Coefficient Shape Transfer Learning for Functional Linear Regression

• URL: http://arxiv.org/abs/2506.11367v2
• Date: Thu, 10 Jul 2025 13:55:15 GMT
• Title: Coefficient Shape Transfer Learning for Functional Linear Regression
• Authors: Shuhao Jiao, Ian W. Mckeague, N. -H. Chan,
• Abstract summary: We develop a novel transfer learning methodology to tackle the challenge of data scarcity in functional linear models.<n>We use samples from the target model (target domain) alongside those from auxiliary models (source domains) to transfer knowledge of coefficient shape from the source domains to the target domain.<n>We rigorously analyze the convergence rates of the proposed estimator and examine the minimax optimality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we develop a novel transfer learning methodology to tackle the challenge of data scarcity in functional linear models. The methodology incorporates samples from the target model (target domain) alongside those from auxiliary models (source domains), transferring knowledge of coefficient shape from the source domains to the target domain. This shape-based knowledge transfer offers two key advantages. First, it is robust to covariate scaling, ensuring effectiveness despite variations in data distributions across different source domains. Second, the notion of coefficient shape homogeneity represents a meaningful advance beyond traditional coefficient homogeneity, allowing the method to exploit a wider range of source domains and achieve significantly improved model estimation. We rigorously analyze the convergence rates of the proposed estimator and examine the minimax optimality. Our findings show that the degree of improvement depends not only on the similarity of coefficient shapes between the target and source domains, but also on coefficient magnitudes and the spectral decay rates of the functional covariates covariance operators. To address situations where only a subset of auxiliary models is informative for the target model, we further develop a data-driven procedure for identifying such informative sources. The effectiveness of the proposed methodology is demonstrated through comprehensive simulation studies and an application to occupation time analysis using physical activity data from the U.S. National Health and Nutrition Examination Survey.

Related papers

• Partial Transportability for Domain Generalization [56.37032680901525]
  Building on the theory of partial identification and transportability, this paper introduces new results for bounding the value of a functional of the target distribution.<n>Our contribution is to provide the first general estimation technique for transportability problems.<n>We propose a gradient-based optimization scheme for making scalable inferences in practice.
  arXiv  Detail & Related papers  (2025-03-30T22:06:37Z)
• Model-free Methods for Event History Analysis and Efficient Adjustment (PhD Thesis) [55.2480439325792]
  This thesis is a series of independent contributions to statistics unified by a model-free perspective.<n>The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning.<n>The second chapter studies the concept of local independence, which describes whether the evolution of one process is directly influenced by another.
  arXiv  Detail & Related papers  (2025-02-11T19:24:09Z)
• You are out of context! [0.0]
  New data can act as forces stretching, compressing, or twisting the geometric relationships learned by a model. We propose a novel drift detection methodology for machine learning (ML) models based on the concept of ''deformation'' in the vector space representation of data.
  arXiv  Detail & Related papers  (2024-11-04T10:17:43Z)
• Influence Functions for Scalable Data Attribution in Diffusion Models [52.92223039302037]
  Diffusion models have led to significant advancements in generative modelling.<n>Yet their widespread adoption poses challenges regarding data attribution and interpretability.<n>We develop an influence functions framework to address these challenges.
  arXiv  Detail & Related papers  (2024-10-17T17:59:02Z)
• Source-Free Domain-Invariant Performance Prediction [68.39031800809553]
  We propose a source-free approach centred on uncertainty-based estimation, using a generative model for calibration in the absence of source data. Our experiments on benchmark object recognition datasets reveal that existing source-based methods fall short with limited source sample availability. Our approach significantly outperforms the current state-of-the-art source-free and source-based methods, affirming its effectiveness in domain-invariant performance estimation.
  arXiv  Detail & Related papers  (2024-08-05T03:18:58Z)
• Quantifying Distribution Shifts and Uncertainties for Enhanced Model Robustness in Machine Learning Applications [0.0]
  This study explores model adaptation and generalization by utilizing synthetic data. We employ quantitative measures such as Kullback-Leibler divergence, Jensen-Shannon distance, and Mahalanobis distance to assess data similarity. Our findings suggest that utilizing statistical measures, such as the Mahalanobis distance, to determine whether model predictions fall within the low-error "interpolation regime" or the high-error "extrapolation regime" provides a complementary method for assessing distribution shift and model uncertainty.
  arXiv  Detail & Related papers  (2024-05-03T10:05:31Z)
• Aggregation Weighting of Federated Learning via Generalization Bound Estimation [65.8630966842025]
  Federated Learning (FL) typically aggregates client model parameters using a weighting approach determined by sample proportions. We replace the aforementioned weighting method with a new strategy that considers the generalization bounds of each local model.
  arXiv  Detail & Related papers  (2023-11-10T08:50:28Z)
• Representation Transfer Learning via Multiple Pre-trained models for Linear Regression [3.5788754401889014]
  We consider the problem of learning a linear regression model on a data domain of interest (target) given few samples. To aid learning, we are provided with a set of pre-trained regression models that are trained on potentially different data domains. We propose a representation transfer based learning method for constructing the target model.
  arXiv  Detail & Related papers  (2023-05-25T19:35:24Z)
• Transfer Learning with Uncertainty Quantification: Random Effect Calibration of Source to Target (RECaST) [1.8047694351309207]
  We develop a statistical framework for model predictions based on transfer learning, called RECaST. We mathematically and empirically demonstrate the validity of our RECaST approach for transfer learning between linear models. We examine our method's performance in a simulation study and in an application to real hospital data.
  arXiv  Detail & Related papers  (2022-11-29T19:39:47Z)
• Variational Model Perturbation for Source-Free Domain Adaptation [64.98560348412518]
  We introduce perturbations into the model parameters by variational Bayesian inference in a probabilistic framework. We demonstrate the theoretical connection to learning Bayesian neural networks, which proves the generalizability of the perturbed model to target domains.
  arXiv  Detail & Related papers  (2022-10-19T08:41:19Z)
• Transfer learning with affine model transformation [18.13383101189326]
  This paper presents a general class of transfer learning regression called affine model transfer. It is shown that the affine model transfer broadly encompasses various existing methods, including the most common procedure based on neural feature extractors.
  arXiv  Detail & Related papers  (2022-10-18T10:50:24Z)
• On Hypothesis Transfer Learning of Functional Linear Models [7.243632426715939]
  We study the transfer learning (TL) for the functional linear regression (FLR) under the Reproducing Kernel Space (RKHS) framework.<n>We measure the similarity across tasks using RKHS distance, allowing the type of information being transferred to be tied to the properties of the imposed RKHS.
  arXiv  Detail & Related papers  (2022-06-09T04:50:16Z)
• SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks [14.564168076456822]
  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.
  arXiv  Detail & Related papers  (2020-08-19T19:11:25Z)

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.