{"action":"created","comment":{"url":"https://api.github.com/repos/shogun-toolbox/shogun/pulls/comments/57525130","id":57525130,"diff_hunk":"@@ -0,0 +1,59 @@\n+===========================\n+Gaussian Process Regression\n+===========================\n+\n+A Gaussian Process is the extension of the Gaussian distribution to infinite dimensions. It is specified by a mean function :math:`m(\\mathbf{x})` and a covariance kernel :math:`k(\\mathbf{x},\\mathbf{x}')` (where :math:`\\mathbf{x}\\in\\mathcal{X}` for some input domain :math:`\\mathcal{X}`). They define a distribution over real valued functions :math:`f(\\cdot)`:\n+\n+.. math::\n+\tf(\\mathbf{x})\\sim\\mathcal{GP}(m(\\mathbf{x}), k(\\mathbf{x},\\mathbf{x}))\n+\n+Any finite set of such function values :math:`\\mathbf{f}` is jointly Gaussian with mean specified by the mean function evaluated at the inputs :math:`\\mathbf{x}_i` and covariance matrix :math:`\\mathbf{C}` with entries :math:`\\mathbf{C}_{ij}=k(\\mathbf{x}_i,\\mathbf{x}_j)`.\n+\n+In our regression model, we take our target variable :math:`\\mathbf{y}` to be our (latent) function values :math:`\\mathbf{f}` plus Gaussian noise:\n+\n+.. math::","path":"doc/cookbook/source/examples/gaussian_processes/gaussian_process_regression.rst","position":14,"original_position":14,"commit_id":"abcc336cad91c39da0a6b2a09080ef732e1e63b9","original_commit_id":"abcc336cad91c39da0a6b2a09080ef732e1e63b9","user":{"login":"karlnapf","id":699071,"avatar_url":"https://avatars.githubusercontent.com/u/699071?v=3","gravatar_id":"","url":"https://api.github.com/users/karlnapf","html_url":"https://github.com/karlnapf","followers_url":"https://api.github.com/users/karlnapf/followers","following_url":"https://api.github.com/users/karlnapf/following{/other_user}","gists_url":"https://api.github.com/users/karlnapf/gists{/gist_id}","starred_url":"https://api.github.com/users/karlnapf/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/karlnapf/subscriptions","organizations_url":"https://api.github.com/users/karlnapf/orgs","repos_url":"https://api.github.com/users/karlnapf/repos","events_url":"https://api.github.com/users/karlnapf/events{/privacy}","received_events_url":"https://api.github.com/users/karlnapf/received_events","type":"User","site_admin":false},"body":"I think this should be p(y_i|f_i)","created_at":"2016-03-27T08:20:22Z","updated_at":"2016-03-27T08:20:22Z","html_url":"https://github.com/shogun-toolbox/shogun/pull/3119#discussion_r57525130","pull_request_url":"https://api.github.com/repos/shogun-toolbox/shogun/pulls/3119","_links":{"self":{"href":"https://api.github.com/repos/shogun-toolbox/shogun/pulls/comments/57525130"},"html":{"href":"https://github.com/shogun-toolbox/shogun/pull/3119#discussion_r57525130"},"pull_request":{"href":"https://api.github.com/repos/shogun-toolbox/shogun/pulls/3119"}}},"pull_request":{"url":"https://api.github.com/repos/shogun-toolbox/shogun/pulls/3119","id":64116514,"html_url":"https://github.com/shogun-toolbox/shogun/pull/3119","diff_url":"https://github.com/shogun-toolbox/shogun/pull/3119.diff","patch_url":"https://github.com/shogun-toolbox/shogun/pull/3119.patch","issue_url":"https://api.github.com/repos/shogun-toolbox/shogun/issues/3119","number":3119,"state":"open","locked":false,"title":"GP exact regression cookbook","user":{"login":"ialong","id":5802525,"avatar_url":"https://avatars.githubusercontent.com/u/5802525?v=3","gravatar_id":"","url":"https://api.github.com/users/ialong","html_url":"https://github.com/ialong","followers_url":"https://api.github.com/users/ialong/followers","following_url":"https://api.github.com/users/ialong/following{/other_user}","gists_url":"https://api.github.com/users/ialong/gists{/gist_id}","starred_url":"https://api.github.com/users/ialong/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/ialong/subscriptions","organizations_url":"https://api.github.com/users/ialong/orgs","repos_url":"https://api.github.com/users/ialong/repos","events_url":"https://api.github.com/users/ialong/events{/privacy}","received_events_url":"https://api.github.com/users/ialong/received_events","type":"User","site_admin":false},"body":"I have added a basic GP regression cookbook, using CExactInferenceMethod. Might want to add model selection in there or leave that for another 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