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When the functional data are not homogeneous, e.g., there exist multiple classes of func-tional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimati...
When the functional data are not homogeneous, e.g., there exist multiple classes of func-tional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimati...
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tut...
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output ...
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate.
In this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process.
We consider stationary processes with long memory which are non–Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study th...
We propose an active set selection framework for Gaussian process classification for cases when the dataset is large enough to render its inference prohibitive. Our scheme consists on a two step alter...
Ito stochastic equations are derived for a class of multidimensional Gaussian processes appearing in connection with generalized spline functions. Some analytic consequences for the spline interpol...
In the paper we study the asymptotic of the tail of distribution function P(A(X, c) > x) for x + m, where A(X, c) is the supremum of X(t)-ct over [0, co). In particular, X(t) is the fractional Brow...
Let (X,,t~ [0, 11) be a oentred stationary Gaussian process defined on (D,A , P) with covariance function satisfying Define the regularized process X' = cp, * X and YE = Xc/oe, where CT~ = var Xf ,...
We consider questions of characterizing a stochastic process X = (X,,t 2 0) by the properties of the first two conditional moments. Our first result is a new version of the classical P. Levy charac...
This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the ...
We derive a class of ergodic transformation of self-similar Gaussian processes that are Volterra, i.e. of type X_t = int^t_0 z_X(t,s)dW_s, t in [0,infty), where z_X is a deterministic kernel and W is ...
We derive a class of ergodic transformation of self-similar Gaussian processes that are Volterra, i.e. of type X_t = int^t_0 z_X(t,s)dW_s, t in [0,infty), where z_X is a deterministic kernel and W is ...

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