Probabilistic Model-Agnostic Meta-Learning (1806.02817v2)

Abstract: Meta-learning for few-shot learning entails acquiring a prior over previous tasks and experiences, such that new tasks be learned from small amounts of data. However, a critical challenge in few-shot learning is task ambiguity: even when a powerful prior can be meta-learned from a large number of prior tasks, a small dataset for a new task can simply be too ambiguous to acquire a single model (e.g., a classifier) for that task that is accurate. In this paper, we propose a probabilistic meta-learning algorithm that can sample models for a new task from a model distribution. Our approach extends model-agnostic meta-learning, which adapts to new tasks via gradient descent, to incorporate a parameter distribution that is trained via a variational lower bound. At meta-test time, our algorithm adapts via a simple procedure that injects noise into gradient descent, and at meta-training time, the model is trained such that this stochastic adaptation procedure produces samples from the approximate model posterior. Our experimental results show that our method can sample plausible classifiers and regressors in ambiguous few-shot learning problems. We also show how reasoning about ambiguity can also be used for downstream active learning problems.

Overview of Probabilistic Model-Agnostic Meta-Learning

This paper proposes a novel approach to address the challenges of few-shot learning through a probabilistic extension of the Model-Agnostic Meta-Learning (MAML) framework. The method aims to tackle task ambiguity by introducing a probabilistic model that can sample various plausible models for a new task from a learned distribution. This approach builds upon the foundation of MAML, leveraging gradient descent for adaptation to new tasks, but extends the method by integrating a parameter distribution trained using a variational lower bound.

Methodology

The core methodology involves reformulating the MAML algorithm within a probabilistic graphical model framework. This involves:

• Probabilistic Inference: The distribution over task-specific model parameters is inferred using structured variational inference. The posterior distribution on these parameters is approximated to enable learning from limited data samples.
• Gradient-Based Adaptation with Noise Injection: At meta-test time, the adaptation process involves injecting noise during gradient descent, which facilitates sampling from the approximate model posterior.
• Learned Prior and Posterior: The approach models a distribution over global parameters, incorporating a learned prior and performing variational inference to adapt the parameters to new tasks efficiently.

Experimental Results

The experiments demonstrate the efficacy of the proposed method across several scenarios, including few-shot regression and classification tasks:

• Few-Shot Regression: The approach captures uncertainty effectively, differentiating between linear and sinusoidal functions.
• Ambiguous Classification: In tasks with high ambiguity, such as those based on the CelebA dataset, the method achieves broader coverage of possible attribute combinations, showcasing its ability to model task uncertainty.
• Comparison with MAML: The probabilistic extension improves upon the deterministic nature of MAML by allowing multiple potential solutions to be evaluated, providing higher accuracy and task coverage.

Implications and Future Directions

The introduction of uncertainty modeling into the MAML framework has significant implications for the field of few-shot learning:

• Uncertainty Estimation: The ability to model multiple plausible solutions offers a quantitative approach to estimating task uncertainty, which can inform active learning strategies.
• Scalability to Complex Tasks: The proposed method retains the scalability of MAML to complex, high-dimensional tasks while adding the richness of probabilistic modeling.
• Future Research: The methodology opens avenues for exploring more intricate posterior parameterizations and extending similar frameworks to reinforcement learning settings to aid in exploration and decision-making under uncertainty.

Through these contributions, the paper provides a structured pathway to integrating probabilistic reasoning in meta-learning frameworks, enhancing the adaptability and robustness of few-shot learning algorithms in ambiguous settings.