Beyond Predictions in Neural ODEs: Identification and Interventions

• URL: http://arxiv.org/abs/2106.12430v1
• Date: Wed, 23 Jun 2021 14:35:38 GMT
• Title: Beyond Predictions in Neural ODEs: Identification and Interventions
• Authors: Hananeh Aliee, Fabian J. Theis, Niki Kilbertus
• Abstract summary: Given large amounts of observational data about a system, can we uncover the rules that govern its evolution? We show that combining simple regularization schemes with flexible neural ODEs can robustly recover the dynamics and causal structures from time-series data. We conclude by showing that we can also make accurate predictions under interventions on variables or the system itself.
• Score: 4.257168718582631
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the rules that govern its evolution? Solving this task holds the great promise of fully understanding the causal interactions and being able to make reliable predictions about the system's behavior under interventions. We take a step towards answering this question for time-series data generated from systems of ordinary differential equations (ODEs). While the governing ODEs might not be identifiable from data alone, we show that combining simple regularization schemes with flexible neural ODEs can robustly recover the dynamics and causal structures from time-series data. Our results on a variety of (non)-linear first and second order systems as well as real data validate our method. We conclude by showing that we can also make accurate predictions under interventions on variables or the system itself.

Related papers

• eXponential FAmily Dynamical Systems (XFADS): Large-scale nonlinear Gaussian state-space modeling [9.52474299688276]
  We introduce a low-rank structured variational autoencoder framework for nonlinear state-space graphical models. We show that our approach consistently demonstrates the ability to learn a more predictive generative model.
  arXiv  Detail & Related papers  (2024-03-03T02:19:49Z)
• Foundational Inference Models for Dynamical Systems [5.549794481031468]
  We offer a fresh perspective on the classical problem of imputing missing time series data, whose underlying dynamics are assumed to be determined by ODEs. We propose a novel supervised learning framework for zero-shot time series imputation, through parametric functions satisfying some (hidden) ODEs. We empirically demonstrate that one and the same (pretrained) recognition model can perform zero-shot imputation across 63 distinct time series with missing values.
  arXiv  Detail & Related papers  (2024-02-12T11:48:54Z)
• Learning the Dynamics of Sparsely Observed Interacting Systems [0.6021787236982659]
  We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression.
  arXiv  Detail & Related papers  (2023-01-27T10:48:28Z)
• Autoregressive GNN-ODE GRU Model for Network Dynamics [7.272158647379444]
  We propose an Autoregressive GNN-ODE GRU Model (AGOG) to learn and capture the continuous network dynamics. Our model can capture the continuous dynamic process of complex systems accurately and make predictions of node states with minimal error.
  arXiv  Detail & Related papers  (2022-11-19T05:43:10Z)
• Causality-Based Multivariate Time Series Anomaly Detection [63.799474860969156]
  We formulate the anomaly detection problem from a causal perspective and view anomalies as instances that do not follow the regular causal mechanism to generate the multivariate data. We then propose a causality-based anomaly detection approach, which first learns the causal structure from data and then infers whether an instance is an anomaly relative to the local causal mechanism. We evaluate our approach with both simulated and public datasets as well as a case study on real-world AIOps applications.
  arXiv  Detail & Related papers  (2022-06-30T06:00:13Z)
• 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)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• 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)
• Identifying nonlinear dynamical systems from multi-modal time series data [3.721528851694675]
  Empirically observed time series in physics, biology, or medicine are commonly generated by some underlying dynamical system (DS) There is an increasing interest to harvest machine learning methods to reconstruct this latent DS in a completely data-driven, unsupervised way. Here we propose a general framework for multi-modal data integration for the purpose of nonlinear DS identification and cross-modal prediction.
  arXiv  Detail & Related papers  (2021-11-04T14:59:28Z)
• Supervised DKRC with Images for Offline System Identification [77.34726150561087]
  Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
  arXiv  Detail & Related papers  (2021-09-06T04:39:06Z)
• Consistency of mechanistic causal discovery in continuous-time using Neural ODEs [85.7910042199734]
  We consider causal discovery in continuous-time for the study of dynamical systems. We propose a causal discovery algorithm based on penalized Neural ODEs.
  arXiv  Detail & Related papers  (2021-05-06T08:48:02Z)

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.