On the importance of structural identifiability for machine learning with partially observed dynamical systems

• URL: http://arxiv.org/abs/2502.04131v1
• Date: Thu, 06 Feb 2025 15:06:52 GMT
• Title: On the importance of structural identifiability for machine learning with partially observed dynamical systems
• Authors: Janis Norden, Elisa Oostwal, Michael Chappell, Peter Tino, Kerstin Bunte,
• Abstract summary: We use structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.
• Score: 0.7864304771129751
• License:
• Abstract: The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, available domain expert knowledge in the form of parametrised mechanistic dynamical models can be used whenever it is available and time series observations may be represented as an element from a given class of parametrised dynamical models. This makes the learning process interpretable and allows the modeller to deal with sparsely and irregularly sampled data in a natural way. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that incorporates knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.

Related papers

• Neural Koopman prior for data assimilation [7.875955593012905]
  We use a neural network architecture to embed dynamical systems in latent spaces. We introduce methods that enable to train such a model for long-term continuous reconstruction. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques.
  arXiv  Detail & Related papers  (2023-09-11T09:04:36Z)
• Robust Graph Representation Learning via Predictive Coding [46.22695915912123]
  Predictive coding is a message-passing framework initially developed to model information processing in the brain. In this work, we build models that rely on the message-passing rule of predictive coding. We show that the proposed models are comparable to standard ones in terms of performance in both inductive and transductive tasks.
  arXiv  Detail & Related papers  (2022-12-09T03:58:22Z)
• 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)
• Generalization Properties of Retrieval-based Models [50.35325326050263]
  Retrieval-based machine learning methods have enjoyed success on a wide range of problems. Despite growing literature showcasing the promise of these models, the theoretical underpinning for such models remains underexplored. We present a formal treatment of retrieval-based models to characterize their generalization ability.
  arXiv  Detail & Related papers  (2022-10-06T00:33:01Z)
• CHALLENGER: Training with Attribution Maps [63.736435657236505]
  We show that utilizing attribution maps for training neural networks can improve regularization of models and thus increase performance. In particular, we show that our generic domain-independent approach yields state-of-the-art results in vision, natural language processing and on time series tasks.
  arXiv  Detail & Related papers  (2022-05-30T13:34:46Z)
• Leveraging the structure of dynamical systems for data-driven modeling [111.45324708884813]
  We consider the impact of the training set and its structure on the quality of the long-term prediction. We show how an informed design of the training set, based on invariants of the system and the structure of the underlying attractor, significantly improves the resulting models.
  arXiv  Detail & Related papers  (2021-12-15T20:09:20Z)
• Model-agnostic multi-objective approach for the evolutionary discovery of mathematical models [55.41644538483948]
  In modern data science, it is more interesting to understand the properties of the model, which parts could be replaced to obtain better results. We use multi-objective evolutionary optimization for composite data-driven model learning to obtain the algorithm's desired properties.
  arXiv  Detail & Related papers  (2021-07-07T11:17:09Z)
• On the Dynamics of Training Attention Models [30.85940880569692]
  We study the dynamics of training a simple attention-based classification model using gradient descent. We prove that training must converge to attending to the discriminative words when the attention output is classified by a linear classifier.
  arXiv  Detail & Related papers  (2020-11-19T18:55:30Z)
• The Role of Isomorphism Classes in Multi-Relational Datasets [6.419762264544509]
  We show that isomorphism leakage overestimates performance in multi-relational inference. We propose isomorphism-aware synthetic benchmarks for model evaluation. We also demonstrate that isomorphism classes can be utilised through a simple prioritisation scheme.
  arXiv  Detail & Related papers  (2020-09-30T12:15:24Z)
• Deducing neighborhoods of classes from a fitted model [68.8204255655161]
  In this article a new kind of interpretable machine learning method is presented. It can help to understand the partitioning of the feature space into predicted classes in a classification model using quantile shifts. Basically, real data points (or specific points of interest) are used and the changes of the prediction after slightly raising or decreasing specific features are observed.
  arXiv  Detail & Related papers  (2020-09-11T16:35:53Z)

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.