Model selection for stochastic dynamics: a parsimonious and principled approach

• URL: http://arxiv.org/abs/2507.04121v1
• Date: Sat, 05 Jul 2025 18:15:26 GMT
• Title: Model selection for stochastic dynamics: a parsimonious and principled approach
• Authors: Andonis Gerardos,
• Abstract summary: This thesis focuses on the discovery of imperfect differential equations (SDEs) and partial differential equations (SPDEs) from noisy and discrete time series.<n>A major challenge is selecting the simplest possible correct model from vast libraries of candidate models.<n>We introduce PASTIS (Parsimonious Inference), a new information criterion derived from extreme value theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This thesis focuses on the discovery of stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) from noisy and discrete time series. A major challenge is selecting the simplest possible correct model from vast libraries of candidate models, where standard information criteria (AIC, BIC) are often limited. We introduce PASTIS (Parsimonious Stochastic Inference), a new information criterion derived from extreme value theory. Its penalty term, $n_\mathcal{B} \ln(n_0/p)$, explicitly incorporates the size of the initial library of candidate parameters ($n_0$), the number of parameters in the considered model ($n_\mathcal{B}$), and a significance threshold ($p$). This significance threshold represents the probability of selecting a model containing more parameters than necessary when comparing many models. Benchmarks on various systems (Lorenz, Ornstein-Uhlenbeck, Lotka-Volterra for SDEs; Gray-Scott for SPDEs) demonstrate that PASTIS outperforms AIC, BIC, cross-validation (CV), and SINDy (a competing method) in terms of exact model identification and predictive capability. Furthermore, real-world data can be subject to large sampling intervals ($\Delta t$) or measurement noise ($\sigma$), which can impair model learning and selection capabilities. To address this, we have developed robust variants of PASTIS, PASTIS-$\Delta t$ and PASTIS-$\sigma$, thus extending the applicability of the approach to imperfect experimental data. PASTIS thus provides a statistically grounded, validated, and practical methodological framework for discovering simple models for processes with stochastic dynamics.

Related papers

• D-Models and E-Models: Diversity-Stability Trade-offs in the Sampling Behavior of Large Language Models [91.21455683212224]
  In large language models (LLMs), the probability of relevance for the next piece of information is linked to the probability of relevance for the next product.<n>But whether fine-grained sampling probabilities faithfully align with task requirements remains an open question.<n>We identify two model types: D-models, whose P_token exhibits large step-to-step variability and poor alignment with P_task; and E-models, whose P_token is more stable and better aligned with P_task.
  arXiv  Detail & Related papers  (2026-01-25T14:59:09Z)
• Distance Is All You Need: Radial Dispersion for Uncertainty Estimation in Large Language Models [13.41454380481593]
  We introduce bfRadial Dispersion Score (RDS), a simple, parameter-free, fully model-agnostic uncertainty metric.<n>RDS naturally extends to per-sample scoring, enabling applications such as best-of-$N$ selection and confidence-based filtering.
  arXiv  Detail & Related papers  (2025-12-04T00:53:49Z)
• Model Correlation Detection via Random Selection Probing [62.093777777813756]
  Existing similarity-based methods require access to model parameters or produce scores without thresholds.<n>We introduce Random Selection Probing (RSP), a hypothesis-testing framework that formulates model correlation detection as a statistical test.<n>RSP produces rigorous p-values that quantify evidence of correlation.
  arXiv  Detail & Related papers  (2025-09-29T01:40:26Z)
• Principled model selection for stochastic dynamics [0.0]
  PASTIS is a principled method combining likelihood-estimation statistics with extreme value theory to suppress superfluous parameters.<n>It reliably identifies minimal models, even with low sampling rates or measurement error.<n>It applies to partial differential equations, and applies to ecological networks and reaction-diffusion dynamics.
  arXiv  Detail & Related papers  (2025-01-17T18:23:16Z)
• 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)
• On Least Square Estimation in Softmax Gating Mixture of Experts [78.3687645289918]
  We investigate the performance of the least squares estimators (LSE) under a deterministic MoE model. We establish a condition called strong identifiability to characterize the convergence behavior of various types of expert functions. Our findings have important practical implications for expert selection.
  arXiv  Detail & Related papers  (2024-02-05T12:31:18Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Value function estimation using conditional diffusion models for control [62.27184818047923]
  We propose a simple algorithm called Diffused Value Function (DVF) It learns a joint multi-step model of the environment-robot interaction dynamics using a diffusion model. We show how DVF can be used to efficiently capture the state visitation measure for multiple controllers.
  arXiv  Detail & Related papers  (2023-06-09T18:40:55Z)
• Bayesian Learning of Coupled Biogeochemical-Physical Models [28.269731698116257]
  Predictive models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is significant uncertainty. We develop a Bayesian model learning methodology that allows handling in the space of candidate models and discovery of new models.
  arXiv  Detail & Related papers  (2022-11-12T17:49:18Z)
• Learning Multivariate CDFs and Copulas using Tensor Factorization [39.24470798045442]
  Learning the multivariate distribution of data is a core challenge in statistics and machine learning. In this work, we aim to learn multivariate cumulative distribution functions (CDFs), as they can handle mixed random variables. We show that any grid sampled version of a joint CDF of mixed random variables admits a universal representation as a naive Bayes model. We demonstrate the superior performance of the proposed model in several synthetic and real datasets and applications including regression, sampling and data imputation.
  arXiv  Detail & Related papers  (2022-10-13T16:18:46Z)
• Improving Robustness and Uncertainty Modelling in Neural Ordinary Differential Equations [0.2538209532048866]
  We propose a novel approach to model uncertainty in NODE by considering a distribution over the end-time $T$ of the ODE solver. We also propose, adaptive latent time NODE (ALT-NODE), which allow each data point to have a distinct posterior distribution over end-times. We demonstrate the effectiveness of the proposed approaches in modelling uncertainty and robustness through experiments on synthetic and several real-world image classification data.
  arXiv  Detail & Related papers  (2021-12-23T16:56:10Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations [5.584060970507507]
  A Parsimony Enhanced Sparse Bayesian Learning (PeSBL) method is developed for discovering the governing Partial Differential Equations (PDEs) of nonlinear dynamical systems. Results of numerical case studies indicate that the governing PDEs of many canonical dynamical systems can be correctly identified using the proposed PeSBL method.
  arXiv  Detail & Related papers  (2021-07-08T00:56:11Z)
• Probabilistic Circuits for Variational Inference in Discrete Graphical Models [101.28528515775842]
  Inference in discrete graphical models with variational methods is difficult. Many sampling-based methods have been proposed for estimating Evidence Lower Bound (ELBO) We propose a new approach that leverages the tractability of probabilistic circuit models, such as Sum Product Networks (SPN) We show that selective-SPNs are suitable as an expressive variational distribution, and prove that when the log-density of the target model is aweighted the corresponding ELBO can be computed analytically.
  arXiv  Detail & Related papers  (2020-10-22T05:04:38Z)

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.