File:Gradient descent Hamiltonian Monte Carlo comparison.svg
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Summary
[edit]DescriptionGradient descent Hamiltonian Monte Carlo comparison.svg |
English: In Bayesian statistics, two classes of technique are commonly used to reconstruct unobserved parameters based on observed data. This plot shows the application of each to a two-dimensional toy problem.
The blue triangle shows maximum a posteriori estimation, in which an optimization algorithm such as gradient descent is used to find the set of parameters that maximizes the posterior probability density. Starting from an arbitrary guess, gradient descent follows the blue path and arrives at the optimal point (the blue triangle), and this set of parameters is accepted as the best answer. The red circles show Hamiltonian Monte Carlo, in which a physics simulation is used to sample the posterior probability distribution. Starting from an arbitrary guess, the simulation stochastically travels along the red path to a variety of likely points, which are all accepted as plausible answers. The two axes of the plot represent two coupled parameters. The shading and contours represent the posterior probability distribution, where white is lower and green is higher. |
Date | |
Source | Own work using: github.com/jkunimune/hamiltonian-mc |
Author | Justinkunimune |
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Licensing
[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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current | 00:01, 25 March 2024 | 617 × 635 (208 KB) | Justinkunimune (talk | contribs) | Uploaded own work with UploadWizard |
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