Playing Billiard in Version Space

A ray-tracing method inspired by ergodic billiards is used to estimate the theoretically best decision rule for a set of linear separable examples. While the Bayes-optimum requires a majority decision over all Perceptrons separating the example set, the problem considered here corresponds to finding the single Perceptron with best average generalization probability. For randomly distributed examples the billiard estimate agrees with known analytic results. In real-life classification problems the generalization error is consistently reduced compared to the maximal stability Perceptron.Comment: uuencoded, gzipped PostScript file, 127576 bytes To recover 1) save file as bayes.uue. Then 2) uudecode bayes.uue and 3) gunzip bayes.ps.g

Evolutionary Algorithms, Markov Decision Processes, Adaptive Critic Designs, and Clustering: Commonalities, Hybridization and Performance

We briefly review and compare the mathematical formulation of Markov decision processes (MDP) and evolutionary algorithms (EA). In so doing, we observe that the adaptive critic design (ACD) approach to MDP can be viewed as a special form of EA. This leads us to pose pertinent questions about possible expansions of the methodology of ACD. This expansive view of EA is not limited to ACD. We discuss how it is possible to consider the powerful chained Lin Kernighan (chained LK) algorithm for the traveling salesman problem (TSP) as a degenerate case of EA. Finally, we review some recent TSP results, using clustering to divide-and-conquer, that provide superior speed and scalability

Searching the Sky with CONFIGR-STARS

SyNAPSE program of the Defense Advanced Projects Research Agency (HRL Laboratories LLC, subcontract #801881-BS under DARPA prime contract HR0011-09-C-0001); CELEST, a National Science Foundation Science of Learning Center (SBE-0354378)CONFIGR-STARS, a new methodology based on a model of the human visual system, is developed for registration of star images. The algorithm first applies CONFIGR, a neural model that connects sparse and noisy image components. CONFIGR produces a web of connections between stars in a reference starmap or in a test patch of unknown location. CONFIGR-STARS splits the resulting, typically highly connected, web into clusters, or "constellations." Cluster geometry is encoded as a signature vector that records edge lengths and angles relative to the cluster’s baseline edge. The location of a test patch cluster is identified by comparing its signature to signatures in the codebook of a reference starmap, where cluster locations are known. Simulations demonstrate robust performance in spite of image perturbations and omissions, and across starmaps from different sources and seasons. Further studies would test CONFIGR-STARS and algorithm variations applied to very large starmaps and to other technologies that may employ geometric signatures. Open-source code, data, and demos are available from http://techlab.bu.edu/STARS/