4,708 research outputs found
Shared Autonomy via Hindsight Optimization
In shared autonomy, user input and robot autonomy are combined to control a
robot to achieve a goal. Often, the robot does not know a priori which goal the
user wants to achieve, and must both predict the user's intended goal, and
assist in achieving that goal. We formulate the problem of shared autonomy as a
Partially Observable Markov Decision Process with uncertainty over the user's
goal. We utilize maximum entropy inverse optimal control to estimate a
distribution over the user's goal based on the history of inputs. Ideally, the
robot assists the user by solving for an action which minimizes the expected
cost-to-go for the (unknown) goal. As solving the POMDP to select the optimal
action is intractable, we use hindsight optimization to approximate the
solution. In a user study, we compare our method to a standard
predict-then-blend approach. We find that our method enables users to
accomplish tasks more quickly while utilizing less input. However, when asked
to rate each system, users were mixed in their assessment, citing a tradeoff
between maintaining control authority and accomplishing tasks quickly
Transient bayesian inference for short and long-tailed GI/G/1 queueing systems
In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues
Time-series Modelling, Stationarity and Bayesian Nonparametric Methods
In this paper we introduce two general non-parametric first-order stationary time-series models for which marginal (invariant) and transition distributions are expressed as infinite-dimensional mixtures. That feature makes them the first Bayesian stationary fully non-parametric models developed so far. We draw on the discussion of using stationary models in practice, as a motivation, and advocate the view that flexible (non-parametric) stationary models might be a source for reliable inferences and predictions. It will be noticed that our models adequately fit in the Bayesian inference framework due to a suitable representation theorem. A stationary scale-mixture model is developed as a particular case along with a computational strategy for posterior inference and predictions. The usefulness of that model is illustrated with the analysis of Euro/USD exchange rate log-returns.Stationarity, Markov processes, Dynamic mixture models, Random probability measures, Conditional random probability measures, Latent processes.
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir
Julian Besag was an outstanding statistical scientist, distinguished for his
pioneering work on the statistical theory and analysis of spatial processes,
especially conditional lattice systems. His work has been seminal in
statistical developments over the last several decades ranging from image
analysis to Markov chain Monte Carlo methods. He clarified the role of
auto-logistic and auto-normal models as instances of Markov random fields and
paved the way for their use in diverse applications. Later work included
investigations into the efficacy of nearest neighbour models to accommodate
spatial dependence in the analysis of data from agricultural field trials,
image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph
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