Analytical results for uncertainty propagation through trained machine learning regression models

• URL: http://arxiv.org/abs/2404.11224v2
• Date: Wed, 8 May 2024 15:50:31 GMT
• Title: Analytical results for uncertainty propagation through trained machine learning regression models
• Authors: Andrew Thompson,
• Abstract summary: This paper addresses the challenge of uncertainty propagation through trained/fixed machine learning (ML) regression models. We present numerical experiments in which we validate our methods and compare them with a Monte Carlo approach from a computational efficiency point of view.
• Score: 0.10878040851637999
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Machine learning (ML) models are increasingly being used in metrology applications. However, for ML models to be credible in a metrology context they should be accompanied by principled uncertainty quantification. This paper addresses the challenge of uncertainty propagation through trained/fixed machine learning (ML) regression models. Analytical expressions for the mean and variance of the model output are obtained/presented for certain input data distributions and for a variety of ML models. Our results cover several popular ML models including linear regression, penalised linear regression, kernel ridge regression, Gaussian Processes (GPs), support vector machines (SVMs) and relevance vector machines (RVMs). We present numerical experiments in which we validate our methods and compare them with a Monte Carlo approach from a computational efficiency point of view. We also illustrate our methods in the context of a metrology application, namely modelling the state-of-health of lithium-ion cells based upon Electrical Impedance Spectroscopy (EIS) data

Related papers

• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Fusion of Gaussian Processes Predictions with Monte Carlo Sampling [61.31380086717422]
  In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes.
  arXiv  Detail & Related papers  (2024-03-03T04:21:21Z)
• Statistical Agnostic Regression: a machine learning method to validate regression models [0.0]
  We introduce Statistical Agnostic Regression (SAR) for evaluating the statistical significance of machine learning (ML)-based linear regression models. We define a threshold that ensures there is sufficient evidence, with a probability of at least $1-eta$, to conclude the existence of a linear relationship in the population between the explanatory (feature) and the response (label) variables.
  arXiv  Detail & Related papers  (2024-02-23T09:19:26Z)
• Probabilistic Unrolling: Scalable, Inverse-Free Maximum Likelihood Estimation for Latent Gaussian Models [69.22568644711113]
  We introduce probabilistic unrolling, a method that combines Monte Carlo sampling with iterative linear solvers to circumvent matrix inversions. Our theoretical analyses reveal that unrolling and backpropagation through the iterations of the solver can accelerate gradient estimation for maximum likelihood estimation. In experiments on simulated and real data, we demonstrate that probabilistic unrolling learns latent Gaussian models up to an order of magnitude faster than gradient EM, with minimal losses in model performance.
  arXiv  Detail & Related papers  (2023-06-05T21:08:34Z)
• Resolving quantitative MRI model degeneracy with machine learning via training data distribution design [2.2086005010186387]
  Quantitative MRI aims to map tissue properties non-invasively via models that relate unknown quantities to measured MRI signals. Estimating these unknowns, which has traditionally required model fitting, can now be done with one-shot machine learning (ML) approaches. Growing empirical evidence appears to suggest ML approaches remain susceptible to model degeneracy.
  arXiv  Detail & Related papers  (2023-03-09T18:10:45Z)
• Bayesian Active Learning for Discrete Latent Variable Models [19.852463786440122]
  Active learning seeks to reduce the amount of data required to fit the parameters of a model. latent variable models play a vital role in neuroscience, psychology, and a variety of other engineering and scientific disciplines.
  arXiv  Detail & Related papers  (2022-02-27T19:07:12Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• An interpretable prediction model for longitudinal dispersion coefficient in natural streams based on evolutionary symbolic regression network [30.99493442296212]
  Various methods have been proposed for predictions of longitudinal dispersion coefficient(LDC) In this paper, we first present an in-depth analysis of those methods and find out their defects. We then design a novel symbolic regression method called evolutionary symbolic regression network(ESRN)
  arXiv  Detail & Related papers  (2021-06-17T07:06:05Z)
• Regression Bugs Are In Your Model! Measuring, Reducing and Analyzing Regressions In NLP Model Updates [68.09049111171862]
  This work focuses on quantifying, reducing and analyzing regression errors in the NLP model updates. We formulate the regression-free model updates into a constrained optimization problem. We empirically analyze how model ensemble reduces regression.
  arXiv  Detail & Related papers  (2021-05-07T03:33:00Z)
• Using machine learning to correct model error in data assimilation and forecast applications [0.0]
  We propose to use this method to correct the error of an existent, knowledge-based model. The resulting surrogate model is an hybrid model between the original (knowledge-based) model and the ML model. Using the hybrid surrogate models for DA yields a significantly better analysis than using the original model.
  arXiv  Detail & Related papers  (2020-10-23T18:30:45Z)
• Transfer Learning without Knowing: Reprogramming Black-box Machine Learning Models with Scarce Data and Limited Resources [78.72922528736011]
  We propose a novel approach, black-box adversarial reprogramming (BAR), that repurposes a well-trained black-box machine learning model. Using zeroth order optimization and multi-label mapping techniques, BAR can reprogram a black-box ML model solely based on its input-output responses. BAR outperforms state-of-the-art methods and yields comparable performance to the vanilla adversarial reprogramming method.
  arXiv  Detail & Related papers  (2020-07-17T01:52:34Z)

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.