8,433 research outputs found
The solution path of the generalized lasso
We present a path algorithm for the generalized lasso problem. This problem
penalizes the 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 (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
PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian GLM inference
Generalized linear models (GLMs) -- such as logistic regression, Poisson
regression, and robust regression -- provide interpretable models for diverse
data types. Probabilistic approaches, particularly Bayesian ones, allow
coherent estimates of uncertainty, incorporation of prior information, and
sharing of power across experiments via hierarchical models. In practice,
however, the approximate Bayesian methods necessary for inference have either
failed to scale to large data sets or failed to provide theoretical guarantees
on the quality of inference. We propose a new approach based on constructing
polynomial approximate sufficient statistics for GLMs (PASS-GLM). We
demonstrate that our method admits a simple algorithm as well as trivial
streaming and distributed extensions that do not compound error across
computations. We provide theoretical guarantees on the quality of point (MAP)
estimates, the approximate posterior, and posterior mean and uncertainty
estimates. We validate our approach empirically in the case of logistic
regression using a quadratic approximation and show competitive performance
with stochastic gradient descent, MCMC, and the Laplace approximation in terms
of speed and multiple measures of accuracy -- including on an advertising data
set with 40 million data points and 20,000 covariates.Comment: In Proceedings of the 31st Annual Conference on Neural Information
Processing Systems (NIPS 2017). v3: corrected typos in Appendix
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
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