The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms

Evolutionary algorithms (EAs), a large class of general purpose optimization algorithms inspired from the natural phenomena, are widely used in various industrial optimizations and often show excellent performance. This paper presents an attempt towards revealing their general power from a statistical view of EAs. By summarizing a large range of EAs into the sampling-and-learning framework, we show that the framework directly admits a general analysis on the probable-absolute-approximate (PAA) query complexity. We particularly focus on the framework with the learning subroutine being restricted as a binary classification, which results in the sampling-and-classification (SAC) algorithms. With the help of the learning theory, we obtain a general upper bound on the PAA query complexity of SAC algorithms. We further compare SAC algorithms with the uniform search in different situations. Under the error-target independence condition, we show that SAC algorithms can achieve polynomial speedup to the uniform search, but not super-polynomial speedup. Under the one-side-error condition, we show that super-polynomial speedup can be achieved. This work only touches the surface of the framework. Its power under other conditions is still open

Do-It-Yourself Single Camera 3D Pointer Input Device

We present a new algorithm for single camera 3D reconstruction, or 3D input for human-computer interfaces, based on precise tracking of an elongated object, such as a pen, having a pattern of colored bands. To configure the system, the user provides no more than one labelled image of a handmade pointer, measurements of its colored bands, and the camera's pinhole projection matrix. Other systems are of much higher cost and complexity, requiring combinations of multiple cameras, stereocameras, and pointers with sensors and lights. Instead of relying on information from multiple devices, we examine our single view more closely, integrating geometric and appearance constraints to robustly track the pointer in the presence of occlusion and distractor objects. By probing objects of known geometry with the pointer, we demonstrate acceptable accuracy of 3D localization.Comment: 8 pages, 6 figures, 2018 15th Conference on Computer and Robot Visio