The solution path of the generalized lasso

We present a path algorithm for the generalized lasso problem. This problem penalizes the $\ell_1$ norm of a matrix D times the coefficient vector, and has a wide range of applications, dictated by the choice of D. Our algorithm is based on solving the dual of the generalized lasso, which greatly facilitates computation of the path. For $D=I$ (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary D, we derive an unbiased estimate of the degrees of freedom of the generalized lasso fit. This estimate turns out to be quite intuitive in many applications.Comment: Published in at http://dx.doi.org/10.1214/11-AOS878 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Alternative Archaeological Representations within Virtual Worlds

Traditional VR methods allow the user to tour and view the virtual world from different perspectives. Increasingly, more interactive and adaptive worlds are being generated, potentially allowing the user to interact with and affect objects in the virtual world. We describe and compare four models of operation that allow the publisher to generate views, with the client manipulating and affecting specific objects in the world. We demonstrate these approaches through a problem in archaeological visualization

Multi-bot Easy Control Hierarchy

The goal of our project is to create a software architecture that makes it possible to easily control a multi-robot system, as well as seamlessly change control modes during operation. The different control schemes first include the ability to implement on-board and off-board controllers. Second, the commands can specify either actuator level, vehicle level, or fleet level behavior. Finally, motion can be specified by giving a waypoint and time constraint, a velocity and heading, or a throttle and angle. Our code is abstracted so that any type of robot - ranging from ones that use a differential drive set up, to three-wheeled holonomic platforms, to quadcopters - can be added to the system by simply writing drivers that interface with the hardware used and by implementing math packages that do the required calculations. Our team has successfully demonstrated piloting a single robots while switching between waypoint navigation and a joystick controller. In addition, we have demonstrated the synchronized control of two robots using joystick control. Future work includes implementing a more robust cluster control, including off-board functionality, and incorporating our architecture into different types of robots

Exact Post-Selection Inference for Sequential Regression Procedures

We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso regularization path, because, as it turns out, selection events for these procedures can be expressed as polyhedral constraints on y. The p-values associated with these tests are exactly uniform under the null distribution, in finite samples, yielding exact type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. The R package "selectiveInference", freely available on the CRAN repository, implements the new inference tools described in this paper.Comment: 26 pages, 5 figure