Gaussian Processes (GPs) and Linear Dynamical Systems (LDSs) are essential
time series and dynamic system modeling tools. GPs can handle complex,
nonlinear dynamics but are computationally demanding, while LDSs offer
efficient computation but lack the expressive power of GPs. To combine their
benefits, we introduce a universal method that allows an LDS to mirror
stationary temporal GPs. This state-space representation, known as the
Markovian Gaussian Process (Markovian GP), leverages the flexibility of kernel
functions while maintaining efficient linear computation. Unlike existing
GP-LDS conversion methods, which require separability for most multi-output
kernels, our approach works universally for single- and multi-output stationary
temporal kernels. We evaluate our method by computing covariance, performing
regression tasks, and applying it to a neuroscience application, demonstrating
that our method provides an accurate state-space representation for stationary
temporal GPs.

引入一种通用方法，允许 LDS 模拟平稳的时间 GPs，这种状态空间表示方法称为马尔可夫高斯过程，通过保持高斯过程的灵活性同时维持高效的线性计算，能够组合 GPs 和 LDS 的优点，而不仅限于分离性多输出核函数，对单输出和多输出的平稳时间核函数普遍有效，通过计算协方差、执行回归任务和神经科学应用进行评估，证明了我们的方法能够提供准确的平稳时间 GPs 的状态空间表示。

马尔可夫高斯过程：一种用于平稳时序高斯过程的通用状态空间表示

Markovian Gaussian Process: A Universal State-Space Representation for  Stationary Temporal Gaussian Process

We demonstrate model-based, visual robot manipulation of linear deformable
objects. Our approach is based on a state-space representation of the physical
system that the robot aims to control. This choice has multiple advantages,
including the ease of incorporating physics priors in the dynamics model and
perception model, and the ease of planning manipulation actions. In addition,
physical states can naturally represent object instances of different
appearances. Therefore, dynamics in the state space can be learned in one
setting and directly used in other visually different settings. This is in
contrast to dynamics learned in pixel space or latent space, where
generalization to visual differences are not guaranteed. Challenges in taking
the state-space approach are the estimation of the high-dimensional state of a
deformable object from raw images, where annotations are very expensive on real
data, and finding a dynamics model that is both accurate, generalizable, and
efficient to compute. We are the first to demonstrate self-supervised training
of rope state estimation on real images, without requiring expensive
annotations. This is achieved by our novel self-supervising learning objective,
which is generalizable across a wide range of visual appearances. With
estimated rope states, we train a fast and differentiable neural network
dynamics model that encodes the physics of mass-spring systems. Our method has
a higher accuracy in predicting future states compared to models that do not
involve explicit state estimation and do not use any physics prior, while only
using 3\% of training data. We also show that our approach achieves more
efficient manipulation, both in simulation and on a real robot, when used
within a model predictive controller.

本文提出了一种基于状态空间表示和自我监督训练技术的视觉机器人操作方法，通过估计可变形物体状态、训练神经网络动力学模型以及采用模型预测控制器，实现高效而准确的物体操纵。