Minimax Sampling with Arbitrary Spaces
نویسندگان
چکیده
We consider non-ideal sampling and reconstruction schemes in which the sampling and reconstruction spaces as well as the input signal can be arbitrary. To obtain a good reconstruction of the signal in the reconstruction space from arbitrary samples, we suggest processing the samples prior to reconstruction with a linear transformation that is designed to minimize the worst-case squarednorm error between the reconstructed signal, and the best possible (but usually unattainable) approximation of the signal in the reconstruction space. We show both theoretically and through a simulation that if the input signal does not lie in the reconstruction space, then this method can outperform the consistent reconstruction method previously proposed for this problem.
منابع مشابه
Full characterizations of minimax inequality, fixed point theorem, saddle point theorem, and KKM principle in arbitrary topological spaces
This paper provides necessary and sufficient conditions for the existence of solutions for some important problems from optimization and non-linear analysis by replacing two typical conditions—continuity and quasiconcavity with a unique condition, weakening topological vector spaces to arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single...
متن کاملOn Adversarial Search Spaces and Sampling-Based Planning
Upper Confidence bounds applied to Trees (UCT), a banditbased Monte-Carlo sampling algorithm for planning, has recently been the subject of great interest in adversarial reasoning. UCT has been shown to outperform traditional minimax based approaches in several challenging domains such as Go and Kriegspiel, although minimax search still prevails in other domains such as Chess. This work provide...
متن کاملOn the Behavior of UCT in Synthetic Search Spaces
UCT and Minimax are two of the most prominent tree-search based adversarial reasoning strategies for a variety of challenging domains, such as Chess and Go. Their complementary strengths in different domains have been the motivation for several works attempting to achieve a better understanding of their vastly different behavior. Rather than using complex games as a testbed for deriving indirec...
متن کاملOn Adaptive Estimation of Linear Functionals
A detailed analysis of minimax estimates of arbitrary linear functionals based on infinite dimensional Gaussian models has been provided by Donoho and Liu. In particular it has been shown that if the parameter space is convex then linear estimates can always be found which have maximum mean squared error within a small constant multiple of the minimax value. These linear estimates do however ha...
متن کاملEffect of separate sampling on classification accuracy
MOTIVATION Measurements are commonly taken from two phenotypes to build a classifier, where the number of data points from each class is predetermined, not random. In this 'separate sampling' scenario, the data cannot be used to estimate the class prior probabilities. Moreover, predetermined class sizes can severely degrade classifier performance, even for large samples. RESULTS We employ sim...
متن کامل