Symmetric Linear Dynamical Systems are Learnable from Few Observations
This addresses the challenge of efficient parameter estimation in dynamical systems for applications like structure discovery, though it is incremental as it builds on existing methods.
The paper tackles the problem of learning parameters of symmetric linear dynamical systems from limited observations, achieving a small maximum element-wise error with only T=O(log N) observations, regardless of sparsity.
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.