Add sharp bits doc #267
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Add sharp bits doc #267
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daniel-dodd
requested changes
May 18, 2023
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Nice stuff @thomaspinder. Just spotted some typo's/inconsistencies, and a few terms that should be defined (like kernel), then it can be merged. Put suggestions of illustrating some of these ideas with diagrams to bring the documentation to life, that could be done in a future PR.
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| equations. By working with $`\mathbf{L} = \operatorname{chol}{\mathbf{A}}`$ instead of | ||
| $`\mathbf{A}`$, we save a significant amount of floating-point operations (flops) by | ||
| solving two triangular systems of equations (one for $`\mathbf{L}`$ and another for | ||
| $`\mathbf{L}^{\top}`$) instead of one dense system of equations. Solving two triangular systems | ||
| of equations has complexity $`\mathcal{O}(n^3/6)`$; a vast improvement compared to | ||
| regular solvers that have $`\mathcal{O}(n^3)`$ complexity in the number of datapoints | ||
| $`n`$. |
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Nice! Maybe you could give here succinct intuition for why this is the case and or we could make a picture of a backward pass to bring this to life.
daniel-dodd
approved these changes
May 18, 2023
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poetry run pre-commit run --all-files --show-diff-on-failurebefore committing.Description
This PR introduces a notebook that details the sharp bits of GPJax e.g., positive definiteness, cubic scaling, and bijectors.
Issue Number: N/A