MCMC Learning

The theory of learning under the uniform distribution is rich and deep, with connections to cryptography, computational complexity, and the analysis of boolean functions to name a few areas. This theory however is very limited due to the fact that the uniform distribution and the corresponding Fourier basis are rarely encountered as a statistical model. A family of distributions that vastly generalizes the uniform distribution on the Boolean cube is that of distributions represented by Markov Random Fields (MRF). Markov Random Fields are one of the main tools for modeling high dimensional data in many areas of statistics and machine learning. In this paper we initiate the investigation of extending central ideas, methods and algorithms from the theory of learning under the uniform distribution to the setup of learning concepts given examples from MRF distributions. In particular, our results establish a novel connection between properties of MCMC sampling of MRFs and learning under the MRF distribution.Comment: 28 pages, 1 figur

Design of a reconfigurable modular manipulator system

Using manipulators with a fixed configuration for specific tasks is appropriate when the task requirements are known beforehand. However, in less predictable situations, such as an outdoor construction site or aboard a space station, a manipulator system requires a wide range of capabilities, probably beyond the limitations of a single, fixed-configuration manipulator. To fulfill this need, researchers have been working on a Reconfigurable Modular Manipulator System (RMMS). Researchers have designed and are constructing a prototype RMMS. The prototype currently consists of two joint modules and four link modules. The joints utilize a conventional harmonic drive and torque motor actuator, with a small servo amplifier included in the assembly. A brushless resolver is used to sense the joint position and velocity. For coupling the modules together, a standard electrical connector and V-band clamps for mechanical connection are used, although more sophisticated designs are under way for future versions. The joint design yields an output torque to 50 ft-lbf at joint speeds up to 1 radian/second. The resolver and associated electronics have resolutions of 0.0001 radians, and absolute accuracies of plus or minus 0.001 radians. Manipulators configured from these prototype modules will have maximum reaches in the 0.5 to 2 meter range. The real-time RMMS controller consists of a Motorola 68020 single-board computer which will perform real time servo control and path planning of the manipulator. This single board computer communicates via shared memory with a SUN3 workstation, which serves as a software development system and robot programming environment. Researchers have designed a bus communication network to provide multiplexed communication between the joint modules and the computer controller. The bus supports identification of modules, sensing of joint states, and commands to the joint actuator. This network has sufficient bandwidth to allow servo sampling rates in excess of 500 Hz

Online Optimization of Smoothed Piecewise Constant Functions

We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and Roughgarden (2016). Majority of the machine learning literature has focused on Lipschitz-continuous functions or functions with bounded gradients. 1 This is with good reason---any learning algorithm suffers linear regret even against piecewise constant functions that are chosen adversarially, arguably the simplest of non-Lipschitz continuous functions. The smoothed setting we consider is inspired by the seminal work of Spielman and Teng (2004) and the recent work of Gupta and Roughgarden---in this setting, the sequence of functions may be chosen by an adversary, however, with some uncertainty in the location of discontinuities. We give algorithms that achieve sublinear regret in the full information and bandit settings