Identifiable Representation and Model Learning for Latent Dynamic Systems

• URL: http://arxiv.org/abs/2410.17882v1
• Date: Wed, 23 Oct 2024 13:55:42 GMT
• Title: Identifiable Representation and Model Learning for Latent Dynamic Systems
• Authors: Congxi Zhang, Yongchun Xie,
• Abstract summary: We study the problem of identifiable representation and model learning for latent dynamic systems. We prove that, for linear or affine nonlinear latent dynamic systems, it is possible to identify the representations up to scaling and determine the models up to some simple transformations.
• Score: 0.0
• License:
• Abstract: Learning identifiable representations and models from low-level observations is useful for an intelligent spacecraft to reliability finish downstream tasks. For temporal observations, to ensure that the data generating process is provably inverted, most existing works either assume the noise variables in the dynamic mechanisms are (conditionally) independent, or require interventions which can directly affect each latent variable. However, in practice, the relationship between the exogenous inputs/interventions and the latent variables may follow some complex deterministic mechanisms. In this work, we study the problem of identifiable representation and model learning for latent dynamic systems. The key idea is that we use an inductive bias inspired by controllable canonical forms, which is invariant, sparse, and input dependent by definition. We prove that, for linear or affine nonlinear latent dynamic systems, it is possible to identify the representations up to scaling and determine the models up to some simple transformations. The results have potential to provide some theoretical guarantees for developing more trustworthy decision-making and control methods for intelligent spacecrafts.

Related papers

• Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics [5.841659874892801]
  Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. Existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity. We propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise.
  arXiv  Detail & Related papers  (2024-08-29T18:58:39Z)
• Data driven modeling for self-similar dynamics [1.0790314700764785]
  We introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge. For deterministic dynamics, our framework can discern whether the dynamics are self-similar. Our method can identify the power law exponents in self-similar systems.
  arXiv  Detail & Related papers  (2023-10-12T12:39:08Z)
• Learning minimal representations of stochastic processes with variational autoencoders [52.99137594502433]
  We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process. Our approach enables for the autonomous discovery of unknown parameters describing processes.
  arXiv  Detail & Related papers  (2023-07-21T14:25:06Z)
• Learning invariant representations of time-homogeneous stochastic dynamical systems [27.127773672738535]
  We study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system. We show that the search for a good representation can be cast as an optimization problem over neural networks.
  arXiv  Detail & Related papers  (2023-07-19T11:32:24Z)
• Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformers [0.6767885381740952]
  We propose a method for learning dynamical systems from high-dimensional empirical data. We focus on the setting in which data are available from multiple different instances of a system. We study behaviour through simple theoretical analyses and extensive experiments on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-21T07:52:07Z)
• Latent Variable Representation for Reinforcement Learning [131.03944557979725]
  It remains unclear theoretically and empirically how latent variable models may facilitate learning, planning, and exploration to improve the sample efficiency of model-based reinforcement learning. We provide a representation view of the latent variable models for state-action value functions, which allows both tractable variational learning algorithm and effective implementation of the optimism/pessimism principle. In particular, we propose a computationally efficient planning algorithm with UCB exploration by incorporating kernel embeddings of latent variable models.
  arXiv  Detail & Related papers  (2022-12-17T00:26:31Z)
• Dynamic Latent Separation for Deep Learning [67.62190501599176]
  A core problem in machine learning is to learn expressive latent variables for model prediction on complex data. Here, we develop an approach that improves expressiveness, provides partial interpretation, and is not restricted to specific applications.
  arXiv  Detail & Related papers  (2022-10-07T17:56:53Z)
• Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs [13.436770170612295]
  We study for the first time uncertainty-aware modeling of continuous-time dynamics of interacting objects. Our model infers both independent dynamics and their interactions with reliable uncertainty estimates.
  arXiv  Detail & Related papers  (2022-05-24T08:36:25Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems [74.80320120264459]
  We present an approach to learn such motions from a limited number of human demonstrations. The complex motions are encoded as rollouts of a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.
  arXiv  Detail & Related papers  (2020-05-27T03:51:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.