Towards Learning Stochastic Population Models by Gradient Descent

• URL: http://arxiv.org/abs/2404.07049v2
• Date: Fri, 28 Jun 2024 13:14:13 GMT
• Title: Towards Learning Stochastic Population Models by Gradient Descent
• Authors: Justin N. Kreikemeyer, Philipp Andelfinger, Adelinde M. Uhrmacher,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of dynamical systems formulates this problem as a linear equation system. Here, we explore several simulation-based optimization approaches, which allow much greater freedom in the objective formulation and weaker conditions on the available data. We show that even for relatively small stochastic population models, simultaneous estimation of parameters and structure poses major challenges for optimization procedures. Particularly, we investigate the application of the local stochastic gradient descent method, commonly used for training machine learning models. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty. We give an outlook on how this challenge can be overcome.

Related papers

• Differentiable Calibration of Inexact Stochastic Simulation Models via Kernel Score Minimization [11.955062839855334]
  We propose to learn differentiable input parameters of simulation models using output-level data via kernel score minimization with gradient descent. We quantify the uncertainties of the learned input parameters using a new normality result that accounts for model inexactness.
  arXiv  Detail & Related papers  (2024-11-08T04:13:52Z)
• On conditional diffusion models for PDE simulations [53.01911265639582]
  We study score-based diffusion models for forecasting and assimilation of sparse observations. We propose an autoregressive sampling approach that significantly improves performance in forecasting. We also propose a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths.
  arXiv  Detail & Related papers  (2024-10-21T18:31:04Z)
• SMILE: Zero-Shot Sparse Mixture of Low-Rank Experts Construction From Pre-Trained Foundation Models [85.67096251281191]
  We present an innovative approach to model fusion called zero-shot Sparse MIxture of Low-rank Experts (SMILE) construction. SMILE allows for the upscaling of source models into an MoE model without extra data or further training. We conduct extensive experiments across diverse scenarios, such as image classification and text generation tasks, using full fine-tuning and LoRA fine-tuning.
  arXiv  Detail & Related papers  (2024-08-19T17:32:15Z)
• Model-based Policy Optimization using Symbolic World Model [46.42871544295734]
  The application of learning-based control methods in robotics presents significant challenges. One is that model-free reinforcement learning algorithms use observation data with low sample efficiency. We suggest approximating transition dynamics with symbolic expressions, which are generated via symbolic regression.
  arXiv  Detail & Related papers  (2024-07-18T13:49:21Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Neural Likelihood Approximation for Integer Valued Time Series Data [0.0]
  We construct a neural likelihood approximation that can be trained using unconditional simulation of the underlying model. We demonstrate our method by performing inference on a number of ecological and epidemiological models.
  arXiv  Detail & Related papers  (2023-10-19T07:51:39Z)
• 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)
• Sufficiently Accurate Model Learning for Planning [119.80502738709937]
  This paper introduces the constrained Sufficiently Accurate model learning approach. It provides examples of such problems, and presents a theorem on how close some approximate solutions can be. The approximate solution quality will depend on the function parameterization, loss and constraint function smoothness, and the number of samples in model learning.
  arXiv  Detail & Related papers  (2021-02-11T16:27:31Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• Learning Stable Nonparametric Dynamical Systems with Gaussian Process Regression [9.126353101382607]
  We learn a nonparametric Lyapunov function based on Gaussian process regression from data. We prove that stabilization of the nominal model based on the nonparametric control Lyapunov function does not modify the behavior of the nominal model at training samples.
  arXiv  Detail & Related papers  (2020-06-14T11:17:17Z)
• Maximum Entropy Model Rollouts: Fast Model Based Policy Optimization without Compounding Errors [10.906666680425754]
  We propose a Dyna-style model-based reinforcement learning algorithm, which we called Maximum Entropy Model Rollouts (MEMR) To eliminate the compounding errors, we only use our model to generate single-step rollouts.
  arXiv  Detail & Related papers  (2020-06-08T21:38:15Z)

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.