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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 ...
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 ...
The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the () can be randomly initialized. In the E-step, the algorithm tries to guess the value of () based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of () of the E-step.
From the point of view of probabilistic modeling, one wants to maximize the likelihood of the data by their chosen parameterized probability distribution () = (|).This distribution is usually chosen to be a Gaussian (|,) which is parameterized by and respectively, and as a member of the exponential family it is easy to work with as a noise distribution.
A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models (Technical Report TR-97-021). International Computer Science Institute. includes a simplified derivation of the EM equations for Gaussian Mixtures and Gaussian Mixture Hidden Markov Models.
In machine learning, ... the one whose Fisher information matrix has the smallest trace is the Gaussian distribution. This is like how, of all bounded sets with a ...
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 ...
In distribution regression, the goal is to regress from probability distributions to reals (or vectors). Many important machine learning and statistical tasks fit into this framework, including multi-instance learning, and point estimation problems without analytical solution (such as hyperparameter or entropy estimation).