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.

This post originally appeared in early 2017, it is being republished as part of New Brunswick Innovation Week.] EhEye (pronounced AI) is a New Brunswick-based startup improving public safety and security via the use of artificially intelligent video analytics. The company's innovative software can automatically detect and extract objects, people, activities, and behaviours of interest from streaming video. CEO James Stewart recently returned from India where he participated in a federally-organized trade mission. An initiative of Global Affairs Canada via the High Commission of Canada in Delhi, the Smart Cities Mission brought Canadian companies to New Delhi and Bengaluru. We sat down with James to learn more.