marginals, and learns the corresponding
diffusion model. This approach provides both a generative method for
high-quality, smoothed trajectories under complex constraints, and an efficient
approximation of the particle smoothing distribution for classical tracking
problems. We demonstrate the approach in time-series generation and
interpolation tasks, including vehicle tracking and single-cell RNA sequencing
data.

从稀疏观测数据中学习动力系统是许多领域（包括生物学、金融学和物理学）的一个关键问题。这篇论文介绍了一种将条件粒子滤波与祖先采样和扩散模型相结合的方法，能够生成与观测数据相符合的逼真轨迹。该方法基于迭代条件粒子滤波与祖先采样生成匹配观测边缘概率的合理轨迹，并学习相应的扩散模型。该方法既为复杂约束下高质量、平滑的轨迹提供了一种生成方法，又有效近似了粒子平滑分布在经典跟踪问题中。我们在时间序列生成和插值任务上展示了该方法，包括车辆追踪和单细胞 RNA 测序数据。

通过扩散生成模型学习近似粒子平滑轨迹

Learning to Approximate Particle Smoothing Trajectories via Diffusion  Generative Models

This work studies the widely adopted ancestral sampling algorithms for
auto-regressive language models, which is not widely studied in the literature.
We use the quality-diversity (Q-D) trade-off to investigate three popular
sampling algorithms (top-k, nucleus and tempered sampling). We focus on the
task of open-ended language generation. We first show that the existing
sampling algorithms have similar performance. After carefully inspecting the
transformations defined by different sampling algorithms, we identify three key
properties that are shared among them: entropy reduction, order preservation,
and slope preservation. To validate the importance of the identified
properties, we design two sets of new sampling algorithms: one set in which
each algorithm satisfies all three properties, and one set in which each
algorithm violates at least one of the properties. We compare their performance
with existing sampling algorithms, and find that violating the identified
properties could lead to drastic performance degradation, as measured by the
Q-D trade-off. On the other hand, we find that the set of sampling algorithms
that satisfies these properties performs on par with the existing sampling
algorithms. Our data and code are available at
this https URL

本研究采用了质量 - 多样性 (Q-D) 折衷方法来研究三种普遍采用的祖先采样算法 (top-k、nucleus 和 tempered sampling) 在无端语言生成任务中的表现，我们证明了现有的采样算法在性能上有相似之处，鉴于此，我们提出了三个共同特性，即：熵减、顺序保持和斜率保持，用两组新的采样算法验证它们对性能的影响以及性能随 Q-D 折衷与违反特性的关系，结果表明，违反这些特性会导致性能严重下降。