AI Seminar

Spectral Approaches to Learning Dynamical Systems

Byron BootsPh.D CandidateSchool of Computer Science at Carnegie Mellon University

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 a 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. Unfortunately, to discover the right state representation and parameters for a dynamical system, 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 for pieces of this problem: e.g., system identification for learning Kalman filters, the Baum-Welsh algorithm for learning hidden Markov models, the Tomasi-Kanade structure-from-motion algorithm, or the many approaches to simultaneous localization and mapping (SLAM) from sensors such as lidars, cameras, or radio beacons. In this talk I will discuss a recently-discovered class of spectral learning algorithms which holds the promise of unifying these separate tools and special cases into a single general-purpose toolkit. These spectral algorithms are computationally efficient, statistically consistent, and have no local optima; in addition, they can be simple to implement, and have state-of-the-art practical performance for some interesting learning problems.

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