Multi-Task Gaussian Processes and Dilated Convolutional Networks for Reconstruction of Reproductive Hormonal Dynamics

Abstract: We present an end-to-end statistical framework for personalized, accurate, and minimally invasive modeling of female reproductive hormonal patterns. Reconstructing and forecasting the evolution of hormonal dynamics is a challenging task, but a critical one to improve general understanding of the menstrual cycle and personalized detection of potential health issues. Our goal is to infer and forecast individual hormone daily levels over time, while accommodating pragmatic and minimally invasive measurement settings. To that end, our approach combines the power of probabilistic generative models (i.e., multi-task Gaussian processes) with the flexibility of neural networks (i.e., a dilated convolutional architecture) to learn complex temporal mappings. To attain accurate hormone level reconstruction with as little data as possible, we propose a sampling mechanism for optimal reconstruction accuracy with limited sampling budget. Our results show the validity of our proposed hormonal dynamic modeling framework, as it provides accurate predictive performance across different realistic sampling budgets and outperforms baselines methods.

• The paper introduces a hybrid framework that combines multi-task Gaussian processes with dilated CNNs to reconstruct reproductive hormonal dynamics from sparse data.
• It leverages synthetic dataset generation and a novel Expected Distance sampling strategy to optimize hormone level measurements.
• The model outperforms traditional methods by accurately predicting estrogen and LH dynamics, underscoring its potential for personalized diagnostics.

Multi-Task Gaussian Processes and Dilated Convolutional Networks for Reconstruction of Reproductive Hormonal Dynamics

Introduction

The paper proposes an end-to-end statistical framework designed to model female reproductive hormonal patterns effectively. This modeling attempts to infer and predict daily hormone levels, adapting the data collection process to be as minimally invasive as possible. The approach innovatively combines multi-task Gaussian processes (MGPs) with dilated convolutional neural networks (DCNNs) to handle the complex temporal mappings required for modeling. The framework incorporates a novel approach in both data generation and method utilization, making it viable for personalized, low-cost hormone level reconstruction with limited data.

Dataset Generation

Given the lack of large-scale datasets on reproductive hormone levels, the study introduces a method to generate synthetic datasets that replicate real-world menstrual cycle characteristics. By referencing a database of self-reported menstrual cycles, and considering empirically grounded models for hormonal dynamics, the research creates a robust synthetic dataset. This synthetic approach enables exploring diverse hormone level patterns, essential for evaluating the proposed computational framework's efficacy.

Multi-Task Gaussian Processes

The utilization of MGPs allows the model to manage the sparsely sampled, irregular hormone level data efficiently. These GPs leverage their probabilistic nature to generate accurate predictions about hormone levels by evaluating both temporal and hormonal dependencies. The ability of MGPs to accommodate these irregular samples underscores their potential in dealing with real-world data, where continuous hormone measurements are impractical.

Figure 1: Reconstruction of hormone levels using MGP and DCNN, showcasing the probabilistic range (blue area) and reconstructed hormonal dynamics (blue dotted line).

Dilated Convolutional Neural Networks

In contrast to traditional recurrent networks, the paper employs DCNNs for robust sequence modeling of hormone levels. The key advantage of DCNNs lies in their ability to capture long-term dependencies effectively while avoiding issues related to gradient instability. The non-causal dilated convolution approach, which considers both past and future data, enhances the model's predictive accuracy and breadth, necessary for forecasting hormonal dynamics accurately.

Figure 2: Structure of the DCNN used for hormonal dynamics, featuring four hidden layers with non-causal, dilated convolutions.

Sampling Strategy Optimization

The research introduces a sampling mechanism inspired by Bayesian optimization principles to identify optimal measurement days. This Expected Distance (ED) strategy is crucial for achieving high reconstruction accuracy with minimal data points. By focusing on the points where reconstruction uncertainty is maximal, the model ensures that each additional measurement provides significant new information, thus maximizing efficiency.

Figure 3: ED sampling strategy for hormonal data, demonstrating the impact of additional samples on model uncertainty and accuracy.

Evaluation and Results

The proposed MGP-DCNN framework was tested against traditional methods, such as standalone GPs and LSTM networks, across various subsampling budgets. Results indicated a clear advantage of the ED-based sampling strategy and the combined use of MGPs with DCNNs. Notably, the framework performed well with minimal measurements, highlighting its practicality and efficiency in real-world applications.

Figure 4: Example of MGP-DCNN prediction performance with limited data, indicating accurate reconstruction of estrogen and LH dynamics.

Discussion

The ability to robustly reconstruct hormonal dynamics with sparse data could transform our approach to reproductive health monitoring. By generating accurate hormonal profiles with minimal invasion, the methodologies presented set a foundation for personalized healthcare solutions. Moreover, the integration of DCNNs in time-series reconstruction tasks highlights an ongoing trend towards leveraging convolutional architectures for non-image data, supporting broader applications across physiological modeling.

Conclusion

Overall, this research presents a statistically rigorous and computationally sound framework for hormonal dynamics modeling. The integration of advanced GP techniques with modern neural architectures offers a promising pathway for improved diagnostics and personalized medicine in reproductive health. Future work may continue to enhance model scalability and explore its application in diverse clinical settings.