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examples/gaussian_processes/MOGP-Coregion-Hadamard.ipynb

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"# Multi-output Gaussian Processes: Coregionalization models using Hamadard product\n",
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"\n",
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":::{post} October, 2022\n",
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":tags: gaussian process, multi-output, coregionalization\n",
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":tags: gaussian process, multi-output\n",
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":category: intermediate\n",
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":author: Danh Phan, Bill Engels, Chris Fonnesbeck\n",
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":::"
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"id": "2e25182d",
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"metadata": {},
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"source": [
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"This notebook shows how to implement the Intrinsic Coregionalization Model (ICM) and the Linear Coregionalization Model (LCM) using a Hamadard product between the Coregion kernel and input kernels. For further information about ICM and LCM, please check out the [talk](https://www.youtube.com/watch?v=ttgUJtVJthA&list=PLpTp0l_CVmgwyAthrUmmdIFiunV1VvicM) on Multi-output Gaussian Processes by Mauricio Alvarez, and [his slides](http://gpss.cc/gpss17/slides/multipleOutputGPs.pdf).\n",
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"This notebook shows how to implement the **Intrinsic Coregionalization Model** (ICM) and the **Linear Coregionalization Model** (LCM) using a Hamadard product between the Coregion kernel and input kernels. For further information about ICM and LCM, please check out the [talk](https://www.youtube.com/watch?v=ttgUJtVJthA&list=PLpTp0l_CVmgwyAthrUmmdIFiunV1VvicM) on Multi-output Gaussian Processes by Mauricio Alvarez, and [his slides](http://gpss.cc/gpss17/slides/multipleOutputGPs.pdf).\n",
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"\n",
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"The advantage of Multi-output Gaussian Processes is their capacity to simultaneously learn and infer many outputs which have the same source of uncertainty from inputs. In this example, we model the average spin rates of several pitchers in different games from a baseball dataset."
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]
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Last updated: Sun Nov 06 2022\n",
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"The watermark extension is already loaded. To reload it, use:\n",
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" %reload_ext watermark\n",
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"Last updated: Sat Nov 12 2022\n",
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"\n",
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"Python implementation: CPython\n",
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"Python version : 3.9.12\n",
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"IPython version : 8.3.0\n",
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"\n",
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"aesara: 2.8.6\n",
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"aeppl : 0.0.36\n",
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"xarray: 2022.3.0\n",
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"\n",
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"pymc : 4.2.1\n",
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"arviz : 0.13.0\n",
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"pandas : 1.4.2\n",
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"aesara : 2.8.6\n",
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"matplotlib: 3.5.2\n",
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"arviz : 0.13.0\n",
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"numpy : 1.22.4\n",
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"matplotlib: 3.5.2\n",
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"\n",
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"Watermark: 2.3.0\n",
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"\n"
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],
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"source": [
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"%load_ext watermark\n",
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"%watermark -n -u -v -iv -w"
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"%watermark -n -u -v -iv -w -p aesara,aeppl,xarray"
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]
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},
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{

myst_nbs/gaussian_processes/MOGP-Coregion-Hadamard.myst.md

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# Multi-output Gaussian Processes: Coregionalization models using Hamadard product
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:::{post} October, 2022
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:tags: gaussian process, multi-output, coregionalization
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:tags: gaussian process, multi-output
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:category: intermediate
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:author: Danh Phan, Bill Engels, Chris Fonnesbeck
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:::
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This notebook shows how to implement the Intrinsic Coregionalization Model (ICM) and the Linear Coregionalization Model (LCM) using a Hamadard product between the Coregion kernel and input kernels. For further information about ICM and LCM, please check out the [talk](https://www.youtube.com/watch?v=ttgUJtVJthA&list=PLpTp0l_CVmgwyAthrUmmdIFiunV1VvicM) on Multi-output Gaussian Processes by Mauricio Alvarez, and [his slides](http://gpss.cc/gpss17/slides/multipleOutputGPs.pdf).
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This notebook shows how to implement the **Intrinsic Coregionalization Model** (ICM) and the **Linear Coregionalization Model** (LCM) using a Hamadard product between the Coregion kernel and input kernels. For further information about ICM and LCM, please check out the [talk](https://www.youtube.com/watch?v=ttgUJtVJthA&list=PLpTp0l_CVmgwyAthrUmmdIFiunV1VvicM) on Multi-output Gaussian Processes by Mauricio Alvarez, and [his slides](http://gpss.cc/gpss17/slides/multipleOutputGPs.pdf).
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The advantage of Multi-output Gaussian Processes is their capacity to simultaneously learn and infer many outputs which have the same source of uncertainty from inputs. In this example, we model the average spin rates of several pitchers in different games from a baseball dataset.
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```{code-cell} ipython3
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%load_ext watermark
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%watermark -n -u -v -iv -w
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%watermark -n -u -v -iv -w -p aesara,aeppl,xarray
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```
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:::{include} ../page_footer.md

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