Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved rates for prediction and identification of partially observed
  linear dynamical systems   Identification of a linear time-invariant dynamical system from partial
observations is a fundamental problem in control theory. Particularly
challenging are systems exhibiting long-term memory. A natural question is how
learn such systems with non-asymptotic statistical rates depending on the
inherent dimensionality (order) $d$ of the system, rather than on the possibly
much larger memory length. We propose an algorithm that given a single
trajectory of length $T$ with gaussian observation noise, learns the system
with a near-optimal rate of $\widetilde O\left(\sqrt\frac{d}{T}\right)$ in
$\mathcal{H}_2$ error, with only logarithmic, rather than polynomial dependence
on memory length. We also give bounds under process noise and improved bounds
for learning a realization of the system. Our algorithm is based on multi-scale
low-rank approximation: SVD applied to Hankel matrices of geometrically
increasing sizes. Our analysis relies on careful application of concentration
bounds on the Fourier domain -- we give sharper concentration bounds for sample
covariance of correlated inputs and for $\mathcal H_\infty$ norm estimation,
which may be of independent interest.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom