Wednesday 18th July 2011
Spectral Approaches to Learning about State
If we hope to build an intelligent agent, we have to solve (at least!) the following problem: by watching an incoming stream of sensor data, hypothesize an external world model which explains that data. For this purpose, an appealing model representation is a dynamical system:
a recursive rule for updating a "state," a concise summary of past experience that we can use to predict future observations. The general problem of learning a dynamical system from a sensor data stream is tricky: to discover the right latent state representation and model parameters, we must solve difficult temporal and structural credit assignment problems, often leading to a search space with a host of (bad) local optima. Responding to these difficulties, researchers have designed many special-purpose tools to solve special cases of this problem: for example, system identification for Kalman filters, the Baum-Welsh algorithm for learning hidden Markov models, the Tomasi-Kanade structure-from-motion algorithm, or the many papers on simultaneous localization and mapping (SLAM) from sensors such as lidars, cameras, or radio beacons. In this talk, I will ask whether we can unify these separate tools and cases into a single general-purpose representation and algorithm. I will discuss our work on spectral learning algorithms for predictive state representations, and relate it to some of the above cases.