Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data
- URL: http://arxiv.org/abs/2409.09973v1
- Date: Mon, 16 Sep 2024 04:10:44 GMT
- Title: Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data
- Authors: Ellen Graham, Marco Carone, Andrea Rotnitzky,
- Abstract summary: We address the goal of conducting inference about a smooth finite-dimensional parameter by utilizing individual-level data from various independent sources.
Recent advancements have led to the development of a comprehensive theory capable of handling scenarios where different data sources align with, possibly distinct subsets of, conditional distributions of a single factorization of the joint target distribution.
We extend the aforementioned comprehensive theory to allow for the fusion of individual-level data from sources aligned with conditional distributions that do not correspond to a single factorization of the target distribution.
- Score: 1.0650780147044159
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We address the goal of conducting inference about a smooth finite-dimensional parameter by utilizing individual-level data from various independent sources. Recent advancements have led to the development of a comprehensive theory capable of handling scenarios where different data sources align with, possibly distinct subsets of, conditional distributions of a single factorization of the joint target distribution. While this theory proves effective in many significant contexts, it falls short in certain common data fusion problems, such as two-sample instrumental variable analysis, settings that integrate data from epidemiological studies with diverse designs (e.g., prospective cohorts and retrospective case-control studies), and studies with variables prone to measurement error that are supplemented by validation studies. In this paper, we extend the aforementioned comprehensive theory to allow for the fusion of individual-level data from sources aligned with conditional distributions that do not correspond to a single factorization of the target distribution. Assuming conditional and marginal distribution alignments, we provide universal results that characterize the class of all influence functions of regular asymptotically linear estimators and the efficient influence function of any pathwise differentiable parameter, irrespective of the number of data sources, the specific parameter of interest, or the statistical model for the target distribution. This theory paves the way for machine-learning debiased, semiparametric efficient estimation.
Related papers
- Learning Divergence Fields for Shift-Robust Graph Representations [73.11818515795761]
In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging problem with interdependent data.
We derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains.
arXiv Detail & Related papers (2024-06-07T14:29:21Z) - Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data [2.6499018693213316]
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables.
The embedding of the flow via the Segre map in the meta-simplex of all discrete joint distributions ensures that any target distribution can be represented in principle.
Our approach has strong motivation from first principles of modeling coupled discrete variables.
arXiv Detail & Related papers (2024-06-06T21:58:33Z) - Synthetic Tabular Data Validation: A Divergence-Based Approach [8.062368743143388]
Divergences quantify discrepancies between data distributions.
Traditional approaches calculate divergences independently for each feature.
We propose a novel approach that uses divergence estimation to overcome the limitations of marginal comparisons.
arXiv Detail & Related papers (2024-05-13T15:07:52Z) - Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data.
Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
arXiv Detail & Related papers (2024-04-24T09:04:36Z) - Scalable Regularised Joint Mixture Models [2.0686407686198263]
In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions.
We propose an approach for heterogeneous data that allows joint learning of (i) explicit multivariate feature distributions, (ii) high-dimensional regression models and (iii) latent group labels.
The approach is demonstrably effective in high dimensions, combining data reduction for computational efficiency with a re-weighting scheme that retains key signals even when the number of features is large.
arXiv Detail & Related papers (2022-05-03T13:38:58Z) - Non-Linear Spectral Dimensionality Reduction Under Uncertainty [107.01839211235583]
We propose a new dimensionality reduction framework, called NGEU, which leverages uncertainty information and directly extends several traditional approaches.
We show that the proposed NGEU formulation exhibits a global closed-form solution, and we analyze, based on the Rademacher complexity, how the underlying uncertainties theoretically affect the generalization ability of the framework.
arXiv Detail & Related papers (2022-02-09T19:01:33Z) - Selecting the suitable resampling strategy for imbalanced data
classification regarding dataset properties [62.997667081978825]
In many application domains such as medicine, information retrieval, cybersecurity, social media, etc., datasets used for inducing classification models often have an unequal distribution of the instances of each class.
This situation, known as imbalanced data classification, causes low predictive performance for the minority class examples.
Oversampling and undersampling techniques are well-known strategies to deal with this problem by balancing the number of examples of each class.
arXiv Detail & Related papers (2021-12-15T18:56:39Z) - Accounting for Unobserved Confounding in Domain Generalization [107.0464488046289]
This paper investigates the problem of learning robust, generalizable prediction models from a combination of datasets.
Part of the challenge of learning robust models lies in the influence of unobserved confounders.
We demonstrate the empirical performance of our approach on healthcare data from different modalities.
arXiv Detail & Related papers (2020-07-21T08:18:06Z) - Asymptotic Analysis of an Ensemble of Randomly Projected Linear
Discriminants [94.46276668068327]
In [1], an ensemble of randomly projected linear discriminants is used to classify datasets.
We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator.
We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
arXiv Detail & Related papers (2020-04-17T12:47:04Z) - Identification Methods With Arbitrary Interventional Distributions as
Inputs [8.185725740857595]
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data.
We use Single World Intervention Graphs and a nested factorization of models associated with mixed graphs to give a very simple view of existing identification theory for experimental data.
arXiv Detail & Related papers (2020-04-02T17:27:18Z) - Meta-analysis of heterogeneous data: integrative sparse regression in
high-dimensions [21.162280861396205]
We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical.
We introduce a global parameter that emphasizes interpretability and statistical efficiency in the presence of heterogeneity.
We demonstrate the benefits of our approach on a large-scale drug treatment dataset involving several different cancer cell-lines.
arXiv Detail & Related papers (2019-12-26T20:30:57Z)
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.