Sparse Gaussian Neural Processes (2504.01650v2)

Abstract: Despite significant recent advances in probabilistic meta-learning, it is common for practitioners to avoid using deep learning models due to a comparative lack of interpretability. Instead, many practitioners simply use non-meta-models such as Gaussian processes with interpretable priors, and conduct the tedious procedure of training their model from scratch for each task they encounter. While this is justifiable for tasks with a limited number of data points, the cubic computational cost of exact Gaussian process inference renders this prohibitive when each task has many observations. To remedy this, we introduce a family of models that meta-learn sparse Gaussian process inference. Not only does this enable rapid prediction on new tasks with sparse Gaussian processes, but since our models have clear interpretations as members of the neural process family, it also allows manual elicitation of priors in a neural process for the first time. In meta-learning regimes for which the number of observed tasks is small or for which expert domain knowledge is available, this offers a crucial advantage.

• The paper introduces Sparse Gaussian Neural Processes (SGNPs), a novel family of models that bridge the gap between interpretable Gaussian Processes and scalable neural-based meta-learning.
• SGNPs achieve scalability and efficiency through amortized variational inference across tasks and the use of sparse variational GP techniques, enabling rapid predictions.
• Experiments show SGNPs deliver superior performance, especially in low-data regimes, offering a more interpretable and scalable solution for probabilistic meta-learning than prior methods.

Sparse Gaussian Neural Processes: A Comprehensive Overview

The paper "Sparse Gaussian Neural Processes" presents a novel approach to bridging the gap between Gaussian Processes (GPs) and neural-based meta-learning models, leveraging the inherent strengths of both methodologies. The authors address the critical challenges in the field of probabilistic meta-learning, where a balance between scalability and interpretability is often hard to achieve.

Motivation and Background

In practical applications, obtaining well-calibrated predictive distributions is essential, particularly in high-stakes environments. Traditional Gaussian Processes are favored for their interpretability and ability to incorporate domain knowledge through priors, but they suffer from computational intractability when the dataset is large due to their $\mathcal{O}(n^3)$ computational complexity. Neural Processes, on the other hand, allow rapid adaptation to new tasks without the need for retraining from scratch, making them appealing for meta-learning. However, they often lack the interpretability associated with GPs.

Introduction of Sparse Gaussian Neural Processes

To reconcile the need for interpretability and scalability, the authors introduce Sparse Gaussian Neural Processes (SGNPs). This family of models aims to perform meta-learning for sparse GP inference, enabling rapid predictions while retaining the ability to incorporate interpretable priors.

1. Amortized Variational Inference: The SGNPs use amortized variational inference across tasks, allowing the model to learn to infer task-specific variational parameters efficiently. This approach significantly reduces the computational burden and allows the model to handle tasks with many observations seamlessly.
2. Interpretability and Efficiency: The model maintains interpretability through its clear connections to the GP framework. It employs sparse variational GP techniques, offering a computationally efficient alternative to exact inference while facilitating meaningful hyperparameter learning across tasks.

Contributions

The paper offers several key contributions:

• Interpretable Neural Process Variants: By introducing interpretability into the neural process framework through sparse GP approximations, the paper enriches the flexibility and applicability of neural processes in real-world tasks.
• Task-Specific Inference Networks: The model employs task-specific inference networks to map observations to variational parameters in a structured manner, promoting more robust generalization across dissimilar tasks.
• Performance Evaluation: The SGNPs demonstrate superior performance on both synthetic and real-world datasets, especially when the number of observed tasks is limited or when exact priors can be specified.

Experimental Evaluation

The experiments conducted cover synthetic 1D regression and 2D classification tasks as well as real-world applications in power consumption forecasting. Across these experiments, SGNPs demonstrated strong numerical performance, rivaling or surpassing traditional GP approaches in terms of predictive log-likelihoods. Particularly notable is the SGNP's ability to maintain robust performance in low-data regimes where other neural process models degrade.

Implications and Future Work

The implications of this research are substantial for both theory and practice:

• Scalability: SGNP offers a scalable solution for deploying GP-based methods in large-scale applications, significantly enhancing the feasibility of using GPs in industry.
• Theoretical Advancements: The integration of amortized inference within the GP framework opens new avenues for combining probabilistic model interpretability with the adaptability of neural networks.
• Future Directions: The research suggests future developments could explore extending the methodology to handle a broader class of variational models, potentially including Bayesian neural networks.

In conclusion, "Sparse Gaussian Neural Processes" marks an essential step forward in the development of probabilistic meta-learning models. By marrying the benefits of GPs and neural networks, it paves the way for more interpretable, scalable, and efficient models suited to a wide array of complex, real-world tasks. This hybrid approach may inspire further research in marrying explicit probabilistic models with neural approximation techniques, continuing to push the boundaries of what is achievable in machine learning.