Robust Local Information Transfer for High-Dimensional Data Analysis with Conditional Spike-and-Slab Prior

Konsep Inti

The authors propose a novel Bayesian transfer learning method named "CONCERT" that allows robust local information transfer for high-dimensional data analysis. CONCERT introduces a conditional spike-and-slab prior to characterize the local similarities between the source and target data, enabling adaptive and simultaneous variable selection and information transfer.

Abstrak

The authors propose a novel Bayesian transfer learning method called "CONCERT" to address the challenges in existing statistical transfer learning methods. The key contributions are:

CONCERT allows robust local information transfer by introducing a conditional spike-and-slab prior on the joint distribution of the target and source parameters. This enables the method to adaptively capture the local similarities between the source and target data, in contrast to the global similarity measures used in existing methods.

CONCERT achieves variable selection and information transfer simultaneously in a one-step procedure, without the need for a two-stage framework. This improves statistical and computational efficiency compared to existing methods.

Theoretical results on variable selection consistency are established for CONCERT, showing that it can detect weaker signals by leveraging information from the sources.

A scalable variational Bayes implementation is developed for CONCERT, making it suitable for high-dimensional problems.

The authors conduct extensive numerical experiments and a real data analysis on genetic data to demonstrate the advantages of CONCERT over existing transfer learning methods, especially in scenarios where the sources contain heterogeneous or redundant information compared to the target.

Statistik

The sample sizes are n0 = 150 for the target data and nk = 100 for each of the K = 10 source datasets. The number of covariates is p = 200.

Kutipan

"To illustrate when the global similarity may fail, we consider the following two cases and illustrate them in Figure 1."
"Motivated by the above challenges, we propose a novel Bayesian transfer learning method to allow robust local information transfer for high-dimensional data analysis."
"We name our proposed method as CONCERT - CONditional spike-and-slab assisted and Covariate-Elaborated Robust Transfer, as it can robustly transfer information from informative covariates from different sources and ensure them work collaboratively to improve the target."

Wawasan Utama Disaring Dari

CONCERT

by Ruqian Zhang... pada arxiv.org 04-08-2024

https://arxiv.org/pdf/2404.03764.pdf

Pertanyaan yang Lebih Dalam

How can the theoretical results on variable selection consistency be extended to the case where the similarity structures are unknown and need to be learned from the data

To extend the theoretical results on variable selection consistency to cases where the similarity structures are unknown, one approach could be to incorporate a learning mechanism for the similarity structures within the CONCERT framework. This could involve introducing latent variables or parameters that capture the underlying similarities between the source and target datasets. By treating these similarities as unknowns to be estimated from the data, the model can adaptively learn the local structures that are most relevant for information transfer. This learning process could be integrated into the variational Bayes framework used for implementation, allowing the model to iteratively update the similarity structures along with the other parameters.

What are the potential limitations of the conditional spike-and-slab prior approach, and how can it be further generalized to handle more complex data structures or model assumptions

One potential limitation of the conditional spike-and-slab prior approach is its reliance on predefined covariate-specific indicators for similarity selection. This may not capture complex relationships or dependencies between covariates in the data. To address this limitation, the approach could be generalized by incorporating more flexible modeling techniques, such as hierarchical Bayesian models or nonparametric methods. These extensions could allow for more nuanced representations of similarity structures, accommodating nonlinear relationships or interactions between covariates. Additionally, incorporating prior knowledge or domain expertise into the model could enhance its ability to capture complex data structures.

Can the CONCERT framework be adapted to other types of high-dimensional models beyond linear regression, such as generalized linear models or time series analysis, and how would the implementation and theoretical guarantees change in those settings

The CONCERT framework can be adapted to other high-dimensional models beyond linear regression, such as generalized linear models (GLMs) or time series analysis, by modifying the likelihood functions and prior distributions accordingly. For GLMs, the conditional spike-and-slab prior can be extended to accommodate different link functions and error distributions. The implementation would involve updating the variational parameters and posterior distributions specific to the chosen model structure. The theoretical guarantees in these settings would need to be reevaluated to ensure the consistency and efficiency of the estimation procedure for the new model assumptions. Additionally, the scalability and computational complexity of the algorithm may vary depending on the complexity of the model and the data structure.