The conditional mean embedding (CME) encodes Markovian stochastic kernels
through their actions on probability distributions embedded within the
reproducing kernel Hilbert spaces (RKHS). The CME plays a key role in several
well-known machine learning tasks such as reinforcement learning, analysis of
dynamical systems, etc. We present an algorithm to learn the CME incrementally
from data via an operator-valued stochastic gradient descent. As is well-known,
function learning in RKHS suffers from scalability challenges from large data.
We utilize a compression mechanism to counter the scalability challenge. The
core contribution of this paper is a finite-sample performance guarantee on the
last iterate of the online compressed operator learning algorithm with
fast-mixing Markovian samples, when the target CME may not be contained in the
hypothesis space. We illustrate the efficacy of our algorithm by applying it to
the analysis of an example dynamical system.

通过算子值随机梯度下降的增量式学习算法，可以逐渐从数据中学习条件均值嵌入（CME），以便在大数据情况下处理可扩展性挑战，并在目标 CME 不包含在假设空间中时，提供在线压缩操作学习算法的有限样本性能保证。