Enabling Mixed Effects Neural Networks for Diverse, Clustered Data Using Monte Carlo Methods (2407.01115v1)

Abstract: Neural networks often assume independence among input data samples, disregarding correlations arising from inherent clustering patterns in real-world datasets (e.g., due to different sites or repeated measurements). Recently, mixed effects neural networks (MENNs) which separate cluster-specific 'random effects' from cluster-invariant 'fixed effects' have been proposed to improve generalization and interpretability for clustered data. However, existing methods only allow for approximate quantification of cluster effects and are limited to regression and binary targets with only one clustering feature. We present MC-GMENN, a novel approach employing Monte Carlo methods to train Generalized Mixed Effects Neural Networks. We empirically demonstrate that MC-GMENN outperforms existing mixed effects deep learning models in terms of generalization performance, time complexity, and quantification of inter-cluster variance. Additionally, MC-GMENN is applicable to a wide range of datasets, including multi-class classification tasks with multiple high-cardinality categorical features. For these datasets, we show that MC-GMENN outperforms conventional encoding and embedding methods, simultaneously offering a principled methodology for interpreting the effects of clustering patterns.

• The paper proposes the MC-GMENN framework, a novel method that leverages Monte Carlo techniques to enhance mixed effects neural network performance on clustered data.
• It employs a Monte Carlo EM algorithm that samples random effects using NUTS and updates fixed effects via gradient descent, balancing efficiency with accuracy.
• Empirical results on real-world multi-class datasets demonstrate improved scalability and unbiased performance compared to traditional encoding and embedding methods.

Enabling Mixed Effects Neural Networks for Diverse, Clustered Data Using Monte Carlo Methods

The paper "Enabling Mixed Effects Neural Networks for Diverse, Clustered Data Using Monte Carlo Methods" by Andrej Tschalzev et al. presents MC-GMENN, a novel framework that leverages Monte Carlo methods to improve the training of Generalized Mixed Effects Neural Networks (GMENN). Motivated by the limitations of existing mixed-effects neural network approaches, the authors propose this framework to better handle clustered data, especially in multi-class classification problems with multiple high-cardinality categorical features.

Introduction and Background

Deep Neural Networks (DNNs) traditionally assume independence among input data samples, an assumption that often breaks down in real-world clustered datasets. Conventional methods such as one-hot encoding or embeddings do incorporate cluster information but suffer from issues like overfitting and lack of interpretability. Generalized linear mixed models (GLMMs) from the statistics domain have addressed clustered data effectively, motivating the integration of these models with DNNs to improve performance and interpretability.

Existing approaches for Mixed Effects Neural Networks (MENNs) use approximate methods like Variational Inference (VI) due to the time inefficiency of Monte Carlo Markov Chain (MCMC) methods in fully Bayesian networks. However, the authors argue that for MENNs, only the random effects parameters need to be sampled. Modern MCMC methods, specifically the No-U-Turn Sampler (NUTS), offer efficient sampling, leading to the MC-GMENN framework.

MC-GMENN Framework

MC-GMENN extends traditional GLMMs using Monte Carlo Expectation Maximization (MCEM) to train neural networks:

1. E-Step: Sample random effects using NUTS, which efficiently traverses complex likelihood surfaces.
2. M-Step: Update the fixed effects parameters using gradient descent, decoupling the expensive sampling procedure from mini-batch updates.

The framework thus combines the strengths of both MCMC and EM, ensuring scalability to large datasets while maintaining the benefits of mixed effects modeling.

Empirical Validation

Three distinct experimental settings validate the efficacy of MC-GMENN:

1. Comparison with Existing MENN Approaches: The method demonstrated superior performance and better inter-cluster variance quantification compared to LMMNN and ARMED, especially in high-cardinality scenarios. This validates the unbiased estimates and time efficiency enabled by the MCEM procedure.
2. Scalability: The framework was tested on multi-class classification datasets with varying complexities such as high-dimensional features, large sample sizes, and multiple clustering features. MC-GMENN consistently outperformed or matched the performance of encoding and embedding methods, proving its scalability and versatility.
3. Real-World Applications: The paper evaluated MC-GMENN across 16 real-world benchmark datasets. It demonstrated strong performance, especially in datasets with multiple high-cardinality features and classes. Additionally, the method provided interpretable models by quantifying random effects accurately.

Implications and Future Directions

MC-GMENN advances the state-of-the-art in handling clustered data within deep learning frameworks, particularly excelling where categorical features exhibit high cardinality or where multiple clustering features exist. It offers an unbiased and efficient alternative to existing methods, thanks to the integration of sophisticated MCMC techniques.

The framework’s ability to scale to diverse data scenarios and provide interpretable models has significant practical implications. It opens up potential applications in medicine for patient-specific predictions or in e-commerce for customer segmentation and personalized recommendations. Theoretical implications include bridging the domains of mixed-effects modeling and deep learning, revealing a promising direction for future research.

Future work could extend MC-GMENN to other domains or investigate further optimizations tailored to specific applications, such as real-time data processing in click-through rate prediction or improving accuracy in human-centered data applications.

Conclusion

The paper by Tschalzev et al. successfully presents a robust and scalable approach for mixed-effects neural networks using Monte Carlo methods. By addressing the limitations of existing methods and demonstrating the applicability of MC-GMENN to a wide range of datasets, the authors significantly contribute to the fields of machine learning and statistical modeling. The approach’s demonstrated scalability, efficiency, and interpretability render it a valuable tool for researchers and practitioners dealing with clustered data in various domains.