Finite Range Decomposition of Gaussian Processes
نویسندگان
چکیده
منابع مشابه
Finite range Decomposition of Gaussian Processes
Let ∆ be the finite difference Laplacian associated to the lattice Z. For dimension d ≥ 3, a ≥ 0 and L a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent G := (a −∆)−1 can be decomposed as an infinite sum of positive semi-definite functions Vn of finite range, Vn(x−y) = 0 for |x−y| ≥ O(L). Equivalently, the Gaussian process on the lattice with covar...
متن کاملFinite-Dimensional Approximation of Gaussian Processes
Gaussian process (GP) prediction suffers from O(n3) scaling with the data set size n. By using a finite-dimensional basis to approximate the GP predictor, the computational complexity can be reduced. We derive optimal finite-dimensional predictors under a number of assumptions, and show the superiority of these predictors over the Projected Bayes Regression method (which is asymptotically optim...
متن کاملThe Rate of Entropy for Gaussian Processes
In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...
متن کاملSafe Exploration in Finite Markov Decision Processes with Gaussian Processes
In classical reinforcement learning agents accept arbitrary short term loss for long term gain when exploring their environment. This is infeasible for safety critical applications such as robotics, where even a single unsafe action may cause system failure or harm the environment. In this paper, we address the problem of safely exploring finite Markov decision processes (MDP). We define safety...
متن کاملDictionary-based decomposition of linear mixtures of Gaussian processes
We consider the problem of detecting and classifying an unknown number of multiple simultaneous Gaussian processes with unknown variances given a nite length observation of their sum and a dictionary of candidate models for the signals. The optimal minimum description length (MDL) detector is presented. Asymptotic and quadratic approximations of the MDL criterion are derived, and reg-ularizatio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2004
ISSN: 0022-4715
DOI: 10.1023/b:joss.0000019818.81237.66