On the use of Statistical Learning Theory for model selection in Structural Health Monitoring

• URL: http://arxiv.org/abs/2501.08050v1
• Date: Tue, 14 Jan 2025 11:56:05 GMT
• Title: On the use of Statistical Learning Theory for model selection in Structural Health Monitoring
• Authors: C. A. Lindley, N. Dervilis, K. Worden,
• Abstract summary: This paper focusses on how well models can generalise in Structural Health Monitoring (SHM) It is demonstrated that incorporating domain knowledge into the regression problem yields a lower guaranteed risk, thereby enhancing generalisation.
• Score: 0.0
• License:
• Abstract: Whenever data-based systems are employed in engineering applications, defining an optimal statistical representation is subject to the problem of model selection. This paper focusses on how well models can generalise in Structural Health Monitoring (SHM). Although statistical model validation in this field is often performed heuristically, it is possible to estimate generalisation more rigorously using the bounds provided by Statistical Learning Theory (SLT). Therefore, this paper explores the selection process of a kernel smoother for modelling the impulse response of a linear oscillator from the perspective of SLT. It is demonstrated that incorporating domain knowledge into the regression problem yields a lower guaranteed risk, thereby enhancing generalisation.

Related papers

• Probability Distribution Learning and Its Application in Deep Learning [0.0]
  This paper introduces a novel theoretical learning framework, termed probability distribution learning (PD learning) PD learning focuses on learning the underlying probability distribution, which is modeled as a random variable within the probability simplex.
  arXiv  Detail & Related papers  (2024-06-09T06:49:22Z)
• 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)
• Inference of Dependency Knowledge Graph for Electronic Health Records [13.35941801610195]
  We propose a framework for deriving a sparse knowledge graph based on the dynamic log-linear topic model. Within this model, the KG embeddings are estimated by performing singular value decomposition on the empirical pointwise mutual information matrix. We then establish entrywise normality for the KG low-rank estimator, enabling the recovery of sparse graph edges with controlled type I error.
  arXiv  Detail & Related papers  (2023-12-25T04:45:36Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• 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)
• Distribution-free Deviation Bounds and The Role of Domain Knowledge in Learning via Model Selection with Cross-validation Risk Estimation [0.0]
  Cross-validation techniques for risk estimation and model selection are widely used in statistics and machine learning. This paper presents learning via model selection with cross-validation risk estimation as a general systematic learning framework.
  arXiv  Detail & Related papers  (2023-03-15T17:18:31Z)
• SimSCOOD: Systematic Analysis of Out-of-Distribution Generalization in Fine-tuned Source Code Models [58.78043959556283]
  We study the behaviors of models under different fine-tuning methodologies, including full fine-tuning and Low-Rank Adaptation (LoRA) fine-tuning methods. Our analysis uncovers that LoRA fine-tuning consistently exhibits significantly better OOD generalization performance than full fine-tuning across various scenarios.
  arXiv  Detail & Related papers  (2022-10-10T16:07:24Z)
• How robust are pre-trained models to distribution shift? [82.08946007821184]
  We show how spurious correlations affect the performance of popular self-supervised learning (SSL) and auto-encoder based models (AE) We develop a novel evaluation scheme with the linear head trained on out-of-distribution (OOD) data, to isolate the performance of the pre-trained models from a potential bias of the linear head used for evaluation.
  arXiv  Detail & Related papers  (2022-06-17T16:18:28Z)
• Causality and Generalizability: Identifiability and Learning Methods [0.0]
  This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. We propose a general framework for distributional robustness with respect to intervention-induced distributions.
  arXiv  Detail & Related papers  (2021-10-04T13:12:11Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Design-unbiased statistical learning in survey sampling [0.0]
  We propose a subsampling Rao-Blackwell method, and develop a statistical learning theory for exactly design-unbiased estimation. Our approach makes use of classic ideas from Statistical Science as well as the rapidly growing field of Machine Learning.
  arXiv  Detail & Related papers  (2020-03-25T14:27:39Z)

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.