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In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random ...
Gaussian functions are used to define some types of artificial neural networks. In fluorescence microscopy a 2D Gaussian function is used to approximate the Airy disk, describing the intensity distribution produced by a point source.
The Gaussian distribution belongs to the family of stable distributions which are the attractors of sums of independent, identically distributed distributions whether or not the mean or variance is finite. Except for the Gaussian which is a limiting case, all stable distributions have heavy tails and infinite variance.
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional normal distribution to higher dimensions.
Each image is a point in the space of all images, and the distribution of naturally-occurring photos is a "cloud" in space, which, by repeatedly adding noise to the images, diffuses out to the rest of the image space, until the cloud becomes all but indistinguishable from a Gaussian distribution (,). A model that can approximately undo the ...
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...
This is the distribution in function space corresponding to the distribution () in parameter space, and the black dots are samples from this distribution. For infinitely wide neural networks, since the distribution over functions computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate ...