用概率方法提升低数据下神经系统识别的可靠性与不确定性估计。
Variational meta-learning inference for low dimensional neural system identification
- 基于变分推断构建参数流形的生成先验，实现概率化元学习。
- 在极端低数据下仍保持与确定性方法相当的预测精度。
- 适合需要可信置信区间的低数据系统建模任务。
深度学习在非线性系统识别中表现优异，但参数量大的神经网络在数据稀缺时易过拟合，且缺乏可靠的不确定性量化。近期提出的流形元学习框架通过将模型参数限制在元学习得到的低维流形上，提升了数据效率。然而该方法为确定性设计。本文提出一种完全概率化的流形元学习扩展，基于压缩变分推断，学习低维参数流形上的生成先验。在任务特定适应阶段，结合最大后验估计与拉普拉斯近似，获得数学上严谨的后验近似。在静态回归任务和Bouc-Wen动力学系统基准测试中，该方法在严重低数据条件下实现了与确定性方法相当的预测精度，并成功提供校准的不确定性边界。
原文摘要 · Abstract (English)
Deep learning has proven highly effective for nonlinear system identification, but heavily parameterized neural networks are prone to overfitting in low-data regimes and lack reliable uncertainty quantification. The recently developed manifold meta-learning framework addresses the data efficiency problem by restricting the model parameters to a meta-learned low-dimensional manifold. However, that method is purely deterministic. We propose a fully probabilistic extension of the manifold meta-learning framework, based on amortized Variational Inference, where a generative prior over the low-dimensional parameter manifold is learned. During task-specific adaptation, we combine Maximum A Posteriori estimation with the Laplace approximation to yield a mathematically grounded posterior approximation. Evaluated on a static regression task and the Bouc--Wen dynamical system benchmark, the proposed approach achieves predictive accuracy comparable to its deterministic counterpart while successfully providing calibrated uncertainty bounds in severely low-data regimes.
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