SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks

• URL: http://arxiv.org/abs/2008.08637v2
• Date: Mon, 6 Dec 2021 03:49:01 GMT
• Title: SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks
• Authors: Weijing Tang, Jiaqi Ma, Qiaozhu Mei, Ji Zhu
• Abstract summary: We propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. We demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models.
• Score: 14.564168076456822
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. One key technical challenge for directly applying maximum likelihood estimation (MLE) to censored data is that evaluating the objective function and its gradients with respect to model parameters requires the calculation of integrals. To address this challenge, we recognize that the MLE for censored data can be viewed as a differential-equation constrained optimization problem, a novel perspective. Following this connection, we model the distribution of event time through an ordinary differential equation and utilize efficient ODE solvers and adjoint sensitivity analysis to numerically evaluate the likelihood and the gradients. Using this approach, we are able to 1) provide a broad family of continuous-time survival distributions without strong structural assumptions, 2) obtain powerful feature representations using neural networks, and 3) allow efficient estimation of the model in large-scale applications using stochastic gradient descent. Through both simulation studies and real-world data examples, we demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models. The implementation of the proposed SODEN approach has been made publicly available at https://github.com/jiaqima/SODEN.

Related papers

• A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems [10.820654486318336]
  This study introduces a training-free conditional diffusion model for learning unknown differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling SDEs. The learned models exhibit significant improvements in predicting both short-term and long-term behaviors of unknown systems.
  arXiv  Detail & Related papers  (2024-10-04T03:07:36Z)
• Towards Learning Stochastic Population Models by Gradient Descent [0.0]
  We show that simultaneous estimation of parameters and structure poses major challenges for optimization procedures. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty.
  arXiv  Detail & Related papers  (2024-04-10T14:38:58Z)
• Latent Semantic Consensus For Deterministic Geometric Model Fitting [109.44565542031384]
  We propose an effective method called Latent Semantic Consensus (LSC) LSC formulates the model fitting problem into two latent semantic spaces based on data points and model hypotheses. LSC is able to provide consistent and reliable solutions within only a few milliseconds for general multi-structural model fitting.
  arXiv  Detail & Related papers  (2024-03-11T05:35:38Z)
• Data-driven Modeling and Inference for Bayesian Gaussian Process ODEs via Double Normalizing Flows [28.62579476863723]
  We introduce normalizing flows to re parameterize the ODE vector field, resulting in a data-driven prior distribution. We also apply normalizing flows to the posterior inference of GP ODEs to resolve the issue of strong mean-field assumptions. We validate the effectiveness of our approach on simulated dynamical systems and real-world human motion data.
  arXiv  Detail & Related papers  (2023-09-17T09:28:47Z)
• Generalizing Backpropagation for Gradient-Based Interpretability [103.2998254573497]
  We show that the gradient of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics.
  arXiv  Detail & Related papers  (2023-07-06T15:19:53Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• 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)
• Model-based Policy Optimization with Unsupervised Model Adaptation [37.09948645461043]
  We investigate how to bridge the gap between real and simulated data due to inaccurate model estimation for better policy optimization. We propose a novel model-based reinforcement learning framework AMPO, which introduces unsupervised model adaptation. Our approach achieves state-of-the-art performance in terms of sample efficiency on a range of continuous control benchmark tasks.
  arXiv  Detail & Related papers  (2020-10-19T14:19:42Z)
• Model-Augmented Actor-Critic: Backpropagating through Paths [81.86992776864729]
  Current model-based reinforcement learning approaches use the model simply as a learned black-box simulator. We show how to make more effective use of the model by exploiting its differentiability.
  arXiv  Detail & Related papers  (2020-05-16T19:18:10Z)

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.