用于低维神经系统识别的变分元学习推理
Variational meta-learning inference for low dimensional neural system identification
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- SUPSI-DTI-IDSIA, Dalle Molle Institute for Artificial Intelligence（瑞士意大利语区大学-信息工程与数学系-人工智能研究所）
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中文总结 AI 辅助
研究针对神经网络在低数据下易过拟合且缺乏可靠不确定性量化的问题，提出基于摊销变分推理的流形元学习框架概率扩展，结合最大后验估计与拉普拉斯近似，在低数据任务中实现高精度并提供校准的不确定性界限。
中文摘要 AI 辅助
深度学习在非线性系统识别中已证明非常有效，但参数众多的神经网络在低数据情况下容易过拟合且缺乏可靠的不确定性量化。最近开发的流形元学习框架通过将模型参数限制在元学习的低维流形上来解决数据效率问题，但该方法是纯确定性的。我们基于摊销变分推理提出了流形元学习框架的完全概率扩展，学习低维参数流形上的生成先验。在特定任务适应过程中，我们将最大后验估计与拉普拉斯近似相结合以产生数学上有依据的后验近似。在静态回归任务和Bouc - Wen动力系统基准上进行评估，该方法在严重低数据情况下实现了与确定性对应方法相当的预测精度，同时成功提供了校准的不确定性界限。
英文摘要
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.
