仅需约 log N 次观测即可准确学习对称动态系统参数。
Symmetric Linear Dynamical Systems are Learnable from Few Observations
- 基于矩方法设计新估计器，无需特定正则化。
- 在单轨迹下，仅用 T=O(log N) 观测即可实现小元素误差恢复。
- 适用于结构发现等场景，对稀疏或密集矩阵均有效。
我们研究从单条时间长度为 T 的轨迹中，在完全或部分观测下学习 N 维随机线性动力系统的参数。提出并分析了一种新估计器，可在不依赖问题特异性正则化的情况下，仅使用 T=O(log N) 次观测，实现对称动态矩阵的小最大元素误差恢复，无论矩阵是稀疏还是密集。该估计器基于矩方法，对结构发现等应用尤为重要。
原文摘要 · Abstract (English)
We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices using only $T=\mathcal{O}(\log N)$ observations, irrespective of whether the matrix is sparse or dense. This estimator is based on the method of moments and does not rely on problem-specific regularization. This is especially important for applications such as structure discovery.
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