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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 ...
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).
In machine learning, diffusion models, ... The equilibrium distribution is the Gaussian distribution (,), with pdf ‖ ‖. This is just the Maxwell ...
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.
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.
Even if the sample originates from a complex non-Gaussian distribution, it can be well-approximated because the CLT allows it to be simplified to a Gaussian distribution. The second reason is that the model's accuracy depends on the simplicity and representational power of the model unit, as well as the data quality.
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 ...